Decimal

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Decimal is a temperament in both the dicot and semaphore families of temperaments. It is also hemipyth, meaning that it has approximations of √2, √3, and √(3/2). It is special in that it is also an exotemperament.

Interval chain

In the following table, odd harmonics and subharmonics 1–7 are labeled in bold.

# Period 0 Period 1
Approx. Ratios Approx. Ratios
-2 3/2 21/20, 15/14
-1 12/7, 7/4 6/5, 5/4
0 1/1 7/5, 10/7
1 8/7, 7/6 8/5, 5/3
2 4/3 28/15, 40/21

One can see that the 10-note mos of the decimal temperament contains the 7-odd-limit tonality diamond.