Knatz.com / Teaching / Scholarship / Glossary /
Definitions, Ironies, Semiotic Whirligigs, Wisecracks …
A scale is a counting system … A rhythm is a counting system …
|Music is a coherent set of discrepancies among counting systems.|
Discrepancy is key. Discrepancy as in macroinformation! Note that scales are odd numbered: 7! 5! Note that the 7-base scale becomes even if you count All of the accidentals: 12! (A mystic number, the base for Babylonian math.) Note that once you make an octave the number becomes even: and THEREFORE there is no middle! The V is oddly between the two tonics. The V is up 5 from the lower tonic, but down IV! from the higher tonic.
Odd, odd, odd. Asymmetry within the symmetry.
And as you get into the other scales, the weird minors, the ascending scale may be additionally different from the descending scale!
These few differences spawn infinities of additional differences.