Overtone Series
The overtone series is a group of pure tones that can be generated when something vibrates. Things can vibrate in different modes, and each mode has a pure tone associated with it. In general, a musical instrument creates vibrations in more than one mode simultaneously, so each note is really made of several pure tones from the overtone series. (continued)
The lowest pure tone is called the fundamental frequency (ff), and the overtone frequencies are multiples of the fundamental (ff, 2ff, 3ff, 4ff, 5ff, etc.) 2ff is an octave above ff, 3ff is a fifth above 2ff, 4ff is an octave above 2ff. 5ff is a major third above 4ff.
As to how the major scale is derived from the overtone series, it is based on the interval of the fifth. If you stack fifths until you have 7 notes, then transpose them into the same octave, you have a major scale. However, the equal tempered scale in use today is derived somewhat differently based on the twelfth root of 2.
By the way, the pentatonic scale is just 5 stacked 5ths. The Lydian-dominant scale can be derived out of the higher overtones 8ff, 9ff, 10ff, 11ff, 12ff, 13ff, 14ff.
Posted by brad under Music Theory |
I have some more in-depth information about the reasoning behind the equal-tempered scale at:
http://mclaury.blogspot.com/2006/06/why-are-there-twelve-notes-per-octave.html
In that article I take the ratios for the perfect fifth and fourth and major and minor third as given, but they are of course derived from the overtone series. I was planning on writing up something like that, but if you’re gonna cover it, just let me know and I’ll just throw up a link to you instead
Comment by Daniel McLaury — June 27, 2006 @ 12:08 pm
Daniel,
I enjoyed your article about the 12-note scale. I didn’t have plans to write about the ratios, but it is a good idea, so let me know if you do.
Brad
Comment by brad — June 27, 2006 @ 12:35 pm