  # yamaha-unit / yu

###### [Joe Monzo]

A musical interval measurement used by Yamaha on several of its popular electronic musical instruments, including its TG and SY series.

A yamaha-unit or yu is the logarithmic division of the 2:1 ratio octave into 210 = 1024 equal parts. It is calculated as the 1024th root of 2 (1024√2, or 2(1/1024) ), with a ratio of approximately 1:. It is an irrational number. The formula for calculating the yamaha-unit value of any ratio r is: yamaha-units = log10r * [1024 / log102] or yamaha-units = log2r * 1024.

A yamaha-unit is:

• exactly 0.29296875 (= 75/256 ~= 3/10) of a savart
• exactly 0.59765625 (= 153/256 ~= 3/5) of a 612-edo schisma
• exactly 0.75 (= 3/4) of a 6mu
• exactly 0.9765625 (= 125/128) of a millioctave
• exactly 8.3388671875 (= 8 347/1024) tinas
• exactly 48 12mus
• exactly 192 14mus

. . . . . . . . .

### yamaha-units calculator

Ratio may be entered as fraction or floating-point decimal number.
(value must be greater than 1)

For EDOs (equal-temperaments), type: "a/b" (without quotes)
where "a" = EDO degree and "b" = EDO cardinality.
(value must be less than 1)

Enter ratio: = yamaha-units

. . . . . . . . .

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