9/8 equal-step tuning
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9/8 equal temperament
Using a Just 9/8 whole tone as the basis of an equal temperament tuning results in an interesting non-octave tuning. As every interval is a multiple of 9/8, the resultant tuning would be a subset of 3-limit Just Intonation. This can be also viewed as generating a subset of baldy temperament.
Below is the scala file I used to generate A Bowl of Tibetan Bells by Chris Vaisvil (composition details)
and A Sonnet for Albert Einstein by Chris Vaisvil (details) ! E:\Cakewalk\scales\9_divided_by_8.scl !
9/8 in 12
12 !
203.91
407.82
611.73
815.64
1019.55
1223.46
1427.37
1631.28
1835.19
2039.1
2243.01
2446.92
Intervals as 3-limit ratios
| Ratio | Cents | |
|---|---|---|
| (9/8)0 | 1/1 | 0.00 |
| (9/8)1 | 9/8 | 203.91 |
| (9/8)2 | 81/64 | 407.82 |
| (9/8)3 | 729/512 | 611.73 |
| (9/8)4 | 6561/4096 | 815.64 |
| (9/8)5 | 59049/32768 | 1019.55 |
| (9/8)6 | 531441/262144 | 1223.46 |
| (9/8)7 | 4782969/2097152 | 1427.37 |
| (9/8)8 | 43046721/16777216 | 1631.28 |
| (9/8)9 | 387420489/134217728 | 1835.19 |
| (9/8)10 | 3486784401/1073741824 | 2039.10 |
| (9/8)11 | 31381059609/8589934592 | 2243.01 |
| (9/8)12 | 282429536481/68719476736 | 2446.92 |