1ed15/14
1 equal division of 15/14 (1ed15/14), also known as ambitonal sequence of 15/14 (AS15/14) or 15/14 equal-step tuning, is an equal multiplication of 15/14-wide semitone. The step size is about 119.4428 cents, corresponding to 10.0466edo.
Using a JI 15/14-wide semitone as the basis of an equal temperament tuning results in an interesting non-octave tuning. As every interval is a multiple of 15/14, the resultant tuning would be a subset of 7-limit just intonation. This can be also viewed as generating a subset of marvel, decoid, or septidiasemi temperament.
Lookalikes: 16edt, 26ed6, 10edo
Intervals as 7-limit ratios
| Ratio | Cents | |
|---|---|---|
| (15/14)0 | 1/1 | 0.0000 |
| (15/14)1 | 15/14 | 119.4428 |
| (15/14)2 | 225/196 | 238.8856 |
| (15/14)3 | 3375/2744 | 358.3284 |
| (15/14)4 | 50625/38416 | 477.7712 |
| (15/14)5 | 759375/537824 | 597.2140 |
| (15/14)6 | 11390625/7529536 | 716.6568 |
| (15/14)7 | 170859375/105413504 | 836.0997 |
| (15/14)8 | 2562890625/1475789056 | 955.5425 |
| (15/14)9 | 38443359375/20661046784 | 1074.9853 |
| (15/14)10 | 576650390625/289254654976 | 1194.4281 |
| (15/14)11 | 8649755859375/4049565169664 | 1313.8709 |
Related temperament
15/14 equal temperament is related to various regular temperaments including marvel, septidiasemi, subsedia, and linus temperaments.
Marvel (22&31&41)
Marvel temperament equates 16/15, 77/72, and 15/14 as a diatonic semitone, tempering out 225/224 and 385/384 in the 11-limit. Rank-two temperaments which temper out 225/224 and 385/384 include miracle, orwell, magic, meanpop, wizard, slender, garibaldi, catakleismic, septimin, and pajarous.
Septidiasemi (10&171)
15/14 equal temperament is closely related to the septidiasemi temperament, which tempers out 2401/2400 and 2152828125/2147483648 in the 7-limit. This temperament is supported by 10, 161, 171, 181, 332, 352, and 503 EDOs.
Subsedia (10&111)
The subsedia temperament is a temperament for the 17-limit, which tempers out 256/255, 352/351, 442/441, 540/539, and 715/714. The generator is ~15/14 = 118.97¢, 16 of them equals ~3/1, and 45 of them equals ~22/1.
Linus temperaments
- Main article: 10th-octave temperaments#Linus (rank-3)
Tempering out the linus comma, 578509309952 / 576650390625 = [11 -10 -10 10⟩ leads a number of regular temperaments including decoid, deca, decal, decimetra, decistearn, and decavish. These have a period of 1/10 octave. Linus rank three temperament can be described as the 130&190&270 temperament, which tempers out 9801/9800 and 391314/390625 in the 11-limit; 1001/1000, 4225/4224, and 4459/4455 in the 13-limit. The 1/10-octave period interval represents 15/14, three of which represents 16/13, and five of which represents both 99/70 and 140/99.