1ed9/8: Difference between revisions
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'''9/8 equal temperament''' | {{todo|merge articles|inline=1|text=Merge into [[9/8]]?}} | ||
'''9/8 equal temperament''' or '''1ed9/8''' is the use of a just [[9/8]] whole tone as the basis of an equal temperament tuning. It 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|3-limit]] [[Just_intonation|Just Intonation]]. This can be also viewed as generating a subset of [[baldy]] temperament. | |||
==Intervals as 3-limit ratios== | ==Intervals as 3-limit ratios== | ||
Latest revision as of 14:12, 1 August 2025
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Todo: merge articles Merge into 9/8? |
9/8 equal temperament or 1ed9/8 is the use of a just 9/8 whole tone as the basis of an equal temperament tuning. It 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.
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 |
Scala file
! 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