8/7ths equal temperament

From Xenharmonic Wiki
Jump to: navigation, search

8/7 equal temperament

Using a Just 8/7 whole tone as the basis of an equal temperament tuning results in an interesting non-octave tuning. As every interval is a multiple of 8/7, the resultant tuning would be a subset of 7-limit Just intonation. This can be also viewed as generating a subset of gamelismic temperaments.

Intervals as 7-limit ratios

Ratio Cents
(8/7)0 1/1 0.0000
(8/7)1 8/7 231.1741
(8/7)2 64/49 462.3482
(8/7)3 512/343 693.5223
(8/7)4 4096/2401 924.6964
(8/7)5 32768/16807 1155.8705
(8/7)6 262144/117649 1387.0446
(8/7)7 2097152/823543 1618.2187
(8/7)8 16777216/5764801 1849.3927
(8/7)9 134217728/40353607 2080.5668
(8/7)10 1073741824/282475249 2311.7409
(8/7)11 8589934592/1977326743 2542.9150