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Music Theory for the Masses

By marktaw in Media
Sat Apr 27, 2002 at 04:01:58 PM EST
Tags: Music (all tags)
Music

My response to an article on Composition that appeared here. It starts out ridiculously simplified but gets advanced pretty fast. It also puts forth for the first time my (I believe unique) harmonic theory of music.

extremely long article (4,000 + words)
Reprinted from www.marktaw.com


What Is Music?

Before we even get into "what is composition" we need to define what music is. The simple answer is "Music is what you say is music" and to be honest I don't know that I can get much better than that. I'm tempted to say something like "Music is a series of sound put together that are intended to have an emotional impact on the listener" but then a baby crying would be music. Then I thought of it from the listener's point of view "Music is a series of sounds that causes a feeling in the listener and that the listener would want to listen to again." Websters tells me that music is "an art of sound in time which expresses ideas and emotions in significant forms through the elements of rhythm, melody, harmony, and color." Color? Perhaps they meant Timbre. Most music has melody, harmony and rhythm, but more experimental music can exclude any or all of those elements.

Here we'll be talking about Western Music that uses the Diatonic (literally "seven tone") scale as developed by Pythagoras, Bach and others, but some of the really theoretical stuff applies to all music. I'm also somewhat biased towards guitar because well, I play guitar better than piano or other chordal instruments, and because you're closer to the music - you actually touch the strings, so some descriptions work better on guitar.

The Basics - Rhythm

Melody, harmony and rhythm. Is that what I said? Let's start with rhythm. Rhythm is simple. You bang two things together (a stick and a drum for example) repeatedly and create a rhythm. You can get a circle of drummers and percussion players together and they can do some really amazing stuff. Lots of Latin, and African music has some amazing rhythms. The off-Broadway show Stomp creates music that is rhythmically interesting but has little to no melody or harmony, though I'd be willing to entertain arguments to the contrary.

A drummer might argue with me, but for most music there are only two rhythms you have to know. 3/4 and 4/4. Ignore the bottom number for now, it'll just confuse you, so it's just 3 and 4. (There are also 3/4, 5/4, 6/8, 7/8, 8/8, 9/8 and so on).

Put simply, you can count while you're playing. A typical rock and roll drum beat - the 4/4 (pronounced "four four") is counted 'One and Two and Three and Four and One and Two and Three and Four.' This corresponds to 'Kick and Snare and Kick and Snare.' If you're coordinated enough to play air drums try it. Alternate between counting and saying Kick and Snare. Most drummers play the kick solidly on the One, the Snare on both Two and Four, and play with the placement of the kick on or near the Three.

The Basics - Notes

Before I talk about melody let's talk a bit about Harmony.

Let's start with one note. What is this note? A note is a vibration carried through the air to our ears. It's tempting to think of this vibration as simple, but it rarely is. This one note we've played is actually a complex series of vibrations.

A pure note, a Sine Wave - sine is a mathematical formula, so you know this is pretty theoretical stuff that doesn't happen much by itself in real life - will have just one vibration, the note itself, known as the Fundamental.

Pluck a guitar string and put a strobe on it and you'll see all sorts of patterns in the string. If you don't have a strobe light, put your guitar so the strings are between your eye and the TV or computer monitor. In America electricity is at 60hz, which is close to B. Play B and the wave will come close to standing still. Tune it up a little bit and it really does. Try playing other notes and see what happens.

The first one is the whole string. This is known as the Fundamental. All of the other vibration are known as Harmonics. While the string is vibrating, gently touch the string at the 12th fret (this is the midway point on the string) and you'll hear the octave (I'll explain this later). This is the string vibrating in two parts - to either side of your finger.

Try to picture this, you have one big wave like girls playing jump rope of the string shaking back and forth. At the same time you have this half string wave of the octave. Pluck the string again and touch the string directly over the 7th fret - now you're cutting the string into thirds. Again at the 5th fret cuts the string into fourths.

If you listen carefully, you can hear each of these tones when you pluck the string. Play the 12th fret harmonic and then play the full string and you'll hear a bit of the 12th fret harmonic in with fundamental. This is what gives an instrument it's Timbre (pronounced Tamber, don't ask me why, I don't know). A Timbre is caused by the overtones made by an instrument. A Sine wave has a particular timbre because of the overtones it has (or in this case, doesn't have). A Piano's overtones cause it to sound clacky compared to a violin.

A guitar's harmonics will be different from a piano's, and this is why they sound different. All sine waves sound alike. Some instruments favor even numbered harmonics, others odd numbered harmonics. Some have fewer harmonics and sound duller, others have more harmonics and sound brighter.

Adding Other Notes - Harmony

Back to that octave. When you put your finger on the 12th fret you cut the string in half. Each of those halves vibrated twice as fast as the original note - the octave. Western music divides the octave up into 12 notes (the Chromatic scale. Chromatic, like colors, a scale of all the colors) this is where we get our 12 frets from. Not all of these sound good with our original note, so we just don't play them. The Greeks were obsessed with the number 7. They thought there were 7 planets, they invented Indigo because they wanted there to be 7 colors. These seven notes are Do Re Mi Fa So La Si Do - the second Do being the octave.

aside: yes they invented Indigo. Remember when you learned about colors, the three primary and three secondary colors, yet when you learned about the rainbow it was ROY G. BIV - Red Orange Yellow Green Blue Indigo Violet. Well, Indigo isn't a real color. They made it up.

So if you went to your guitar, and on two different strings, played a note and it's octave (say, an open A and the 7th fret on the D string) you'd see that they sound good together, sort of blending in to one another. This is because their vibrations work well together.

Now that you're adding notes, you're going to have to have names for the different notes. The lowest note is called the Root note. This isn't 100% accurate, just accept that for now. We then name them according to the order in which they happen on that seven tone scale. - 2nd, 3rd, etc. the 8th note is the Octave (oct - eight). Remember, the octave is the same note as the original, just twice as fast.

Let's add another note now. This is another one that works well the root note - the 5th. On the guitar this would be open A and 2nd fret on the D string. To my ears the 5th has a sort of holy sound, like chanting monks. You were playing the octave of this note when you were playing the 7th fret harmonic, so you can see why these notes would work well together.

Adding Color - the 3rd.

Okay, we have the beginnings of a chord here, a root note and a 5th. The most common addition to these is the 3rd, making your chord 1, 3, 5 - the triad.

This note doesn't really fit into the harmonic structure of the root note, so it begins to add another color. Until now it was like you were painting with different shades of the same color. Now you're adding another color.

Because the 3rd doesn't fit easily into the harmonic structure of the root note, it's got a few interesting qualities.

First, the 5th is easily definable because it exists as a harmonic of the fundamental (root). It's almost scientifically definable, and if it's off it sound wrong because a version of it already exists in the root. The 3rd, on the other hand, isn't scientifically definable. This makes the 3rd more of a human note. If you were to sing a 5th you'd lock on to the root and sing an exact 5th. Singing a third is different, there's a whole range that can pass for a 3rd, making it a subtle note that allows for a great deal of expression.

The way this note's vibration interacts with the root note's vibration colors the sound of the chord.

On your keyboard or guitar, there's less room for expression, it's just there, you put your finger down and that's it. The third. But even here there's some room for expression. The area that encompasses the third crosses two notes! This is what's known as Major and Minor. You have the Major Third and the Minor Third. They're right next to each other, and they sound very different. Major chords are usually characterized as happy, and Minor as sad.

Play the open A on your guitar and the 2nd fret on the B string. How would you characterize this sound? I know it's hard to tell because it's so stark, but it's happy. To see what I mean, now play the open A and the 1st fret on the B string. Ahhh. Now that sounds sad!

There's quit a bit more to chord construction than this, especially when it comes to fun stuff like inversions (putting notes other than the root in the bass), or adding notes (like the "7th chord"), or raising or lowering the 3rd or 5th to create suspended, augmented, or dimished chords... but this is a heck of a lot more than most people know. You know now the difference between the major and minor triad.

This lesson is a bit low on the math - there are two half steps that make up a whole step, a minor third is one and a half steps away from the root, etc. and I admit that stuff is important, but there are plenty of places you can learn that, and I'll address it a little later in more depth.

Chord Progressions pt 1 (keys and more chord construction).

Music, of course, exists in time - you learned that when you played the A with it's major third. Not particularly thrilling. From here on out I'm going to assume you know not necessarily how to construct chords, but how to play them. C major, a minor, etc. You can get a book and study the shapes on the instrument of your choice. Of course, that instrument has to be able to play chords, so keyboard is in, saxophone is out. Even if you play an instrument that can't play chords, it'll pay off if you learn to play another that can. In rock and roll guitar is good because you'll have to communicate with guitarists. In composition piano is good because it has a bigger range than guitar.

Do you remember when I said that there were 7 notes that go well with the root note? Well, the fun part is you can combine those notes together as we did before (remember 1, 3 and 5 - the major and minor triads). You can start from nearly any place (except for the 7) and construct a major or minor chord just by skipping numbers.

When I was talking about chord construction, I called the bottom note in the chord the Root. Now I'm going to introduce the concept of a "Key" and it also has a root note.

The same way different notes worked with the root note of the chord, different chords work well with the root chord of the key! (confused yet?)

For the sake of simplicity let's use the key of C major. C major is C, D, E, F, G, A, B, C (do, re, me, fa, so, la, si, do). These are the notes in C major, and a C major chord uses C, E, and G (1, 3 and 5, feel free to count them).

Now any of those notes can create a chord as well. You just skip notes the same way we've been doing. To construct a d chord (d happens to be minor, so we use the lowercase "d"), simply start on D and skip every other note - D, F, A.

The numbers bit. The space between two consecutive notes on the chromatic (remember, chromatic is 12 tones, all of the possible colors) is called a half step. I have no idea why. Two half steps is called a whole step. Now to get the 7 tone (diatonic) scale, you have to drop 5 tones. The space between C and D is a whole step - there's a note in between them (called either C# or Db (C sharp or D flat, when one note has two names it's called enharmonic).

The 12 tone scale starting on C is C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C. Feel free to count them, just remember C natural (not sharp or flat) happens twice. Sharp means up, Flat means down. When you're singing "flat" it means you're either a little or a lot below the note. You can be so far flat you're actually sharp of the next lowest note.

The 7 tone scale starting on C is simply C, D, E, F, G, A, B, C. Our musical notation was made to look nice in the key of C major, again, don't ask me why, maybe it was really designed to look good in A minor (A, B, C, D, E, F, G, A). We dropped a note between C and D, so that's a whole step. We didn't drop a space between E and F so that's a half step.

The Major scale is constructed of "Whole Whole Half Whole Whole Whole Half" and the minor scale "Whole Half Whole Whole Half Whole Whole." PHEW quite the mouth full.

Also we have Key, Chord, and Scale. The 7 tone scale starting on C is a 'C Major Scale.' When you're talking about chords in that scale it's the "key of C major." Any particular chord in that scale is, well, that chord, named either for it's letter name "e minor chord" or for it's number in the scale "iii chord" - We use roman numerals for chords in a key so as not to confuse ourselves with notes in a chord. Lowercase always for minor chords.

Note that even if a chord starts on the ii of the key, the first note in the chord is the 1 of that chord, so a ii7 (pronounced "two seven") is a chord that starts on the ii of the scale, but has the 7th tone of that chord in it. (!?!)

A Major key looks like this: I, ii, iii, VI, V, vi, vii. A minor key looks like this: I, ii, III, vi, v, VI, VII.

I don't expect you to get any of this if you don't already understand music, you'd need a lot more practice at seeing these patterns to get it.

Chord Progressions part 2, Music in Time

So now we more or less know the chords that make up a key. Now it's time to talk about Chord Progressions. The most common chord progression is I, IV, V. The good ole 'one four five' that makes up lots and lots and lots of rock and roll music. Everything from Wild Thing to twelve bar blues is made up of this progression. It's a very compact progression.

In the key of C it's C, F and G. In the key of A minor it's a minord minor and e minor. On a guitar it's easy to recognize this shape, especially with barre chords (one string over, two frets up), on a keyboard it takes a little more work, but a with a little practice you should be able to play the "one four five" anywhere on the keyboard/guitar/etc.

While there are songs that don't really change chords, and others that seem to change chords randomly. Most of the songs you hear on the radio have standard chord progressions that can be learned, the I, IV, V is a good example of this.

This is where the fun begins, where the listening comes into play. You can't go too far wrong if you stick to the chords in a particular key. Each of these chords have different characteristics, different relationships to the root chord -aka- the I chord (pronounced one chord).

Think of it as a color wheel. You start at blue, this is the predominant color in the painting. Opposite blue is orange, next to blue is green and purple. Diagonal to blue are red and yellow. Well, you start at the root chord, and move out to the other chords in the scale. These are actually given names, which I can never recall, but if you want them here they are (I looked them up). These are notated for a major key.

I - the root or one chord, Tonic
ii - the two chord, the Supertonic
iii - the three chord, the Mediant
IV - the four chord, the Sub Dominant
V - the five chord, the Dominant
vi - the six chord, the Submediant
vii - the seven chord, Leading Tone

The names give you some indication as to the function of each, the fact that certain chords have similar names can further help. The iii and vi chord (Mediant and Submediant) have similar sounds, serve similar purposes. The ii and IV also serve similar purposes (despite their naming).

Plenty has been written about the relationship of these chords to each other, it's a very complicated subject. Playing the progression I - IV - V is different from playing I - iii - V, and the V changes a bit based on what preceded it. Here's some of my observations, but take it with a grain of salt, go listen for yourself, learn how to play some songs you know and name the chords as you play them, listen to them, how do they feel, are they anxious? are they calm? how would you describe them? Naming things is what music theory is, feel free to create your own words for things but remember that in order to communicate with other musicians you should know the common language (which is what this essay is all about).

The number one rule you'll find is that the V chord makes you want to return to the I chord. Try it. In the key of C play "C, G, G, G, G, G, G, G, C" and you get that "ahhhh" when you play the final C. You haven't even defined a key before playing G, yet somehow you want to return home.

The iii or the vi chords (the vi is the 'relative minor' of the tonic, more on this later) has an anxious traveling feel. In a lot of songs these are used for the bridge, the bridge is actually in a different key from the rest of the song, the key of the relative minor (vi compared to the tonic). That means you re-build out from the vi chord (it becomes the one chord of this new, minor, key). So a song that's primarily I, IV, V will move to vi or iii for the bridge. This isn't hard and fast, it just happens a lot, like 60% of the time.

The IV chord has a sort of relaxed feel to it when compared to the I chord. Play C, C, C, F, F, F, C, C, C and you'll see what I mean. (or not, you're might perceive any of these relationships different than I do).

Staying away from the tonic for a long time (often called wandering) increases the AHH you get when you finally do return. A good example of this is the "Heart and Soul" chord progresion.

In the winter of 2001 the Gap played this song "Give a Little Bit" by Supertramp over and over and over and over and over and over again. The song starts with a I, IV, V progression over the 'give a little bit' part. Then we go wandering for 'See the man with the lonely eyes' he jumps to a iii chord, then goes to a vi, then a ii, then a V (remember the V makes you want to return to the tonic) and when you can't take it any more, he returns to the one (ahh) "Give a little bit..."

This is known as the Heart and Soul progression because of that song every kid knows how to play on the piano. That wandering (iii, vi, ii, V, and return to I) is a progression based on the "cycle of fifths." I've never found the cycle of fifths particularly exciting, but this is a good example of it. Note the wandering feel of this progression. (No, I'm not going to go into it, there are plenty of other resources that will help you with the Cycle of 5ths.)

Again, listen to a lot of songs and learn how to play them. After a while you'll gain a repertoire of chord progressions. Listening to the Supertramp song just now reminded me of the Ednaswap song Natalie Imbruglia covered "Torn." The bridge to that song started on, I believe a vi (possibly a iii) chord. I know the sound, and I can name it. Next time I hear it I'll be able to name it as well, or if I can't when I look it up I'll smack myself on the head and add that knowledge to my repertoire. That's the power of music theory.

Melody

Any instrument can play a melody. Drummers have been known to tune drums to notes and play melodies on them. Traditional arrangments are organized into Soprano, Alto, Tenor and Bass (SATB). Bass being the deepest, Soprano being the highest. This is also known as Four Part Harmony. The notes in Soprano and Alto overlap, same for Tenor and Alto, Tenor and Bass.

You can have melody in any of these parts and in any composition you might want to have melodies going on in all of them at different times or at the same time. Usually the melody is defined by the Soprano, but that's definately not a rule. Melodies in the other lines are typically known as counterpoint. They accentuate in one way or another the melody.

In SATB, typically only one person is "singing" (or playing) the third, the other three notes are either root, octave of root, or 5th (or octave of 5th). Again, once you know the root, the octave and 5th are almost mathematically defined, the third is where the expression happens.

Melody should obey lots of the chord progression rules and guidelines, singing on the 5th will make you want to return to the root, as will singing on the 7th. Melody is fun because you can sing the note or within the chord, or even outside the chord. If you're rooted in the key of C, you can sing around a G chord or on the note G itself. I remember a song my band used to do that was rooted in G, and while we were playing an a minor chord, the singer was singing a D, the 5th of G. Now this isn't in the a minor chord, but worked because it led into the G - it added to the tension that was resolved when everyone, instruments and vocals went to G.

Like all of the parts of music, some would say especially so, the music should be interesting. Sometimes I listen to country music and other folk musics that are based on common chord progressions & rhythms, such as 12 Bar Blues, and I think that lyrics and melody are the most important aspects here, from a creative standpoint. The common form is just a vessel, a convention (like 7 tone scales) that let you be creative lyrically and melodically without worrying about the rest. Then there are songs that have a set melody and you just invent lyrics.

Melodies can slide up the scale or chord slowly, or jump. Each one has their own affect and you should come to know each of them in time. Going up or down a scale or chord using adjacent notes might sound smoother or more natural, but it might also be less interesting. Jumping around might seem artificial but it's more interesting. You can use a mix of the two to create natural sounding interesting melodies. Again, experiment and see what works for you, get to learn how different ideas sound.

The End

"Writing about music is like dancing about architecture - it's a really stupid thing to want to do."
-unknown (often attributed to Frank Zappa or Elvis Costello)

If you can actually grasp everything in this 4,000 + word essay, you'll have a pretty solid understanding of music theory. I know some people would disagree with me, and say you're just scratching the tip of the iceberg, and that I did more damange than good, but hey, I think I'm doing good here. This is where things get exciting, as you build your vocabulary you'll become more critical of the music you listen to, you'll recognize more of the things you're hearing, and your own compositions will become better.

Questions or comments are welcome. If I totally flubbed something, let me know.

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Music Theory for the Masses | 103 comments (93 topical, 10 editorial, 0 hidden)
Supertramp progression ... (4.00 / 1) (#5)
by pyramid termite on Sat Apr 27, 2002 at 08:19:45 AM EST

... isn't how you described it. It's C-D-C-D D-G-D-G, which isn't quite a I-IV-V riff. The other part is Em7-Asus4-A-C-Dsus4-D-Em7-Asus4-A-C-D-G/D-Am/D-G/D-D-G/D-Am/D-G/D then skipping the first C, on to the original riff. It's akin to the "Heart and Soul" progression but it's different. Sorry for the dense notation, but this is a trickier song than it sounds like. There's a bridge and another polychordal riff in there, but I didn't bother with working it out on guitar.
On the Internet, anyone can accuse you of being a dog.
I should have added ... (none / 0) (#6)
by pyramid termite on Sat Apr 27, 2002 at 08:35:53 AM EST

... that the reason I didn't put the chords in I-IV-V format, is that the song is deceptively tricky there - one would look at the chords, G, C and D and say - OK, it's in the key of G, so G should be the home chord. But clearly, it's not - D's the chord the song goes back to, which suggests the key of D. Also the other riff tends to reinforce this idea - but it still sounds like a slight key change when it kicks in. There's a bit of ambiguity there as to what key the song's actually in, which is one way to add tension to a song.
On the Internet, anyone can accuse you of being a dog.
[ Parent ]
Well spotted (none / 0) (#15)
by WildDonkey on Sat Apr 27, 2002 at 05:19:14 PM EST

Supertramp music sounds simple, but it never is.

[ Parent ]
Thanks for the correction (none / 0) (#19)
by marktaw on Sat Apr 27, 2002 at 06:56:23 PM EST

I was just sitting in the couch with my guitar during one of those gap commercials, and then downloaded the MP3 and it sounded right to me. So I wouldn't call what I did an official transcription, it just sounded right to me.

[ Parent ]
Chords (none / 0) (#79)
by ardeel on Wed May 01, 2002 at 02:39:35 PM EST

It would have been good, I think, to see a reference to the "three chord trick" as well as "one, four, five": I sometimes wonder what people make of the phrase "three chords" in songs.

A good example I remember of a song with an ambiguous key is "IT" by Prince: don't have it here but I think it sounds like it's in D but you find out that it's in A towards the end when more instruments kick in. Up until then, your mind "fills in the blanks".

Don't know the Supertramp song offhand (well, I probably do, but just don't know its name!). Trying to download it now...

[ Parent ]

limited views (4.33 / 3) (#12)
by chocolatetrumpet on Sat Apr 27, 2002 at 04:08:06 PM EST

"Music is a series of sounds that causes a feeling in the listener and that the listener would want to listen to again."

This is a very limited view about what is music. Some people have different answers to the question, what is music?

The truth is in the ice cream.

If a symphony isn't played in a forest... (none / 0) (#20)
by marktaw on Sat Apr 27, 2002 at 07:06:48 PM EST

...and there are dozens of people who payed to hear it, is it really a symphony?

Seriously though, I do say: Most music has melody, harmony and rhythm, but more experimental music can exclude any or all of those elements.

I saw art not as something that consisted of a communication from the artist to an audience but rather as an activity of sounds in which the artist found a way to let the sounds be themselves. And, in being themselves, to open the minds of people who made them or listened to them to other possibilities than they had previously considered. - John Cage

Okay, I'll accept that theory as well. It's no less subjective than what I said. I believe my first definition is "Music is what you say is music" and I believe this certainly fits that definition.



[ Parent ]
Actually his view is very wide (none / 0) (#26)
by Bnonn on Sat Apr 27, 2002 at 10:19:26 PM EST

Considering he says that music is what you say it is.

[ Parent ]
Where is your new theory of harmony? (3.00 / 2) (#13)
by Jonathan Walther on Sat Apr 27, 2002 at 04:08:06 PM EST

I read the whole article waiting to for it.

(Luke '22:36 '19:13) => ("Sell your coat and buy a gun." . "Occupy until I come.")


It was near the beginning. (none / 0) (#18)
by marktaw on Sat Apr 27, 2002 at 06:52:45 PM EST

Maybe I didn't state it well, or maybe it isn't that new. I've never heard anyone talk of notes in a chord in relation to the natural harmonics of that note.... Actually, I didn't get into it that much. How do the harmonics of a third play with the harmonics of the root? What would a chord of pure sine ways sound like, etc. Maybe I should write another article just exploring this...

[ Parent ]
Harmonics (none / 0) (#22)
by Joe Groff on Sat Apr 27, 2002 at 08:13:21 PM EST

The ratio of an octave is 2/1 (of course).
A perfect fifth is 3/2.
A perfect fourth is 4/3.
A major third is 5/4. (You're wrong when you say there is no relation between a root and its major third)
A minor third is 6/5.

Note that pianos and other chromatic instruments are tuned using what's called the tempered scale, where the ratio between every two adjacent semitones is 2**1/12 (approx. 1.0594). This way, while the harmonics aren't perfect, they're close enough in every key that you don't have to retune everytime you change keys. So technically, while an octave is still 2/1, a perfect fifth is 1.4983, a perfect fourth is 1.3348, a major third is 1.2600, and so on.
--
How long must I travel on
to be just where you are?

[ Parent ]

Thanks (none / 0) (#28)
by marktaw on Sat Apr 27, 2002 at 10:41:00 PM EST

Thanks for the correction. I was aware of a mathematical relationship - you must be able to define it somehow. However, I would posit that the 5th is more precisely defined than the 3rd, and most even tempered tunings place the 3rd (major and minor) in the wrong place.

I was interested in exploring Buzz Feiten tuned guitars, which are supposed to be able to play correctly in any key (I assume with adjustments). I've certainly had a lot of fun playing with, I believe it's 8th fret harmonics. Once you hear it, you know what's been missing.

I think a precisely placed 3rd would sound beautiful, but there is quite a bit more room for expression there than there is for an octave or 5th.

[ Parent ]
Tempered tunings (none / 0) (#57)
by x31eq on Mon Apr 29, 2002 at 06:50:07 AM EST

Meantone temperaments, the dominant European tunings of the 16th and 17th centuries, have major thirds tuned closer to ratios than fifths. So what you say is true of one temperament in particular, not temperaments in general.

[ Parent ]
Pure sine waves (none / 0) (#24)
by Iesu II on Sat Apr 27, 2002 at 09:34:08 PM EST

...are pretty boring. :)

An equal-tempered chord of pure sine waves sounds very, very dry. The timbre is very weak-sounding since we are used to almost all sounds being complex. The chord sounds slightly more dissonant than otherwise to some people; this is because the sine waves let you hear the beating of the equal-tempered comma (corrective tuning) more easily than, say, flutes.

Several sine waves played in just harmonic relationships (i.e., simple whole-number multiples and ratios) tend to sound like a single pitch, as the ear ears them as harmonics of whatever fundamental they might share.

Let me know if anyone wants elaborations of any of the above...



[ Parent ]

Harmonic Experience (none / 0) (#40)
by jzitt on Sun Apr 28, 2002 at 03:16:38 AM EST

I've never heard anyone talk of notes in a chord in relation to the natural harmonics of that note....

Curious -- I've usually heard the practice (what is mistakenly called the "theory") of harmony introduced in just those terms.

The book you're looking for is Harmonic Experience: Tonal Harmony from Its Natural Origins to Its Modern Expression by W. A. Mathieu.

[ Parent ]

Nitpick (4.33 / 3) (#14)
by Joe Groff on Sat Apr 27, 2002 at 04:28:22 PM EST

In the key of A minor it's a minor, d minor and e minor.

It's very rare that you hear the minor v chord in a minor key. The v chord has none of the tension or draw of the dominant (V) chord, since it lacks the major seventh of the scale as its third. This is where the harmonic minor scale comes from (which is the minor scale with a major seventh). In a minor scale, the principal chords will almost always be i-iv-V, or sometimes i-IV-V. Great article otherwise.
--
How long must I travel on
to be just where you are?

Minor Keys (none / 0) (#17)
by marktaw on Sat Apr 27, 2002 at 06:50:00 PM EST

Thanks for the compliment.

The "a minor" I'm talking about is the Aeolian mode. If C is the Ionian mode, A is the Aeolian mode which would be:

  • i minor - a
  • ii minor - b (diminished, really)
  • III major - C
  • iv minor - d
  • v minor - e
  • VI major- F
  • VII major - G
  • I minor - a

See how the a minor overlaps C major perfectly? Perhaps you're thinking of a different mode. Sounds like you're thinking of Lydian or maybe an artificial key.



[ Parent ]
Harmonic, melodic minor (none / 0) (#31)
by Macrobat on Sat Apr 27, 2002 at 11:17:32 PM EST

What he's saying is, when used as the basis for harmony, classical composers almost always substitute the V7 chord for the v7. The seventh note is kept minor for most of the melody, except during a V-i resolution, where it's altered. If you keep on the V chord long enough, the scale is temporarily changed to the harmonic minor, which is just the regular minor with a major 7th. If the 6th is emphasized in the melody, it may also be moved up a half-step, making the melodic minor scale. All standard classical music techniques.

"Hardly used" will not fetch a better price for your brain.
[ Parent ]

Harmonic, Melodic, and other Minor keys (none / 0) (#34)
by marktaw on Sat Apr 27, 2002 at 11:44:06 PM EST

I think I'm about to contradict myself, but I define minor as usually having a flat third, sometimes having a flat sixth or a flat seventh. Of course, I don't think I need to talk about variations on a norm, I'm posting to a web site that spells corrosion "kuro5hin."

Again, this was meant to be a "music 101," that's why I didn't go into modes and artifical scales.

:) <- smiley face<br>


[ Parent ]
Music Theory on the Web (4.00 / 3) (#16)
by RicciAdams on Sat Apr 27, 2002 at 05:37:59 PM EST

Anybody who wants to learn more about theory is invited to visit my website at http://www.musictheory.net.

I hope you enjoy the site! Please contact me with any questions or comments!

III+ (none / 0) (#66)
by Fon2d2 on Mon Apr 29, 2002 at 05:01:30 PM EST

Under minor scale composition it says you should never use the III+ chord but that's not really true and I know of at least one song that uses it. The introduction Nobody Home by Pink Floyd has the following chord progression: Am C+ C D7 F or in roman numeral notation (i III+ III IV7 VI).

[ Parent ]
Perhaps useful...in 1910 (2.25 / 4) (#21)
by sobcek on Sat Apr 27, 2002 at 07:56:57 PM EST

Well, not really then either. This is music theory 0.5 sort of stuff, and doesn't really apply to most of the music from the last century (and the works of Jacques Ibert and Saint-Saens do not count as music...). What I would say is that good composers refuse to take theory as gospel and are constantly redefining the broader concepts of music for themselves. How do density, register, timbre, etc. combine to create music? Is 12 notes in an octave enough? While your information is adequately presented, it would be nice if you mentioned alternate (and highly relevant) views.

12 notes is not enough ... (none / 0) (#23)
by pyramid termite on Sat Apr 27, 2002 at 08:48:32 PM EST

... even for popular music. Blue notes are very common, not to mention even more subtle intonations.
On the Internet, anyone can accuse you of being a dog.
[ Parent ]
I Wrote this as a Response to another Article (none / 0) (#27)
by marktaw on Sat Apr 27, 2002 at 10:34:24 PM EST

I'm familar with microtonal music, or at least the concept, and I certainly know about "bending" notes and such. This was meant as a "music theory 101" and not comprehensive review, and I do admit to being more classically bent than modern. Thanks for the comments.

[ Parent ]
Ahem (none / 0) (#52)
by Sanityman on Mon Apr 29, 2002 at 03:53:11 AM EST

Picasso knew how to draw.

Sanityman



--
If you don't see the fnords, they can't eat you.
"You can't spray cheese whiz™ on the body of Christ!"


[ Parent ]
A bunny's thoughts (none / 0) (#25)
by Uber Bunny on Sat Apr 27, 2002 at 09:45:05 PM EST

The only radical music ever made was in the early 20th century. It consisted of a 12 chromatic range of notes and every song must contain an equal number of these 12 tones held out for an equal duration.

It's interesting that these incredibly hard pieces to write (because of the above rule) sound so horrible. They make my silky smooth white bunny hair stand up on end!

What Would Google Do?
Atonal music quote (none / 0) (#29)
by marktaw on Sat Apr 27, 2002 at 10:44:11 PM EST

I don't know where this came from, but a tonal composer (plays in a key) asked an atonal composer(plays in no particular key) to teach him atonal composition. The atonal composer said to him, "Unless you feel you've exhausted yourself in tonal composition, don't get into atonal composition."

[ Parent ]
THere's beauty out there (none / 0) (#39)
by jzitt on Sun Apr 28, 2002 at 03:06:24 AM EST

It consisted of a 12 chromatic range of notes and every song must contain an equal number of these 12 tones held out for an equal duration.

Can you name a single piece that this describes? Sure, 12-tone serial composition, in its simplest form, involved having each of the twelve tones within an octave (not considering the problem of octave transpositions, which is odd) appear an equal number of times, but the bit about "equal duration" is just, well, inaccurate.

It is also, to my ears, at least, far from true that they all sound "horrible". Anton Webern, Charles Wuorinen, Arnold Schoenberg and other have created 12-tome works of unearthly beauty.

But there's good news in this: if you've only found "horrible" 12-tone music, and think that was "the only radical music ever made", you have a whole lot of wonderful listening yet to discover!

Two very good sources of adventurous listening online are Herb Levy's weekly webcast Mappings and John Schaefer's radio show New Sounds.

Happy New Ears!

[ Parent ]

Equal time (none / 0) (#56)
by x31eq on Mon Apr 29, 2002 at 06:46:05 AM EST

It may refer to Total Serialism, where rhythm and dynamics get serialised as well. Used strictly it would lead to all dynamics being equally represented and also all lengths of notes. Something Boulez and Stockhausen played with. I don't know if they linked duration to pitch so all notes really would be around for the same length of time.

Webern took the first steps towards total serialism, in his string quartet (Op. 28). That is a beautiful piece, but I haven't heard anything as good with stricter applications.



[ Parent ]
About theory literates and nowadays music culture (5.00 / 3) (#30)
by Juan Rojo on Sat Apr 27, 2002 at 10:45:58 PM EST

Music literates think everything in music has been done, so it's time to go the wicked way with names such arbo part or the kronos cuartet, and who like to call anything that uses harmony in the traditional way "populist music". I've studied music for nearly 10 years now, and dedicated almost as much to composing. For you all that you think you know everything, that you understand the "populist" music styles so well that they are not worth listening to. If you call yourself a music composer that puts down everything for the sake of "being populist and something that's now new", what i'm going to say to YOU, if you match that description, is basically, YOU ARE FULL OF CRAP, YOU ARGUMENT SUCKS. I've heard so much people saying such a bastardized argument. And I did the try with as much as them as I could, by just doing things such as "ok, do you know what a reggae is? do a reggae like bob marley", or "do synthpop like queen or 80's michael jackson". result.. they cant compose anything "populist" worth crap. Yet they continue saying that they'd rather do music that sounds more like doing cat /dev/urandom > /dev/midi.


There is so much stuff that music theory doesnt cover. It's basically, teaching someone how to write, or how to make a film, and then expecting them to do a novel, or a movie. There is still an enormous room for inspiration. Something I do agree is that most of modern music and most of what you hear on radio takes a minimalist approach and becomes boring fast. But let's face it, even in theory and musical terms, most of the stuff you hear today is poor. Songs that are made up of two alternating phrases repeating over and over, using all the same instruments and maybe slight modifications over time, and a guitar solo visiting sometime... AND OF COURSE! IF THERE'S NOT SOMEONE SINGUING, IT'S ELEVATOR MUSIC!! Yes, it's sad that most people has to get used to listening to such kind of music that requieres nearly no music culture to understand. But even with that, calling "populist " to something that still uses some harmony, or melodies is proof of stupidity. I can understand that some strict music composers that think that music doesnt go beyond the classical scope of instruments which can be grouped by a full orchestra dont even give a place to all the wonderful timbres that can be created with electronic equipment. My personal opinion on this matter is that "contemporaneous" music (not as in the timeline but the name which -music literate people- gives to a horrible randomization of notes you hear by current composers of that brand) is shitting over 500 years of music history.


soooooooooo


To me, the innovation in music culture lays of in a triangle, where the strongest poles could be considered:


1-Contemporaneous:


As stated before, music written with conventional instruments, could be described as music that evolves into randomness.


2-Popular/Radio


As stated before also, is based into 2 or 3 musical phrases repeating and alternating over time, mandatory instruments are drums, guitar and a singuer. here you can find jazz (not the kind you'll hear by chick corea, more like the typical blues or 5ths-based 4/4 improvisation) ,rock,pop,latin,etc


3-Electronic


Music entirely made with electornic instruments by so called DJs,DRs,etc. Focuses on hard beats, electronic effects such as *ir -filters/flanger/chorus/reverb/ringmods/echo/eq/distortion/overload/ETC! applied to instruments produced by coupling oscilators (sine/saw/square/noise/etc) in certain kinds of routings(additive/substractive/fm/etc). This kind of styles were originally called "Techno" because they were made purely electronic equipment. Later evolved to stuff such as trance, goa, rave, house, jungle, dnb,etc. with yet early spinoff such as electronic ambient, noise, etc. This kind of music had its beginings in people such as isao tomita, and in the 80's found a home in rock/pop bands and videogames.


There is a lot that can be done in music, and new stuff keeps apearing and dissapearing. Even at the beginings of the 20th century many important composers such as schoemberg kept saying that music was dead and proposed using different scales and ways of composing. Yet, people such as debussy or stravisnky kept coming up with spinoffs to music. And the most important thing, music is an art, listening to music we usually feel things, but not everyone feels the same with the same piece or style. It's not nearly as simple as saying "major chord is happy", "minor chord is sad" and "disonance means suspense or feeling bad!". There is an entire culture involved and things keep changing! new generations keep coming... and music as we know it is not dead!


But as my last point, even when the art of listening to music has changed so much in the last century, adapting to the way of our modern life (and i wont say "evolved" because that would be insulting in many cases), I do find VERY sad that present generations dont care about the music of the past. "Classical music" (an horrible term, since it's applied to everything from medieval, renacentist and baroque to russian romanticism and impressionism.. geez just look at the ID3 tags, they have stuff such as "Christian Gangsta Rap","Booty Bass" or "Negerpunk" and completely lack "waltz, minuet" or "Medieval".. the only way you can label something pre-1900's is "Classical" "Chamber", "Sonata" or "Symphony"). What happens when you ask someone about classical music? they say "mozart is boring!" "zzz" "ah i hear some in the elevator". Damn it!

Subject (5.00 / 1) (#35)
by Andrew Dvorak on Sun Apr 28, 2002 at 12:45:26 AM EST

There is so much stuff that music theory doesnt cover. It's basically, teaching someone how to write, or how to make a film, and then expecting them to do a novel, or a movie. There is still an enormous room for inspiration. Something I do agree is that most of modern music and most of what you hear on radio takes a minimalist approach and becomes boring fast. But let's face it, even in theory and musical terms,(...)
It is important for everybody to learn music theory in school, regardless of if they don't plan on using it in the future. I think this for the same reason that everybody must learn math, or everybody must learn science (social and physical) in school. The purpose is not only to develop a diverse understanding of what is out there, but to develop important RealLife skills (ie. logic, communication, etc..)

Here in Chicago, we have many of the standard sets of stations (ie. Rock, Jazz, Classical.) We also have a great public radio station which features many other genres of programming from a few cultures (isn't this one of the goals of public radio.. cultural programming?).

I like to think that my music-listening tastes are extremely diversified. I listen to anything and everything. I've listened to music from South America, Central America, Asia, Australia, Africa (!), Middle East, North America, everywhere. I would like to stress how much I appreciate much of the music that came out of and comes out of Africa (the most culture-rich continent in the world, IMHO). As somebody who is into composing a bit, I have to listen to pretty much EVERYTHING! Because, as a composer, what you write is a result of what you listen to. It's like being an artist or a writer .. what you create is a direct result of what you are exposed to. Only once you understand your inspirations can you fully exploit your potential in creation.

The following, as in the above, is a result of observations I have made. It may be inaccurate due to my extreme interest in "Jazz music" (whatever that may be, however you define Jazz music):

  • Jazz seems to be the largest genre, with its many sub-genres
  • Jazz has the most innovation and creation going on
  • Jazz allows for the most creation and innovation to occur.
By Jazz, I might mean Blues, and that's an error I probably made .. Please correct me if I'm wrong. Thanks.

andy @ OReally . net



[ Parent ]
Yes, i'm sorry about it. (none / 0) (#36)
by Juan Rojo on Sun Apr 28, 2002 at 01:45:19 AM EST

I didnt give enough importance to jazz and that's my mistake. And you are right, as music theory related, jazz has made an enormous spin off from it, basically expanding theory on almost every aspect. from rynthms, chording, counterpoint, dissonance, scales, melodies, improvisation, and the way you play instruments. To me jazz itself isnt a "music style" anymore since until half of the 20's century. but something that you "apply" to other styles. I cant really say what pure jazz is, since you have stuff that went from scott joplin or george gerswhin to.. elvis ;).. to chick corea, pat metheny, etc. I cant really say what pure jazz is anymore, and you have to call many styles either derivates of jazz, or influenced by it. So, i'm sorry about it, since i supposed that depending the point of view, you can consider jazz large developing style... or not.

[ Parent ]
Depends on who you ask (none / 0) (#43)
by Sawzall on Sun Apr 28, 2002 at 10:21:31 AM EST

(isn't this one of the goals of public radio.. cultural programming?).

National Public Radio basically just fired (called reorganizaion) the Cultural Programming part of the company. Why? It depends on who you ask. The company line is that almost no station wants diverse cultural progamming on their station, that what they really want is a "connected stream" of say Jazz, or Classical, Talk, ect. The station wants a Format. Many public radio stations are going to a Adult Alternative Contempory, whatever the hell that is.

Radio is a vast wasteland of programmed stuff. There are electronic tools for it - select your Format, basically hit shuffle play, and magically a playlist pops out. It has all been group-thinked into what belongs with what.

On the otherhand, there does exist some real DJ's who actually think about what they are playing. Sadly, they are limited to the non-NPR community radio station (of which there are thankfully a couple of hundred in the US) and now XM and the Dog. Why? Neither depends on grabbing as many people as possible. In the "normal" public radio world, they depend on listener's dollars (and local corporate support) to keep running, so they hunt for the numbers. Community radio does not care. In the case of XM and Sirius, they are aiming to grab the edges, and given 100 streams of programs, the total numbers add up. It will be interesting to see if it works. I know that now that I have XM, I will keep it till Rock and Roll (the names of the Satellites) spin off into a useless orbit.

Don't even get me started on LPFM and IBOC. Ending off-topic rant now.

[ Parent ]

A few thoughts (5.00 / 2) (#42)
by pyramid termite on Sun Apr 28, 2002 at 08:18:47 AM EST

I'm not sure I'd say that everything in music has been done, but there's a certain sense I've gotten that the last 20 years have been more of a time of refinement and reinvention than real innovation. The only kind of music I've heard that doesn't have a clear counterpart in the roots of the 70s is drums and bass - electronica in general was already there (Can, Steve Hillage, Gong, Kraftwerk) - add the 80s innovation of sampling and you've pretty much got all the elements of modern electric music. Tomita was a latecomer - the true pioneers in electronica were Verese, Stockhausen, Subnotnick, Babbitt and a few others, all of whom were 20th century academic composers. The idea of randomness in music can be pretty much blamed on Cage, but a lot of his innovations have made their way into the mainstream too. Thanks to his habit of playing several radios and TVs at once and calling it music he opened ears as to what music could be and became a direct influence on anyone who takes a spoken word sample and puts it into a dance song.

Popular music is a lot harder art than most people realize. We've all heard the jazz and formal musicians say, "Well, it takes years and years to master our instruments so we can play our music and with your music any kid with a guitar and a few lessons can do it ..." Well, true any kid with a guitar can do it badly - sometimes, in the case of the Kingsmens' Louie Louie, that actually adds to the appeal of the record. But once one gets into the big leagues to stay as a popular musician, one finds out that there's another instrument that exists that takes years to master - the modern recording studio and all the effects and capabilities that come with it. On your average jazz session, the musicians come in, and pretty much play their live show while the engineer/producer worries about how it's going to sound. He doesn't have to worry much - there's a good established practice on how to record jazz drums, piano, sax, bass, etc. and all he has to do is follow the established practice. One to three days in the studio and the album's done. Symphonic music is a little harder to record then that - getting the best sound out of the room by "dialing it in" and finding the best spots for microphone placement is an art, but it's an art with a great deal of precedent and knowledge. Again, it takes less than a week.

Now the popular musician is faced with a confusing world of choices to make when he records his music - unless it's a narrow genre like punk or metal, he's got to choose his instruments and how they're going to sound, what kind of groove they're going to play, what microphones to use and how to place them, what effects are going to be placed on the instruments, what the drums are going to be and how they're going to be tuned and miked (if real ones), and how it's all going to be mixed together with care taken not to have instruments cancelling each other out in the mix or being buried. It's complicated, even more complicated than I've indicated, and although popular musicians get a lot of help from technicians in this process, it's still one that requires a great deal of detailed, complex knowledge that can take years and years to get right. Not everyone in the music business pulls this off successfully - contrast the clarity and genius of the production of something like Pink Floyd's "Dark Side of the Moon" to the sonic sludge of some of today's CDs, where, for example, some producers have decided - oh, big bass is in these days, let's pump it up right around 50-100hz and never mind that the kick's drowning in a sea of mud because we didn't bother to EQ that right ... Let's just put a ton of reverb on anything and it'll sound deep ... I could go on, but there's a lot of good and bad out there.

I'm not sure Schoenberg ever said that music was dead - what he was saying, at least early on, was that the rules that western harmony had been based upon were rather articifial and artibrary and that the innovators of music kept having to go outside of them to produce works of genius. By the early 20th century, the rules had been stretched to the point where they really couldn't be broken without snapping into lots of little pieces. I think he saw this as a dilemma, and unwilling to say, well, we'll just stay within these boundaries and do what we can within them, let's try to make up new rules and see if we get anywhere with them. Thus we have serial 12 tone music, which didn't do much of anything except give people who score horror movies a good effect for chilling and frightening scenes. Many other composers fretted over this dilemma - the obvious thing to do, in retrospect, was to expand the instrumentation and the language of rhythm, innovations that electronic, rock and jazz musicians have come up with not knowing there was a dilemma. Whether the academic world likes it or not (and many of them don't mind), the ball's in the popular musician's court.
On the Internet, anyone can accuse you of being a dog.
[ Parent ]
In C (none / 0) (#46)
by jzitt on Sun Apr 28, 2002 at 04:49:52 PM EST

I'm not sure Schoenberg ever said that music was dead - what he was saying, at least early on, was that the rules that western harmony had been based upon were rather articifial and artibrary and that the innovators of music kept having to go outside of them to produce works of genius.

One thing Schoenberg did say: There's still a lot of good music yet to be written in C major.

[ Parent ]

Dub (none / 0) (#54)
by x31eq on Mon Apr 29, 2002 at 06:36:54 AM EST

When you say Drum and Bass "doesn't have a clear counterpart in the roots of the 70s" are you missing Dub? You don't mention it in your examples and it was a direct influence on the Drum and Bass pioneers. Even the phrase "drum and bass" though not earth-shatteringly original gets used on Dub records.

[ Parent ]
Not missing dub ... (none / 0) (#61)
by pyramid termite on Mon Apr 29, 2002 at 08:41:03 AM EST

It's obviously a direct influence, but the groove is far, far different. Speeding up the tempo to above 150 bpm was a radical idea, and so was adding a good amount of techno to the mix. Can at times came within shouting distance of d&b, but if there's any 70s music with the same kind of supercharged stuttering, stopping feel, I'd like to know about it. I will say that Dub's one of the most underrated influences of the last 30 years.
On the Internet, anyone can accuse you of being a dog.
[ Parent ]
Chances are you've been influenced... (none / 0) (#44)
by sobcek on Sun Apr 28, 2002 at 03:35:55 PM EST

...by the same non-populist music you hate. The electro-acoustic revolution of the mid-century brings you the electronic music that you now enjoy. Guess who was pushing the technology?

And if you don't believe me, some examples:

1. Realtime pitch correction. You have no idea how overused this is. Most singers out there are not terribly pitch-gifted, and pitch drift is fairly common. Enter auto-pitch correct. Not the work of electronic classicists, but you bet it stems from FFT and resonant filter analysis techniques...

2. Granular synthesis. Iannis Xenakis adopted this technique to music. (He suggested it; Roads and Truax popularized it) Lots of programs use this for realtime time-stretching (without pitch shift).

3. Acoustic room modelling. Ever wonder why those reverbs sound realistic?...

And the list goes on. The point is that pop music, as derivative as it may be, owes much in terms of its production technology to the "classical" electro-acoustic establishment.

P.S. I'd like to ask that people not consider 12-tone music adventurous or the most "out" thing that's happened in music. Quite frankly, it was an experiment which went horribly wrong (courtesy of the mid-century total serialists and their almost religious fanatacism). There have been substantially more interesting developments since 1920!

I'd like to recommend that persons unfamiliar with electro-acoustic music check out music from more recent composers; it's considerably more accessible in some ways. A very simple place to start might be with a recording of Larry Austin's Taragato! (sic)


[ Parent ]
Sorry to nitpick (none / 0) (#55)
by Herring on Mon Apr 29, 2002 at 06:42:15 AM EST

But in studying music for 10 years, you might have learned how to spell Arvo Pärt.

I like his work a lot - and compared with some of the stuff I listen to, it's really quite "normal". For instance, Spiegel im Spiegel is very simple and very definitely in F major. Even stuff like Tabula Rasa is quite conventional - apart from the "prepared" piano. Cantus in memorium Benjamin Britten is just a descending A minor scale (played at difference speeds). Debussy messes around with concepts of harmony a lot more than Arvo does.

I do think that some things go too far. I'm not sure I'd describe Lockwood's Piano Burning as music (that's Annea, not Scott).


Say lol what again motherfucker, say lol what again, I dare you, no I double dare you
[ Parent ]
Wow (none / 0) (#62)
by pyramid termite on Mon Apr 29, 2002 at 08:43:16 AM EST

I've got to admit, I'm dying to know what a piano burning would sound like. She stole that idea from Jerry Lee Lewis, anyway.
On the Internet, anyone can accuse you of being a dog.
[ Parent ]
Music (4.00 / 1) (#32)
by Miscreant on Sat Apr 27, 2002 at 11:28:00 PM EST

This is an extremely narrow, traditional western view of music for a site that is usually about broad discussion and topics. Music is simpler than what you can imagine. Everything streams from simple ratios of numbers and thus, melody, harmony, rhythm and colour (or timbre) are not only related stongly, but can be seen as almost totally similar. Our problem is Western music has inbred itsself with these concepts of a "scale" and of "bars" and "sections". While this makes it easier for us to make music that isnt bad... it constrains composition immensely. thumbs down k5 :( Im sure im not the only one who would much rather see a broader, more modern view of musical theory.

yeah! sure! (5.00 / 1) (#33)
by Juan Rojo on Sat Apr 27, 2002 at 11:32:17 PM EST

and computers are a bunch of wires, transistors and diodes. I've built one when i was in the kindergarden, since they're sooo simple.

[ Parent ]
re: (none / 0) (#37)
by Miscreant on Sun Apr 28, 2002 at 02:25:42 AM EST

I didnt say composition was easy....

Yes though, it is just a "bunch of wires".... but connecting them to make something usefull is the hard part, and if you want to use someone elses circuit board to do all your work, then you dont get very far anyway. nor do you learn about computers.

[ Parent ]

microtonal music (none / 0) (#64)
by joshewah on Mon Apr 29, 2002 at 03:00:13 PM EST

A few years ago I did some research into microtonal music and joined a mailing list about it. This article does only cover the 12 tone scale, which is what most "western" music is made with. I however have been a long time fan of Sonic Youth who are big on retuning guitars and using what may sound like dissonance to the un-adjusted ear. I truely delved into the microtonal music after discovering Glenn Branca (by way of members of sonic youth performing on his works. He has done 10 symphonies which make extensive use of microtonality in such beatiful ways that it is hard to describe here. Here is an interview with Branca where he talks more about his works: http://www.hyperreal.org/intersection/zines/est/intervs/branca.html.

[ Parent ]
Music "Theory" (5.00 / 2) (#38)
by jzitt on Sun Apr 28, 2002 at 02:34:30 AM EST

While this is a pretty good intro to the fairly narrow (but important!) area of how popular composers tend to use chords in song-based compositions using western harmonic structures on equal-tempered instruments (not to mention the breezy way it disposes of all rhythms not based on breaking a repetitive time slice into either three or four chunks), it doesn't have a whole lot ot do with "theory" in the way that it is used in other fields. James Tenney lays this out well in his article "John Cage and the Theory of Harmony" (in a section that doesn't yet refer to Cage). To quote at length, courtesy of The James Tenney Project:
"It seems to me that what a true theory of harmony would have to be now is a theory of harmonic perception (one component in a more general theory of musical perception) -- consistent with the most recent data available from the fields of acoustics and psychoacoustics, but also taking into account the greatly extended range of musical experiences available to us today. I would suggest, in addition, that such a theory ought to satisfy the following conditions:

"First, it should be descriptive -- not pre- (or pro-) scriptive == and thus, aesthetically neutral. That is, it would not presume to tell a composer what should or should not be done, but rather what the results might be if a given thing is done.

"Second, it should be culturally/stylistically general -- as relevant to music of the 20th (or 21st!) century as it is to 18th (or 13th) century music, and as pertinent to the music of India or Africa or the Brazilian rain-forest as it is to that of Western Europe or North America.

"Finally -- in order that such a theory might qualify as a "theory" at all, in the most pervasive sense in which that word is currently used (outside of music, at least) -- it should be (whenever and to the maximum extent possible) quantitative. Unless the propositions, deductions, and predictions of the theory are formulated quantitatively, there is no way to verify the theory, and thus no basis for comparison with other theoretical systems."



finally sounds like science (4.00 / 1) (#41)
by tautology on Sun Apr 28, 2002 at 06:34:30 AM EST

Thank you for pointing that out. It is funny how humanity has yet to deal with the gaping hole in our approach to music theory, which was at least noticed by 1863:

The horizons of physics, philosophy, and art have of late been too widely separated, and, as a consequence, the language, the methods, and the aims of any one of these studies present a certain amount of difficulty for the student of any other of them; and possibly this is the principal cause why the problem here undertaken has not been long ago more thoroughly considered and advanced towards its solution.

Hermann Helmholtz, On The Sensations of Tone as a Physiological Basis for The Theory of Music, Introduction

The problem he is referring to, of course, is a physically descriptive theory of music. There are so many things for humanity to be proud of... but our music theory is not one of them. Are we going to advance this field one bit?

[ Parent ]

harmonic perception is inseparable from style (4.00 / 2) (#51)
by klash on Mon Apr 29, 2002 at 01:46:48 AM EST

Perhaps the reason you find music theory lacking in scientific rigor is that music is not science the way physics or biology is.

I think that musical perception would be much more comparable to psychology. How reasonable does it sound to come up with an all-encompassing, descriptive theory for how people of any culture or time period will perceive and respond to any situation? Oh, and you have to be able to measure it.

Sure, you will be able to come up with extremes: just as anyone from any time period or culture would be unhappy if you walk up to them and sock them in the face, most people would find a tri-tone dissonant and unpleasant. But does a suspended 4th have an inherent psychoacoustic instability and need to resolve? Bach and Herbie Hancock might have different answers, and even modern listeners would have different answers depending on whether they were listening to Bach or Herbie Hancock.

In my opinion, you simply cannot separate harmonic perception from musical style (just as you cannot separate behavior from culture) and expect to have anything meaningful left to talk about. If you try to transcend musical style in formulating a theory of harmonic perception, then all you can do is talk about sonorities in isolation, at which point your theory will cease to have anything to do with music.

[ Parent ]

psychology can be separated (none / 0) (#53)
by tautology on Mon Apr 29, 2002 at 05:04:30 AM EST

Perhaps the reason you find music theory lacking in scientific rigor is that music is not science the way physics or biology is.

I think that musical perception would be much more comparable to psychology. ...

Musical conception is comparable to psychology, not musical perception (read: harmonic perception), which is comparable to physics or biology.

... How reasonable does it sound to come up with an all-encompassing, descriptive theory for how people of any culture or time period will perceive and respond to any situation?

In a scientific music theory, we must be orthogonal and separate our predictions of the perception level and the response level. The perception level is physiological (empirical), while the conceptual response level is psychological (rational).

If you treat music theory orthogonally then it is very useful to study a descriptive theory of harmonic perception. Psychology has its own issues, but those issues should not be carried into our study of perception.



[ Parent ]
"scientific music theory" (none / 0) (#59)
by klash on Mon Apr 29, 2002 at 07:36:00 AM EST

"Scientific music theory" is an oxymoron, because music is not science.

Feel free to study emperical perception of sound (if you believe such a thing exists), but don't expect musicians to care, because it has nothing to do with music.

[ Parent ]

so called "theory" (none / 0) (#63)
by tautology on Mon Apr 29, 2002 at 10:14:45 AM EST

Music composition is art. Music theory is science. All theory can be done scientifically. When I compose, I am not being a scientist, but when I study how I compose in a positivistic manner, I am a scientist.

Music "theory", as you understand it, is merely a history of the practice of music composition. It is not theory at all.

I am a musician and a composer, and I care. I have read a lot about philosophy of science, and it must not be an oxymoron if I can approach music theory scientifically and get something done.



[ Parent ]
the name is here to stay (none / 0) (#67)
by klash on Mon Apr 29, 2002 at 05:34:53 PM EST

Music "theory", as you understand it, is merely a history of the practice of music composition. It is not theory at all.

You may not like the name, but the fact of the matter is that this is what the term is almost universally accepted to mean. You cannot arbitrarily redefine terms and expect people to know what you are talking about, even if your definition is more "correct."

I don't know why you are so intent on making music serve your philosophy. Music is the end, analysis the means. Composers who confuse these priorities quickly sink into obscurity or infamy, one of the two. Does anyone really like Webern?

[ Parent ]

Well then... (none / 0) (#68)
by tautology on Mon Apr 29, 2002 at 10:57:23 PM EST

So I guess we should just ignore real theory, then? People have clarified the meanings of words since the beginning of time. Should we ignore that too?

It is not that I am making music serve my philosophy, but rather that my philosophy serves my music, effectively. Why don't you just admit that it can be useful for a composer to study how we perceive sound? It works for me, and that is greater than anything you can cite.

How can we truly know what our musical conceptions are without an orthogonal approach? You see, I don't just want to write music, I want to write better music. Most music sucks, which is the perfect reason to change the common practice. Is there anything better to guide change than analysis?



[ Parent ]
I like Webern (none / 0) (#69)
by x31eq on Tue Apr 30, 2002 at 04:16:52 AM EST

Really, I do. Does anybody out there really dislike Webern? In the sense of being able to list five of his works and what you don't like about them?

[ Parent ]
Comm: Music Theory (2.00 / 2) (#45)
by Lindt on Sun Apr 28, 2002 at 04:35:48 PM EST

Other then being dry, and boaring, and anilitical, its great. But music theory is pretty boaring. Its a good intro into the mechanics of music, and with a little more physics, could well be a short lesson in sound mechanics. Not quite IMO front page worthy, but still a good solid artical non the-less. +1

You pushed me down in the queue!!! Damn you!!! Damn you to hell!!!-Webwench

Could you please misspell a few more words? (3.00 / 1) (#48)
by Shimmer on Sun Apr 28, 2002 at 06:44:48 PM EST

So I can be sure you're mot serious. Thx

Wizard needs food badly.
[ Parent ]
Mass Music Theory (none / 0) (#47)
by stpna5 on Sun Apr 28, 2002 at 06:17:00 PM EST

Ok basic screed, if flawed. No damge done though. Lots of enormous generalizations here--"most drummers" play...etc. I think since you use some western pop music examples it leads me to mention the following:(The classical notion of major and minor diatonic rules went out the window some time between 1492 and yesterday on the American continent so these Roman numerals representing scale steps are either/neither/both.)That progression mentioned is actually a I, VI, II, V and its doo wop variant I, VI, IV, V. These both relate in one direction toward the I, IV, V of zillions of rock songs and in the other direction to the II, V, I of zillions of pop songs even before the rock era. This lovely academic exercise of using tonal/polytonal/diatonic/chromatic paradigms is useful up to a point but not music, nor any all- encompassing theory. You will find no use for these concepts to explain the blues (and how far to bend a guitar string if you are T-Bone Walker and it's 1950) which is uniquely American as are its offshoots including, jazz, funk, and rock et al. The African based polyrhythms and scales and the European based equal tempered harmonic structures echoed back across the planet again when so-called French Impressionist harmonies and extensions became the basis for modern classical American music-- jazz. (Not Lite or Smooth or other lamebrain marketing constructs, etc.)Jazz. These forms and styles became the primary cultural export of the US before even films, tv and now hip hop. Once you leave our diatonic cultural zipcode you should forget the twelve semitones in an octave rule too.(Viz India!) Otherwise someone may utter nonsense like "The blues is only......" As musician Greg Phillinganes once said, "Anybody who thinks the blues is simple should find another line of work."

Question about frequency (none / 0) (#49)
by pexatus on Mon Apr 29, 2002 at 12:48:56 AM EST

Pluck a guitar string and put a strobe on it and you'll see all sorts of patterns in the string. If you don't have a strobe light, put your guitar so the strings are between your eye and the TV or computer monitor. In America electricity is at 60hz, which is close to B. Play B and the wave will come close to standing still. Tune it up a little bit and it really does. Try playing other notes and see what happens.

Slightly off-topic engineering question, but can anyone think of why the refresh rate of the monitor does not also affect this? My monitor refreshes at 60 Hz, and my roommate's is 85 Hz. The "standing wave" note on my guitar is the same for both monitors, so obviously marktaw's right that only the electrcity frequency matters, but why? A monitor refreshing at 85 Hz is like a whole lot of little strobe lights flashing at 85 Hz.

Possibility (none / 0) (#50)
by pexatus on Mon Apr 29, 2002 at 01:09:03 AM EST

Suppose the monitor refreshes by taking the entire refresh period to draw the screen, so that as soon as it's done drawing the bottom right pixel, it speeds back to the top left. (I don't know if it works like this or if it gets done drawing long before it starts drawing again). A monitor IS like a million little strobe lights, but under this assumption, each strobe light, while having the same frequency, would be out of phase with all the others by a tiny amount. Then any effect on the guitar string would not be consistent (and hence not noticable) from pixel to pixel.

Sorry to take up space having this discussion with myself.

[ Parent ]

I don't think so (none / 0) (#72)
by p3d0 on Tue Apr 30, 2002 at 11:46:38 AM EST

It's the monitor, not the electricity that matters.  My guess is, you happened to choose a note with a frequency like 204 or something.  Both 60 and 85 Hz monitors would produce something that looks like a standing wave if the string was vibrating at 204Hz.
--
Patrick Doyle
My comments do not reflect the opinions of my employer.
[ Parent ]
Its your eyes, not the monitor (none / 0) (#95)
by JonesBoy on Tue May 07, 2002 at 08:31:06 PM EST

A slow monitor refresh rate may be visible, but only if it is 60hz or lower.   Incandecent light bulbs do not flicker because the wire does not cool fast enough to blink visibly.   Neon light blink can be visible.  

Your eyes are working on a frame by frame basis, at roughly 60 hz.   Take a look at a spoked car tire speeding up in sunlight.   It will seem to stand still, then reverse direction, then stand still again.   The light isn't acting as a strobe, your brain is.

Now take 2 pieces of screen, and put them on top of each other.   Rotate one of them.   You will see patterns where the screens cross.   These are called moire patterns.

When you hold the guitar up to the monitor (or TV) the scan lines are creating an interferance pattern with the monitor.   This enhances the outline of the string.   Since your eyes and the string are at the same frequency, you see the standing wave.

You can see the interferance patterns with your fingers too.   Open you hand and spread your fingers out as wide as possible.   Sit in front of your monitor with 1 eye closed.   With your fingers horizontal, move your hand up and down in front of your face as fast as possible.   You don't have to move your hand far, just fast.   You will see the scan lines of your monitor as horizontal black stripes.   Now rotate your hand so your fingers are vertical, and move your hand right and left, again as fast as possible, as close to your face as possible.   You will now see diagonal lines.   Neat, huh?
Speeding never killed anyone. Stopping did.
[ Parent ]

Re: Its your eyes, not the monitor (none / 0) (#97)
by pexatus on Wed May 08, 2002 at 04:08:57 PM EST

Now rotate your hand so your fingers are vertical, and move your hand right and left, again as fast as possible, as close to your face as possible.   You will now see diagonal lines.

I never got that before, though I always noticed that the horizontal motion would make my fingers appear diagonal when I knew I was holding them up straight vertically.  That's cool.

One question, though: if a wheel spinning at 60 Hz appears to stand still, without being held up against a 60 Hz Monitor, why does my guitar string only stand still when I hold it up to a monitor?  If I hold it up to a regular light bulb, it doesn't stand still.

[ Parent ]

corrections (none / 0) (#99)
by darweidu on Sat May 11, 2002 at 02:05:18 AM EST

car wheels are illuminated by car headlights, which are at 60Hz. If it were the case that it was our eyes, then you would always see electronic machinery behaving oddly, since most of it operates at 60hz. Our eyes don't have a framerate. Although we have a limited rate of viewing details, it isn't something as simple as 60hz - it's actually continuous, and updates in chunks at a time with hefty interpolation and extrapolation.

[ Parent ]
Car headlights (none / 0) (#101)
by JonesBoy on Tue May 14, 2002 at 09:08:52 AM EST

Is this a troll?

Car headlights are DC incandecent.   They don't have a frequency.   Even if they were AC, like a household lightbulb, they wouldn't flash at 60 hz (see my original post).

Most household machinery does not operate at 60 hz.   If it did, you would see some aliasing between movements, or motion blur would mess up the whole thing.

I agree that we don't have framerates like a projector, but it is a good comparison which explains a variety of visual phenomena.

Speeding never killed anyone. Stopping did.
[ Parent ]

Why the monitor is needed (none / 0) (#100)
by JonesBoy on Tue May 14, 2002 at 09:04:40 AM EST

Because it is vibrating at a higher multiple of 60hz.   It is too fast for your eyes to see, but with the interferance pattern, it can 'freeze' it in place.
Speeding never killed anyone. Stopping did.
[ Parent ]
Greeks, 7 (none / 0) (#58)
by x31eq on Mon Apr 29, 2002 at 07:13:29 AM EST

We know little of Pythagoras's music theory, and he doesn't really deserve credit for the diatonic scale. The first mention is in a tablet from Mesopotamia which describes tuning by the cycle of fifths.

The Greeks in general thought in terms of 3 note tetrachords rather than 7 note octaves. The first Greek description of a "Pythagorean" diatonic tetrachord is in Plato (Timaeus?).

I thought Newton was to blame for "indigo" because he decided the spectrum should have 7 colors to match, among other things, the 7 note musical scale. Nothing to do with the Greeks.

Naming the notes around what we now call A minor is a historical accident in which Boethius is implicated somewhere. The intention was to match Greek usage, where they thought alpha referred to the equivalent of our A but I think they even got that wrong.

Indian music also uses 7 named notes to the octave, as a subset of a 12 note chromatic scale (and an enigmatic 22 note scale). So this practice probably didn't originate with the Greeks either. May have been Babylonian (they gave us the 7 day week) or it may be such an obvious idea it has multiple origins. If you really insist on European supremacy it could have been taken over with the spice trade, or Alexander's army. But it's unlikely they would have been interested in music theory.



A drink with jam and bread? (3.00 / 3) (#60)
by Rasman on Mon Apr 29, 2002 at 07:49:56 AM EST

Isn't it "do re mi fa so la TI do"?

european thing (none / 0) (#70)
by kubalaa on Tue Apr 30, 2002 at 08:09:24 AM EST

I don't know the precise boundaries of this phenomenon, but some Italians I know were taught "Si" instead of "Ti". So it's not universal.

[ Parent ]
Tonic Sol-Fa (none / 0) (#93)
by divbyzero on Mon May 06, 2002 at 04:49:18 PM EST

While Tonic Sol-Fa is based in Latin (it comes from the first syllables of the respective words in a particular plainchant that walked up the scale), it tends to be modified slightly when used by speakers of different languages (English, Italian, etc).

The way I learned it included provisions for the full chromatic scale (picture a piano keyboard):

  [Di][Ri]    [Fi][Si][Li]
[Do][Re][Mi][Fa][So][La][Ti][Do]

In that version, Si was the augmented fifth, not the seventh.



[ Parent ]
what you are thinking of (none / 0) (#94)
by adequate nathan on Tue May 07, 2002 at 08:15:01 PM EST

Fixed-pitch solfege vs the disgusting perversion known as "movable do." The first is a universal musical language; the second is a technique for mistraining impressionable choristers.

Do = C (including C double-flat to C double-sharp)
Re = D (incl., etc.)
Mi = E
Fa = F
So = G
La = A
Si = B

Movable do is considered harmful because it is chauvinistically biased toward tonal music; it is not compatible with the fixed-do identification system used in Europe; and it is useless for solfeging instrumental music by pitch-names.

Nathan
"For me -- ugghhh, arrgghh."
-Canadian Prime Minister Jean Chrétien, in Frank magazine, Jan. 20th 2003

Join the petition: Rusty! Make dumped stories & discussion public!
[ Parent ]

Different going down (none / 0) (#102)
by tunesmith on Sun May 26, 2002 at 02:12:44 AM EST

do
ti teh
la leh
sol seh (?)
fa
me meh
re rah (!)
do

Yes, I have a blog.
[ Parent ]
Sound snippets would've been nice (none / 0) (#65)
by AstroLePtiRobot on Mon Apr 29, 2002 at 04:11:46 PM EST

Great article, but it would have been way cooler for the reader if you had made links to sounds so we can get a feel of what you're saying without having to dig out the old guitar from the closet. :)

Do Re Mi Fa So La Ti Do (4.00 / 1) (#71)
by kshea on Tue Apr 30, 2002 at 10:44:13 AM EST

DO... the stuff, that buys me beer...
RAY... the guy that sells me beer...
ME... the guy... who drinks the beer,
FAR... a long way to get beer...
SO... I'll have another beer...
LA... I'll have another beer...
TEA... no thanks, I'm drinking beer...
That will bring us back to... Doh!

---Homer Simpson

Doh, a deer! (none / 0) (#81)
by Rasman on Thu May 02, 2002 at 05:25:21 AM EST

My favorite Simpsons reference to this song is when they're all in the car with Homer driving and he slams on the brakes to see a doe in the headlights...

Homer: DOH!
Marge: A deer!
Lisa: A female deer!


[ Parent ]
my own attempt at an explanation (5.00 / 3) (#73)
by christfokkar on Tue Apr 30, 2002 at 08:22:30 PM EST

Good article. It would be nice if more people understood that their perceptions of "good music" are actually grounded in 300 year old ideas. However, I thought the article took on too much, so I'll try a simpler tack.



What is music?

Music is structured sound. All music conforms to some system of conventions, as does all writing, art, and film. The system may be abstract or weird, but there must be some system in order for people to "get it." You can say there is music in ambient sounds such as traffic or conversation, but only because you are identifying some system within.

Harmony and Rhythm

These are the basic building blocks of music. Harmony is simultaneous notes (chords). Rhythm is a pattern of emphasis over time. To a lesser extent, there is also melody (pattern of notes over time), and timbre (the actual sound of the instrument, violin vs. guitar for example).

Rhythm

Western rhythm has mostly focused on 3-beat (waltz) and 4-beat patterns. All classical music up to 1900 is one or the other. Most rock music is in 4. All blues is in 4. All techno is in 4.

3 and 4 are nice because they are symmetric. However, 5, 7, 11, and 13 are just as viable. "Progressive" bands such as Tool, Dream Theater, Primus, and even Led Zeppelin have written songs with these odd rhythms. Non-western music (eastern, native, etc) have generally been more tolerant of these odd rhythms. Western composers did not embrace these rhythms until the 20th century.

Harmony

Harmony is a complex subject. For starters, it should be noted that Western harmony was largely developed by the Catholic church. Clear, clean chords were preferred over harsh ones, which sounded "evil."

Bach codified the Western harmonic system in the 1700's, indicating a clear preference of which chords to use when, and how. The result is a harmonic "language" that most people understand innately. When you think that a Metallica or Nirvana song, a trance anthem, or Britney's latest hit sound "good," it is probably because you are hearing a bit of Bach in it.

Scales

In order to build a harmonic system, first you need a scale. The most basic scale is the pentatonic (5-tone) scale, which is indicated by the black keys on a keyboard. Pentatonic scales are common in non-western music; indeed, if you play anything on those black keys, it will probably sound "traditional" or "chinese".

A superset of that is the diatonic (7-tone) scale, which is indicated by the white keys. Both the pentatonic and diatonic scales are structured with a certain sequence of whole and half steps. Because of this built-in asymmetrical structure, one tone can be identified as the "key" or the "tonic," standing out from the others in its stability and in the tendency of other tones to move towards it.

Another superset is the chromatic (13-tone) scale, which is indicated by both black and white keys, and has a constant half-step between each tone. It is symmetrical, there is no tonic or key.

Basics of Western Harmony

Western harmony is built around the concept of organizing chords into three categories. The first category (tonic, or I) is clean, clear, and stable. The second category (dominant, or V) sounds climactic. The third category (subdominant, or IV) is developmental.

All classical music up to 1900 conforms to the pattern I-IV-V-I. The tonic (I) sets the scene. The subdominant (IV) gets things going. The dominant (V) is the climax, and the dominant resolves back to the tonic. Like a fractal, I-IV-V is everywhere in classical music, from the overall structure of symphonies down to the shortest passages.

One thing you will never see in classical music is the opposite, I-V-IV. This would be like letting the air out of a balloon slowly instead of popping it. However, you do see I-V-IV in blues. Thus in rock music, you see a mix of classical I-IV-V and blues I-V-IV.

Brief History of Western Music

Medieval/Renaissance Period

In the medieval period, music composition was largely performed by Catholic monks. They used a variety of diatonic scales, corresponding to the white keys starting from different notes. Certain chords were good and others were evil. An emphasis was placed on the smoothness and holiness of the sound.

Baroque Period (early 1700's)

The Baroque period was dominated by Bach. Whereas the medievalist composers had 6 or 7 different scales at their disposal, the baroque composers settled on just two - major (C) and minor (A). Harmony became very strict and rigorous, I-IV-V was codified and absolute.

Classical (late 1700's)

The Classical period was dominated by Mozart and Beethoven. Music became less mathematical and more playful. Piano replaced the harpsichord, and composers started to take wind instruments more seriously. Beethoven's highly emotional Sixth and Ninth Symphonies presaged the Romantic period to follow.

Romantic (1800's)

The Romantic period featured many luminaries, such as Wagner, Tchaikovsky, and Brahms. The Romantic composers greatly expanded the harmonic language, placing emphasis on emotion rather than strict mathematical structure. The I-IV-V rule still held, but was analogous to dribbling in the NBA - in other words, largely obscured by acrobatics. Deep winds such as the tuba allowed more oomph. Romantic music is a crowd-pleaser; film scores by Horner and Williams have distinctly Romantic underpinnings.

Twentieth Century

In the 20th century, all the rules were thrown out the window. Twentieth century composers experimented with new scales (whole-tone, octatonic, etc), odd rhythms (5, 7), and entirely new harmonies. Music became highly abstract, almost unlistenable. While a lot of these experiments failed to produce viable new systems, music in general became a lot more diverse. Notables include Gershwin and Copland, who created, for the first time, a distinctly "American" sound.

Blues

Blues introduced the ideas of improvisation, I-V-IV harmony, and repetition, while adhering to a strict rhythm of 4.

Rock

As best I can tell, rock was an outgrowth of the drumset, electric guitar, and electric bass. Rock incorporated most of the previous rhythmic and harmonic styles, and added new ones such as "power chords" (power chords, also known as empty chords, were a big no-no for classical composers).

Minimalism and Techno

Minimalism is highly repetitive music, which makes an impact by adding layers over time instead of through explicit, rigorous structure. Native drumming, for example, can be considered minimalist. Philip Glass, Terry Riley, and Steve Reich pioneered minimalism in the 60's-80's, with techno being their ultimate legacy.

What's the point of all this?

Very often, I hear musicians say, "I can do whatever I want," and I hear listeners say, "Good music is whatever I think it is."

Well, those are true. However, years of listening to Beethoven, Copland, and Led Zeppelin have granted us a shared aesthetic. You CAN do whatever you want, but that's because the music you write will (fortunately) come out similar to what you've already heard.

It's unconscious, but it's there. If you go to a piano, you will instinctively play a diatonic scale. You will instinctively play in major and minor keys. You will instinctively select a rhythm of 4. It's what "sounds right" but it's the furthest thing from an accident. It's a language, just like English, and just like math.



Correction: chromatic scale is 12 tones... (none / 0) (#74)
by christfokkar on Tue Apr 30, 2002 at 11:26:37 PM EST

...not 13.

[ Parent ]
part two: functional harmony (5.00 / 2) (#75)
by christfokkar on Wed May 01, 2002 at 01:36:38 AM EST

As a follow-up to my last post, I'll try to explain functional harmony, or the reason why I-IV-V forms the basis for so much classical music.

To start, let's look at the fundamental axioms, or assumptions, that classical music makes.

Axiom 1: Consonance

Classical music is predicated on a preference for consonant (clear) harmonies over dissonant (harsh) ones, where a harmony is either an interval (two tones), or a chord (three or more).

The most consonant interval is the octave (C-C).  Next most consonant is the fifth (C-G), and then the major third (C-E).  

By contrast, the most dissonant intervals include the chromatic half-step (C-C#), the augmented fourth (C-F#), and the major seventh (C-B).

Medieval music focused on using the most consonant intervals; the augmented fourth, for example, was outlawed.  However, by the Baroque period, chords were classified as well, and by situation.  This classification is subjective, but it is internally consistent, and it forms the basis for "functional" harmony.

Axiom 2: Tonality

Medieval composers used several different diatonic scales, but by the Baroque period, composers had settled on just major (C) and minor (A).  Why?  Because these scales have the most obvious tonality.

Tonality is the effect of one note in the scale sounding distinctly more "important" than the others.  In the C major scale, the tonality is C.  This is largely because of the leading tone, or the half-step preceeding C.  If you go from B to C, there is the sense that you have arrived at a destination.

Functional harmony is a system that continually reinforces the tonality of a piece of music.  In other words, when Bach and Beethoven wrote music in C major, they made it damn obvious that it was in C major.  It wasn't until the Romantic period that composers started to obfuscate the tonality.

Axiom 3: Voice Leading

Functional harmony is descended from medieval four-voice chorales.  Each voice - bass, tenor, alto, and soprano - takes one note of a chord.  When moving to the next chord, each voice is supposed to move up or down as little as possible.  No big leaps.  

In addition, voices should generally move in opposite directions - if the bass is going down, the soprano should go up.  This is known as counterpoint, and classical composers believed that counterpoint sounded stronger than all the voices moving up or down at once.

Thus, voice leading (moving as little as possible) and counterpoint (moving in opposite directions) form the situational aspects of functional harmony.  In a given situation, some chords will allow for smooth voice leading, others not.

Harmonic Classification

Now that we understand the classical mindset, let's turn to how they classified chords.  

Each chord in the scale is given a roman numeral based on its root.  This is just a naming scheme, and it is pretty simple. In C, we have:

CEG (I)
DFA (II)
EGB (III)
FAC (IV)
GBD (V)
ACE (VI)
BDF (VII)

Next, the chords are organized into functional groups.  The tonic group emphasizes the tonality of the music, and includes I.  These chords are declarative, stable.  (VI falls into this group as well, but VI is deceptive because it is the relative minor.)

The dominant group consists of V and VII.  These chords have the leading tone (B), and the effect is climactic.  When you hear the leading tone, you expect the tonic to follow.

The subdominant group consists of II and IV.  These chords move to the dominant the way that the dominant moves to the tonic.  

Thus, every chord has its function.  A tonic chord establishes the key of the piece.  A subdominant chord predicts that a dominant will follow.  A dominant chord predicts that the tonic will follow.  Functional harmony is all about predictability.

Note: The odd man out is the III chord, which was considered confusing and wasn't widely used until the Romantic era.

Why It Works

To understand this system, you have to look at the voice leading.  The simplest example is the dominant GBD moving to the tonic CEG.  What are the benefits of this arrangement?

  1.  Leading tone (B) to tonic (C) provides climax and resolution.
  2.  Fifth in the bass (G->C).  Remember, the fifth is the most consonant interval after the octave.
  3.  Shared G
  4.  D moves easily to E
By contrast, imagine moving from IV (FAC) to the tonic CEG.  It's allowed, but it sounds different.  How?
  1.  Shared C is fine but provides no climax like the leading tone does, just more of the same note.
  2.  F->C (fourth) in the bass is not as strong as the fifth.  In fact, the fourth is an inverted fifth and could be considered confusing.
The rules of voice leading are simple enough, but the details fill entire textbooks.  This is probably the most I can convey in the space of a single comment.

Pop Music

Popular music uses many of these conventions, but breaks them just as often.  These are the most common ways:

  1.  Classical music is I-IV-V-I, but blues is I-IV-V-IV-I.  Whereas classical music provides a distinct climax and resolution, blues ambles up and down, up and down.
  2.  Classical chords are identified by the root and the third.  Thus, in CEG, the C and the E are essential but the G is optional.  Power chords, on the other hand, are just a fifth: CG.  There are no power chords in classical music because they are not considered chords.
  3.  In classical music, C->D simultaneous with G->A is called parallel fifths - two voices, moving the same amount in the same direction, a fifth apart.  It's not contrapuntal, and it's outlawed.  Pop music is much more forgiving of parallel motion.


[ Parent ]
Counterpoint (none / 0) (#77)
by x31eq on Wed May 01, 2002 at 09:43:11 AM EST

Counterpoint is a set of rules allowing a number of melodies to sound together with pleasing harmony while preserving their independence. Contrary motion is only one part of counterpoint, for Fux' sake!



[ Parent ]
Tritones (3.00 / 1) (#78)
by x31eq on Wed May 01, 2002 at 12:23:59 PM EST

The augmented fourth was not outlawed in all medieval music. According to the Internet's favourite expert on Medieval music,

Again, the tritone, far from being viewed as "diabolic," is treated as an interval which can be pleasing and even "consonant" in the right context.

but it was

With the shift from medieval to Renaissance style during the 15th-century, and the advent of an approach where the formerly active thirds and sixths are treated as increasingly stable and even conclusive, the tritone indeed takes on a new vertical role.


[ Parent ]
Do not underestimate the power of the III chord (none / 0) (#92)
by divbyzero on Mon May 06, 2002 at 04:40:58 PM EST

A popular use of the III chord (either major or minor) is to transition temporarily into a different tonal center, a topic which is sorely missing in this article.  Granted, it is not as elementary a concept as some of the others you chose to cover, but it is not that difficult to grasp, and you cannot make a fair contrast between the High Classical and Romantic periods without discussing it.

Of course, III is not the only point of departure for other tonal centers ...

[ Parent ]

Corrections (3.00 / 1) (#76)
by x31eq on Wed May 01, 2002 at 09:35:02 AM EST

Western rhythm has mostly focused on 3-beat (waltz) and 4-beat patterns. All classical music up to 1900 is one or the other. Most rock music is in 4. All blues is in 4. All techno is in 4.

The waltz was an Austrian folk dance which became popular in European ballrooms in the 19th Century. It isn't a generic name for 3 beat rhythms. You're missing the huge popularity of 6 beat rhythms from "all classical music".

 

Bach codified the Western harmonic system in the 1700's, indicating a clear preference of which chords to use when, and how. The result is a harmonic "language" that most people understand innately. When you think that a Metallica or Nirvana song, a trance anthem, or Britney's latest hit sound "good," it is probably because you are hearing a bit of Bach in it.

Bach didn't "codify" anything. The basic harmonic principles were in place by the time he came on the scene. The key theoretical work is usually given as Rameau. Are you really suggesting there have been no "good" ideas since Bach?

 

Another superset is the chromatic (13-tone) scale, which is indicated by both black and white keys, and has a constant half-step between each tone. It is symmetrical, there is no tonic or key.

As another poster has said, you'll get very strange results if you have 13 notes to your chromatic scale. The 12 notes were only considered symmetrical some time in the 18th Century.

 

All classical music up to 1900 conforms to the pattern I-IV-V-I.

All of it? What do you mean by "classical music"? A Phrygian cadence, for example, doesn't follow that pattern at all.

 

In the medieval period, music composition was largely performed by Catholic monks. They used a variety of diatonic scales, corresponding to the white keys starting from different notes. Certain chords were good and others were evil. An emphasis was placed on the smoothness and holiness of the sound.

Firstly, why the sexism? Were Hildegard of Bingen's nuns not performing music compositions? Also, you're missing all folk music, but perhaps you only mean written music. Still, how about the Troubadours and Trouvères? And you've ignored the "Renaissance" part of "Medieval/Renaissance" and completely missed out Mannerism. Oops, so much for Palestrina, Gesualdo, et al.

 

The Baroque period was dominated by Bach.

(*cough*) (*cough*) Bach may be the only Baroque composer you can name, but a provincial choir master hardly dominated the period. How about Vivaldi, Handel, Monteverdi?

 

Classical (late 1700's)

When you say "70's" you presumably mean 1970-1979. But here you say "1700's" when you presumably mean "the 18th Century" as 1700-1709 was not the Classical era. Whereas it did continue long into the 19th Century.

 

The Classical period was dominated by Mozart and Beethoven.

And there you go again! That's a completely anachronistic statement. Mozart never got a prominent appointment in Vienna, he certainly didn't dominate the period. Even going by popularity today, what happened to Haydn and Schubert?

 

Music became less mathematical and more playful.

What on earth is this supposed to mean?

 

film scores by Horner and Williams have distinctly Romantic underpinnings   .  .  .   In the 20th century, all the rules were thrown out the window.

These two statements are contradictory. Of course all the rules weren't thrown out. If they had been, why would you bother explaining them to us?

 

Blues introduced the ideas of improvisation, I-V-IV harmony, and repetition, while adhering to a strict rhythm of 4.

None of these ideas were "introduced" by blues. They're some of the things that have been around since Bach's day.

 

Minimalism is highly repetitive music, which makes an impact by adding layers over time instead of through explicit, rigorous structure.

Minimalism typically involves gradual changes rather than adding or removing layers. This gives it as explicit and rigorous structure as any other music you're likely to hear.

 

Native drumming, for example, can be considered minimalist.

What do you mean by "native drumming"? Native to whom? And although some African drumming styles were an influence on the minimnalists, it's a bit much to retrospectively define the original as minimalism.

 

Philip Glass, Terry Riley, and Steve Reich pioneered minimalism in the 60's-80's, with techno being their ultimate legacy.

Techno has almost nothing to do with the Minimalist composers you mention. All three of them are still writing music, so it's a bit harsh of you to dismiss everything they wrote since the 80s. Along with other composers influenced by Minimalism, such as Andriessen, Martland, Torke and all the "Holy Minimalists" like Pärt.

Really, with all the music history on the web, why do you subject us to this?



[ Parent ]
massive egotism (none / 0) (#80)
by christfokkar on Wed May 01, 2002 at 07:08:09 PM EST

You're missing the huge popularity of 6 beat rhythms from "all classical music".

Oh yeah, silly me, lumping 6 with 3 and 8 with 4.  What an awful, confusing generalization for the novice reader.

As another poster has said, you'll get very strange results if you have 13 notes to your chromatic scale.

I think that poster was me, correcting myself.

All of it? What do you mean by "classical music"? A Phrygian cadence, for example, doesn't follow that pattern at all.

A Phrygian cadence is IV6-V, unless you mean in the phrygian mode, where it's VII6-I.  Either way, the pattern is followed.

Bach may be the only Baroque composer you can name, but a provincial choir master hardly dominated the period. How about Vivaldi, Handel, Monteverdi?

How about them?

Mozart never got a prominent appointment in Vienna, he certainly didn't dominate the period. Even going by popularity today, what happened to Haydn and Schubert?

I was going by popularity today.

None of these ideas were "introduced" by blues. They're some of the things that have been around since Bach's day.

Then maybe you'd like to tell us what makes blues distinct?

And although some African drumming styles were an influence on the minimnalists, it's a bit much to retrospectively define the original as minimalism.

It's a bit much to define anything as minimalist.  Even the composers themselves hate the word.  Still, the word exists.

Techno has almost nothing to do with the Minimalist composers you mention.

I doubt that.  For me, it wasn't much of a leap to go from Einstein on the Beach to trance records.  It's the same shit, more or less: repetitive electronic music that makes an impact by being immersive rather than expressive.

Now, of course, you're going to tell me that Riley's In C isn't electronic.  God, you're such a troll.

Really, with all the music history on the web, why do you subject us to this?

Really, with all the things you could be doing with your time, why do you subject us to your massive ego?

[ Parent ]

Techno and stuff (4.00 / 1) (#83)
by x31eq on Fri May 03, 2002 at 08:04:59 AM EST

Oh yeah, silly me, lumping 6 with 3 and 8 with 4. What an awful, confusing generalization for the novice reader.

Yes, deriving 6 from 3 would be confusing as it has more to do with 2. Which you didn't mention either. Leaving compound rhythms to a more advanced stage is one thing, but pretending they don't exist is quite another. You could always leave rhythm out altogether if you don't have much to say about it.

 

I think that poster was me, correcting myself.

Yes, sorry, I didn't check the authorship

 

A Phrygian cadence is IV6-V, unless you mean in the phrygian mode, where it's VII6-I. Either way, the pattern is followed.

I don't see VII in I-IV-V-I. I don't expect a novice would see the connection at all.

 

I was going by popularity today.

Then you shouldn't have described it as "history". It's bad form in history to impose present attitudes on the past.

 

I doubt that. For me, it wasn't much of a leap to go from Einstein on the Beach to trance records. It's the same shit, more or less: repetitive electronic music that makes an impact by being immersive rather than expressive.

Saying something is a "legacy" implies causation, rather than mere similarity. Repetition is hardly a new idea in music. If you think techno composers were directly influenced by the mimimalists, find some evidence instead of throwing out glib, misleading statements.

Trance may be an exception, but the techno I've heard doesn't undergo the gradual changes of minimalism at all. They only appear similar in short excerpts.

I dug out an old interview with Juan Atkins in The Wire. He mentions funk a lot. "Anybody 30 and over that's making music has had some brush with funk ... Once you get over the technology it comes down to the groove." And a quote from Derrick May describing techno as "Kraftwerk meeting George Clinton in an elevator." Hendrix also crops up. No classical composers at all.

BTW, Kraftwerk's Radioactivity was released in 1975, the year before Einstein on the Beach was written. Recordings of the latter took a few years, and I don't know of a performance in Detroit.

 

Now, of course, you're going to tell me that Riley's In C isn't electronic. God, you're such a troll.

Thanks for putting words into my mouth. I think I can leave the dialogue in your capable hands. Be sure to mention It's Gonna Rain and Come Out because I usually do sooner or later.



[ Parent ]
Kraftwerk (5.00 / 1) (#86)
by pyramid termite on Fri May 03, 2002 at 09:20:22 AM EST

My copy of the All Music Guide to Electronica says, "Kraftwerk emerged from the same German experimental music community of the 60s which also spawned Can and Tangerine Dream; primary members Florian Schnieder and Ralf Hutter first met as classical music students at the Dusseldorf Conservatory ..." I think the link between 20th century "serious" music and techno has been established.
On the Internet, anyone can accuse you of being a dog.
[ Parent ]
dance music (none / 0) (#87)
by christfokkar on Fri May 03, 2002 at 12:25:01 PM EST

Trance may be an exception, but the techno I've heard doesn't undergo the gradual changes of minimalism at all. They only appear similar in short excerpts.

I think I understand what you're saying: most dance music is melodic, and at some point the gradualness and repetition yield to some sort of obvious structural change.

However, listening to Reich just now, I see that his music is just as frequently punctuated by obvious change.  It is frequently melodic, frequently adds or removes many layers at once, has tempo changes, and other elements of structure.

So the question becomes, how do you define minimalism?  Most minimalist traits - gradualism, absence of melody, minimal instrumentation, abstractness - are as frequently discarded as they are endorsed.  The only trait that I see common across all minimalist music is massive repetition of short motives, which is a different kind of repetition than the kind used by classical composers.  

I have to admit that a lot of dance music resembles pop or rock in its structure, but there is other dance music that is as gradual and layered as In C.  But across the spectrum of dance music, there is present the pounding repetition of minimalism.


[ Parent ]

Minimalism (none / 0) (#90)
by x31eq on Fri May 03, 2002 at 04:59:24 PM EST

What Reich are you listening to? I'm more familiar with him than the other original minimalists. His early music does have gradual changes, mostly to do with phase shifting rhythms. Things like drumming and clapping. Which all started with those tape pieces I said I would mention. But he's moved on from that, so you could say he isn't minimalist any more.

If we're going to use the wider definition that includes things like Andriessen and late Reich it really does boil down to classical music of the late 20th Century (and with every sign of continuing into the 21st) that makes heavy use of repetition. Like you said. Usually with strong rhythms and simple harmonies.

These features are good for distinguishing it from other late C20th classical music, but are obviously shared by most traditional or pop music. So there are all kinds of similarities, many of which are coincidental. Most direct influence is on minimalism from pop rather than the other way round. Some things, like layering, came to minimalism directly from traditional music.

I've heard "trance" is supposed to borrow from traditional music, but never really understood what it was.

There was a CD out a few years back of dance music inspired by Reich. One of the comments he made was that the rhythms were so boring -- all 4/4. He generally didn't seem to be in touch with that scene at all. Although apparently it came about because he was having some kind of influence on it. There's also The Orb's infamous sampling of Electric Counterpoint of course.



[ Parent ]
trance, reich (none / 0) (#96)
by christfokkar on Wed May 08, 2002 at 01:25:54 AM EST

What Reich are you listening to?

The examples for my post were Different Trains, Electric Counterpoint, and Tehillim.  I've heard his out-of-phase experiments, although not recently.

I've heard "trance" is supposed to borrow from traditional music, but never really understood what it was.

Trance is anything that sounds spaced-out or futuristic.  Colloquial definition, but it's accurate.  Trance tends to be emotional in the extreme - either effusively happy or eminently demonic - as opposed to pure techno (intellectual, not emotional), or house (bumpin' frat-party vibe).  Some trance is full of pop anthems and vocals, other trance is really blunt and repetitive.

Oakenfold, Sasha, and Digweed are the usual starting points for trance listening, but today these artists are pretty pop-oriented and mass market.  Bedrock is a good record label for deeper, more repetitive stuff.  Goa trance (Indian/Israeli influence) tends to be even more deep, bassy, and repetitive.  Goa might be the "traditional" sub-genre you heard of.

There was a CD out a few years back of dance music inspired by Reich. One of the comments he made was that the rhythms were so boring -- all 4/4. He generally didn't seem to be in touch with that scene at all.

Yes, I've been a fan of odd rythms ever since my music education began in earnest.  When I started on dance music, I was equally dismayed.  But after picking up some deejay skills, I now appreciate the workable simplicity of 4/4.  It's much easier on the deejay, and a dancing crowd probably expects that rhythmic predictability too.

[ Parent ]

guides (none / 0) (#98)
by darweidu on Sat May 11, 2002 at 01:59:16 AM EST

http://dancemusic.about.com/library/blgenres.htm?once=true& http://www.ishkur.com/features/music/guide.htm

[ Parent ]
dance music pt 2: layering (none / 0) (#88)
by christfokkar on Fri May 03, 2002 at 12:44:46 PM EST

Oh yeah, the other thing is layering.  While a lot of dance music may not play out with gradual layering, what's significant is that dance music is pretty universally created with a layering technique.  

Between layering and repetition, I think it's fair to say that dance music and minimalism have a lot in common.  

I'd like to know what other elements of minimalism you consider significant.  You've mentioned gradualism, but I think this is more a matter of degree than of whether it's present or not.

Keep in mind, I never said that minimalism and techno were the same thing.  What I was trying to say is that with or without a historical connection, techno is the popularization of the minimalist composers' major ideas.


[ Parent ]

Blues (4.00 / 1) (#85)
by pyramid termite on Fri May 03, 2002 at 09:09:25 AM EST

Then maybe you'd like to tell us what makes blues distinct?

I'd say, aside from the classic 12 bar progression often used, quarter-tones (blues notes) and African derived rhythm. None by themselves would be distinct but the combination is.

And, yes, I'd call techno a product of 20th century "serious" music, including, but not limited to minimalism.
On the Internet, anyone can accuse you of being a dog.
[ Parent ]
Folk and country (3.00 / 1) (#84)
by pyramid termite on Fri May 03, 2002 at 09:00:49 AM EST

You've forgotten these. Otherwise, an excellent write-up.
On the Internet, anyone can accuse you of being a dog.
[ Parent ]
update (none / 0) (#89)
by christfokkar on Fri May 03, 2002 at 02:49:34 PM EST

Based on microtonal's numerous objections, these are the parts of my post that I think need clarification:

These are the basic building blocks of music. Harmony...Rhythm...melody...timbre.

I could probably be more specific.  Pitch and key are the basic building-blocks of harmony, melody, and vocalization (counterpoint), and these together with rhythm and phrasing form the core of music theory.  Peripherally there is timbre, tempo, instrumentation, form, and a lot of other things.

Western rhythm has mostly focused on 3-beat (waltz) and 4-beat patterns. All classical music up to 1900 is one or the other.

All classical music up to 1900 is in 2, 3, 4, 6, or 8.  My point is that classical composers constrained themselves to rhythmic duples and triples.  Six can be interpreted as either, and the interpretation can be inferred from the key signaure, or from the tempo or phrasing.

Bach codified the Western harmonic system in the 1700's

Bach didn't invent the harmonic system, but his work is regarded today as some of the clearest, most unambiguous expressions of music theory.

Brief History of Western Music

This section is pretty brief, keep that in mind.  A more explicit differentiation between classical eras requires discussing the evolution of form: minuet, sonata, symphony, etc.

Rock

Probably just as important as the instrumentation is the influence that african styles had on this otherwise white form of music.  In fact, one of the most dominant themes of the 20th century is black artistry: jazz, blues, funk, rap, and turntablism (scratch mixing) to name a few examples.

Philip Glass, Terry Riley, and Steve Reich pioneered minimalism in the 60's-80's, with techno being their ultimate legacy.

By legacy, I mean that techno is the popularization of minimalist ideas: short repetition and layered technique.

[ Parent ]

2,3,4,6 or 8 eh? (none / 0) (#103)
by lb008d on Mon Jul 01, 2002 at 05:33:23 PM EST

All classical music up to 1900 is in 2, 3, 4, 6, or 8.

Go listen to the second movement of Tchaikovsky's Sixth Symphony or to the "Promenade" theme in Mussorgsky's Pictures at an Exhibition and re-phrase that statement.

You also forgot 12 and 16.

[ Parent ]

the masses create music (1.00 / 1) (#82)
by turmeric on Thu May 02, 2002 at 08:13:00 PM EST

the theoreticians and academics merely describe it. the classical geniuses like beethoven, chopin, and grieg, merely tune into the music of the common people, sheperds, mazurkas, dances, waltzes, and put it into symphonies. music is humanity, you do not need theory to create it, you merely need emotion.

Music Theory for the Masses | 103 comments (93 topical, 10 editorial, 0 hidden)
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