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ubertuber · 01-19-2005, 07:10 AM

Dbass, my bad - I misunderstood which direction you were coming from. (By the way it was Pythagoras, and there is a point in there that I'll come back to).

I personally agree with your point that infants whose ears have not been sensitized to diatonic harmony probably don't dinstinguish A as a discrete note from other pitches that are between our pitch system. I believe that perfect pitch is simply the ability to produce and recognize pitches without reference. Even people with perfect pitch can train their ears, because what is important is not what you hear, but what you do with it.

Back to Pythagoras and tempering scales, which you mentioned (apologies if I'm either being too pedantic and repeating stuff you know or boring non-musicians to tears, but I promise to come back to a point). Pythagoras formulated the divisions of an octave by reducing the length of a vibrating string by proportions. From this division we get notes, that when sounded together, produce perfect harmony. However, they only work in relation to one another within the original key - meaning that the pitch g in the key of c is substantially different from the pitch g in the key of f - so much so that you can't really use a fixed-pitch instrument (piano, xylophone, harp, organ, etc.) in more than about 3 keys effectively if it is tuned by Pythagoras' proportional method. Not only that, but if you take the value of half and whole steps formulated by Pythagoras in the key of C and use them to construct a scale from D to D, your first and last D won't be an octave apart!

Fast forward to Bach's time (1685-1750) and this has become a problem. The solution was to temper the octave (split it equally). This is the system by which pianos and other fixed-pitch instruments are tuned today. Every key is now the same amount out of tune. This renders the instrument playable, but simply not in tune. Chords don't ring like they should, leading tones don't lean as hard as they should... But we've become used to it. Variable pitch instruments, like brass and wind instruments, will often play perfect harmony in orchestral music. This means lowering major thirds in chords, raising minor thirds, lowering minor 7ths, etc. The sound is amazing. My experience is that string players don't bother with this so much - perhaps it is because the tradition is to play with such wide vibrato - I don't know. If a string quartet or section in an orchestra was to play without vibrato, they'd quickly realize how out of tune they are. I've seen it happen!

At any rate, some of the people who say that perfect pitch is tied to the diatonic scale will complain about having to listen to out-of-tune music, referring to Rennaisance music with a higher pitch or organs which are often tuned low or high. These are the same people who use an out-of-tune piano as their standard of reference, which is the only way you could have the idea that 440 is the only place for an a to be in tune. An A in an F major chord has to be much lower than 440 to be in tune, while an A in a f# minor chord has to be higher than 400! Hell, the orchestras and pianos here are all tuning at A441 and 442, intentionally - to produce a brighter (sharper) sound. My point is that pitch is where we say it is. We can have great reasons for picking a particular place for our notes, but those places can and should be variable.

Now, you can make an argument for some aspects of diatonic melody and harmony being inherent in physics, which is the overtone series. This term refers to the phenomenon in which a pitch on a resonating string sounds at the note you hear easily, but it also produces pitch information for other notes above it. Invariably, these notes come in this order (related to the originally sounding pitch):

octave, fifth, octave, major third, perfect fifth, minor seventh, octave, major second, etc.

It is important to note that these other pitches are contained within the original pitch, not in sympathetic resonance with other strings or nearby objects (though overtones will certainly generate sympathetic vibrations in other things, and teachers use this effect to demonstrate the overtone series on a piano). You can see this if you ever get to play with a chromatic strobe tuner with multiple dials (one for each note, and costing thousands of dollars). They will all respond to one pitch, indicating the relative intonation of the overtones in that pitch. In fact, it is the relative strength of overtones in a pitch (and speed with which they stack up) that define timbre for the ear, making the difference between a trumpet, oboe, french horn, and voice all playing the same pitch. The ear is very sensitive - much more so than the brain. Anyway, people have used this presence of the overtone series to argue that functional harmony and our 12 note scale are not just conventions, but expressions of physics. However, even in this system of thought it doesn't matter whether you start your A on 440, 442 or even 357. It is the relative placement of intervals that matters.

01-19-2005, 07:10 AM	#43 (permalink)
ubertuber spudly Location: Ellay	Dbass, my bad - I misunderstood which direction you were coming from. (By the way it was Pythagoras, and there is a point in there that I'll come back to). I personally agree with your point that infants whose ears have not been sensitized to diatonic harmony probably don't dinstinguish A as a discrete note from other pitches that are between our pitch system. I believe that perfect pitch is simply the ability to produce and recognize pitches without reference. Even people with perfect pitch can train their ears, because what is important is not what you hear, but what you do with it. Back to Pythagoras and tempering scales, which you mentioned (apologies if I'm either being too pedantic and repeating stuff you know or boring non-musicians to tears, but I promise to come back to a point). Pythagoras formulated the divisions of an octave by reducing the length of a vibrating string by proportions. From this division we get notes, that when sounded together, produce perfect harmony. However, they only work in relation to one another within the original key - meaning that the pitch g in the key of c is substantially different from the pitch g in the key of f - so much so that you can't really use a fixed-pitch instrument (piano, xylophone, harp, organ, etc.) in more than about 3 keys effectively if it is tuned by Pythagoras' proportional method. Not only that, but if you take the value of half and whole steps formulated by Pythagoras in the key of C and use them to construct a scale from D to D, your first and last D won't be an octave apart! Fast forward to Bach's time (1685-1750) and this has become a problem. The solution was to temper the octave (split it equally). This is the system by which pianos and other fixed-pitch instruments are tuned today. Every key is now the same amount out of tune. This renders the instrument playable, but simply not in tune. Chords don't ring like they should, leading tones don't lean as hard as they should... But we've become used to it. Variable pitch instruments, like brass and wind instruments, will often play perfect harmony in orchestral music. This means lowering major thirds in chords, raising minor thirds, lowering minor 7ths, etc. The sound is amazing. My experience is that string players don't bother with this so much - perhaps it is because the tradition is to play with such wide vibrato - I don't know. If a string quartet or section in an orchestra was to play without vibrato, they'd quickly realize how out of tune they are. I've seen it happen! At any rate, some of the people who say that perfect pitch is tied to the diatonic scale will complain about having to listen to out-of-tune music, referring to Rennaisance music with a higher pitch or organs which are often tuned low or high. These are the same people who use an out-of-tune piano as their standard of reference, which is the only way you could have the idea that 440 is the only place for an a to be in tune. An A in an F major chord has to be much lower than 440 to be in tune, while an A in a f# minor chord has to be higher than 400! Hell, the orchestras and pianos here are all tuning at A441 and 442, intentionally - to produce a brighter (sharper) sound. My point is that pitch is where we say it is. We can have great reasons for picking a particular place for our notes, but those places can and should be variable. Now, you can make an argument for some aspects of diatonic melody and harmony being inherent in physics, which is the overtone series. This term refers to the phenomenon in which a pitch on a resonating string sounds at the note you hear easily, but it also produces pitch information for other notes above it. Invariably, these notes come in this order (related to the originally sounding pitch): octave, fifth, octave, major third, perfect fifth, minor seventh, octave, major second, etc. It is important to note that these other pitches are contained within the original pitch, not in sympathetic resonance with other strings or nearby objects (though overtones will certainly generate sympathetic vibrations in other things, and teachers use this effect to demonstrate the overtone series on a piano). You can see this if you ever get to play with a chromatic strobe tuner with multiple dials (one for each note, and costing thousands of dollars). They will all respond to one pitch, indicating the relative intonation of the overtones in that pitch. In fact, it is the relative strength of overtones in a pitch (and speed with which they stack up) that define timbre for the ear, making the difference between a trumpet, oboe, french horn, and voice all playing the same pitch. The ear is very sensitive - much more so than the brain. Anyway, people have used this presence of the overtone series to argue that functional harmony and our 12 note scale are not just conventions, but expressions of physics. However, even in this system of thought it doesn't matter whether you start your A on 440, 442 or even 357. It is the relative placement of intervals that matters. __________________ Cogito ergo spud -- I think, therefore I yam Last edited by ubertuber; 01-19-2005 at 07:18 AM..