10/9ths equal temperament

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10/9 equal temperament

Using a Just 10/9 whole tone as the basis of an equal temperament tuning results in an interesting non-octave tuning. As every interval is a multiple of 10/9, the resultant tuning would be a subset of 5-limit Just intonation. This can be also viewed as generating a subset of minortonic temperament.

Intervals as 5-limit ratios

Ratio Cents
(10/9)0 1/1 0.0000
(10/9)1 10/9 182.4037
(10/9)2 100/81 364.8074
(10/9)3 1000/729 547.2111
(10/9)4 10000/6561 729.6148
(10/9)5 100000/59049 912.0186
(10/9)6 1000000/531441 1094.4223
(10/9)7 10000000/4782969 1276.8260
(10/9)8 100000000/43046721 1459.2297
(10/9)9 1000000000/387420489 1641.6334
(10/9)10 10000000000/3486784401 1824.0371
(10/9)11 100000000000/31381059609 2006.4408
(10/9)12 1000000000000/282429536481 2188.8445
(10/9)13 10000000000000/2541865828329 2371.2483
(10/9)14 100000000000000/22876792454961 2553.6520