Maths vs. Music - Tuning and harmony

[Thumpalumpacus]

As an interesting side note into the study of vibration, the naturally arising mathematic order in music gives us the 8 note octave with 12 semitones.  
http://www.math.uwaterloo.ca/~mrubinst/tuning/12.html

An octave has twelve, not eight, agreed-upon notes. An octave has twelve chromatic notes, of which eight are diatonic, in Western European music, but can have as little as four or as many as all twelve agreed-upon notes, in Western nomenclature, depending on scale and idiom. A pentatonic octave has (you guessed it!) five notes. There are also things like hexatonics, gypsy scales, and so on. The Western major scale (non-musicians, think do-re-mi-fa-so-la-ti-do) of eight notes is only one of many, many scales. It just so happens that it's the one you're acculturated to hearing.

However, those aren't the only notes one can play. There are notes in between the notes, which is why the Indians invented the sitar (with its scalloped fretboard for bending to those notes) and why the Africans invented slides for stringed instruments. You could also look up the "blue notes" used in American blues, located between the m3 and M3, the b5 and the perfect 5, and between the submediant 6 and the leading tone.

They are notes too. They just don't have formalized names.

Go to 3:18 in this clip, listen for about twelve seconds, and name all the notes that he plays.





I guarantee you can't, because a good 50% (at least!) of them are well between the "Western notes". Ain't no names for them ... and there ain't no magic theory sprouting from your head explaining them, either.

There's no "mathematical order" to music. Octaves subdivide on resonances, no doubt -- but that doesn't mean that western tempered tuning, which is your obvious referent, is the only physical expression of music. Mathematics is a language we use in order to speak with each other, but the mathematics doesn't define the music.

The finger pointing at the moon is not the moon. Music theory does not prescribe music, it describes it ... as any musician would know.