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Monzos and vals, the vectors regular temperament theory is written in. Monzos and vals, the two vectors regular temperament theory is written in.
A monzo is an interval written as the exponents of the primes that
multiply out to its ratio, so the syntonic comma 81/80 is
2^-4 * 3^4 * 5^-1 and reads [-4 4 -1⟩. A val is the other side of the
same coin: a map from those primes to how many steps of some tuning each
one is worth, so twelve-tone equal temperament is ⟨12 19 28] — twelve
steps to the octave, nineteen to the twelfth, twenty-eight to the
seventeenth. Pairing the two says how wide an interval comes out in a
tuning, and a val that maps a comma to nothing is a tuning that tempers it
out: ⟨12 19 28] sends [-4 4 -1⟩ to zero, which is why four fifths and
a major third are the same note on a piano.
Structs§
- Monzo
- An interval written as the exponents of the primes making up its ratio.
- Val
- How many steps of a tuning each prime is worth.