| For the Interdisciplinary Study of Cycles http://www.cyclesresearchinstitute.org |
Vladimir Ladma's Research
|
| For the Interdisciplinary Study of Cycles http://www.cyclesresearchinstitute.org |
Vladimir Ladma's Research
Let us assume various n-tone groupings (f1,...,fn) within octave
(frequency ratio fn/f1 = 2/1).
E.g. u1=(1/1, 3/2, 2/1) a u2=(1/1, 4/3, 2/1).
Rates between tones are p1=(3/2, 4/3) a p2=(4/3, 3/2).
Every rational number (fraction) has unique partition
as multiple of primes with integer exponents.
Let Pmax is the highest prime and Emax the highest exponent
(common for all primes).
Examples:
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Classes of tuning
Let each two tones in ratio 2/1 are equivalent (octave identity).
We say, two groupings are equivalent (the same class), if they
have the same rates between particular tones (except rotation).
Because p2 is rotation of p1, u1 and u2 are equivalent.
Source codes (Objective C)
Music theory