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Physics, Astronomy & Cosmology / Re: What are half notes in music?
« on: 18/05/2014 06:35:30 »
First of all, thanks to everyone who replied, your inputs have been very helpful. Second, I guess the question was really about half tones.
I have been doing some research, and the tone/half-tone oddity does indeed go back to the ancient greeks and the perfect fifth. Evidently the greeks liked fractions and disliked irrational numbers. The frequency of oscillation of the fifth is 1.5 times the oscillation of the root. All the notes in the greek system are obtained by going up and down from the root by ratios of 1.5.
The only way I can explain this is by example. If we start at C (261.6Hz) and go up one fifth by multiplying by 1.5 we get G (392.4Hz). If we then go up from G by another fifth we get D (588.6Hz) although this is 2x the D in in fundamental range (which would be 294.3) . Continue up and down and the result are the familiar C-D-E-F-G-A-B notes with half steps at the familiar places. My terminology is likely off, but I hope the point is clear.
Using the 1.5 ratios the note frequencies came out slightly different from the logarithmic ratios we use today, although very close. Another oddity of the greek system is the sharps and flats. In today's system the shrp of one note falls exactly on the flat of the next note. However using the 1.5 ratio this was not the case. Perhaps this is why we have flats and sharps when we really only need one or the other.
The one thing I haven't figured out is why the odd half steps "sound right". Is it learned? Is it natural? Is it that we like a little bit of dissonance?
Anyway, thanks for all your help!
I have been doing some research, and the tone/half-tone oddity does indeed go back to the ancient greeks and the perfect fifth. Evidently the greeks liked fractions and disliked irrational numbers. The frequency of oscillation of the fifth is 1.5 times the oscillation of the root. All the notes in the greek system are obtained by going up and down from the root by ratios of 1.5.
The only way I can explain this is by example. If we start at C (261.6Hz) and go up one fifth by multiplying by 1.5 we get G (392.4Hz). If we then go up from G by another fifth we get D (588.6Hz) although this is 2x the D in in fundamental range (which would be 294.3) . Continue up and down and the result are the familiar C-D-E-F-G-A-B notes with half steps at the familiar places. My terminology is likely off, but I hope the point is clear.
Using the 1.5 ratios the note frequencies came out slightly different from the logarithmic ratios we use today, although very close. Another oddity of the greek system is the sharps and flats. In today's system the shrp of one note falls exactly on the flat of the next note. However using the 1.5 ratio this was not the case. Perhaps this is why we have flats and sharps when we really only need one or the other.
The one thing I haven't figured out is why the odd half steps "sound right". Is it learned? Is it natural? Is it that we like a little bit of dissonance?
Anyway, thanks for all your help!