 The Clarinet BBoard
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Author: Ken Mills
Date: 2006-02-24 22:48
Dear People; How did the Greeks get the 12 different notes? That is the question (for us at any rate) and they created the language. And these intervals (notes) are universal, after all when you pluck a a guitar string it vibrates in halves, thirds, fourths, etc, and these harmonics can be slightly heard when one note is played. The frets on the guitar neck get a little closer and closer as you go down just like the series of quotients above. In math we call this the haramonic series. The Greeks blew on the trumpet (the valves did not get invented until 1812) and besides the octave one gets that fourth (or fifth). The interval of the fourth sounds the first two notes of Here Comes the Bride. One fourth on top of the last note played went 12 notes until you got back to where you started (with the octave adjustment of course). How does a trumpet or bugle overblow in fourths? So do squeeks on the clarinet. Oh by the way, the perfect fourth is not in a single note's harmonics while we get mostly the octave of course and the sharp four, etc. You Should Hear Me, Ken
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Author: BobD
Date: 2006-02-25 11:09
What's that flute like old instrument that they still play in the Andes...pan pipes ? Could that be the answer?
Bob Draznik
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Author: EEBaum
Date: 2006-02-26 01:56
The perfect 4th is easily produced when a perfect 5th overblows to the next octave. A perfect 4th in relation to the fundamental, true, you won't get. A perfect 4th in relation to any note that's one of the harmonics that sounds a fifth, sure.
Frets on the guitar are tuned to notes on the equal-tempered scale, ((12th root of 2) * previous) not the harmonic series (1/(fundamental*n)). The first fret would be halfway down the string, and they would get stupidly close together toward the bridge, if it was based on the harmonic series.
Fourths/fifths played entirely one atop the other leave a little bit of a remainder when you go all the way around to what you'd expect to be the same pitch some-odd octaves up. There's a name for that ratio, which escapes me at the moment.
As for 12 notes, consult with the harmonic series for the original inspiration. The fourth octave on a C gives C E G Bb, the 5th gives C D E F G A Bb B C (with varying degrees of intonation). By choosing the harmonic frequencies of certain pitches to be the important ones (e.g. 5th and 3rd, or 5th and 4th, or all notes derived from series of 5ths and leaving the pesky remainder), certain notes are hard-set to certain ratios, depending on your intonation system of choice. This can leave you with huge gaps between pitches. People notice that the space between D and E is about twice as big as between E and F, so they figure another note can just as well go inside. Based on 5ths, it leaves us about enough room for 12 notes, which was widely accepted.
For another possible explanation, see modes. Depending on where in the scale you start, you have different sets of large and small gaps between pitches. Stack them all on top of each other and they tend to correlate in about 12 quasi-equidistant spots.
I have a chart from one of my theory classes that illustrates it really well... it's harder to describe in words.
Equal temperament is merely a contrivance to allow for modulation that is kind on the ears without the introduction of hundreds of new keys to the piano.
(edit: fixed some math)
-Alex
www.mostlydifferent.com
Post Edited (2006-02-26 05:58)
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Author: Ken Mills
Date: 2006-02-27 22:37
Thank You EEBaum, If you pinch the guitar string half way down the neck then you will get the octave above the note when the string was open, only a third of the way down will get a lower note than half way was, and only a fourth of the way down will get guess what? a note that is a sharp fourth in the western scale that we use from the open string's note, I think. Then the math gets tougher. Let us leave the A string at 440 hertz and nature will take it from there for our mutual enjoyment. I can play the chromatic scale from middle C up one octave on the trumpet, so I know what the Greeks were talking about with the C to G to octave C (no values pressed) in that two note melody that I referenced. I think that the trumpet started it all. Ken PS, I can do squats with a barbell to help me play
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