Homothetic just intonation: Difference between revisions
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* [https://medium.com/@maksuihin/homothetic-just-intonation-b468777f724b Homothetic Just Intonation] by Sui-hin Mak | * [https://medium.com/@maksuihin/homothetic-just-intonation-b468777f724b Homothetic Just Intonation] by Sui-hin Mak | ||
Revision as of 14:11, 14 July 2019
Homothetic just intonation is a kind of extended just intonation conceived by Sui-hin Mak. The term 'homothetic' refers to the homothetic formula x₀ = (r₂x₁ + r₁x₂) / (r₁ + r₂). The tuning aims at producing the pitches in between notes of an existing prime limit JI pitch collection.
Octave-equivalent 31-tone homothetic just scale generated by 11-limit JI:
| frequency
ratio |
cents
value |
names |
|---|---|---|
| 1/1 | 0 | unison |
| 546/517 | 94.484004 | large homothetic semitone |
| 241/220 | 156.835547 | |
| 243/220 | 172.143348 | |
| 2213/1980 | 192.603625 | quasi-meantone |
| 1981/1748 | 216.628435 | |
| 97/84 | 249.114503 | homothetic semifourth |
| 569/480 | 294.473096 | small homothetic supraminor third, quasi-Pythagorean minor third |
| 1201/990 | 334.482865 | large homothetic supraminor third |
| 977/792 | 363.429758 | |
| 1223/968 | 404.814542 | |
| 281/220 | 423.679928 | |
| 573/437 | 469.082231 | homothetic sub-fourth |
| 511/376 | 531.108755 | homothetic acute fourth |
| 1107/800 | 562.299980 | homothetic augmented fourth |
| 99/70 | 600.088324 | quasi-tempered tritone |
| 159/110 | 637.827890 | homothetic diminished fifth |
| 761/517 | 669.278608 | homothetic quasi-catafifth |
| 6001/3933 | 731.487292 | homothetic super-fifth |
| 1973/1260 | 776.360667 | |
| 1219/770 | 795.321330 | |
| 981/605 | 836.781593 | |
| 399/242 | 865.658039 | |
| 27/16 | 905.865003 | Pythagorean major sixth |
| 97/56 | 951.069504 | homothetic semitwelve |
| 3085/1748 | 983.478365 | |
| 4429/2475 | 1007.462966 | quasi-meantone minor seventh |
| 2191/1210 | 1027.898924 | homothetic minor seventh |
| 241/132 | 1042.194260 | homothetic neutral seventh |
| 535/282 | 1108.612475 | homothetic major seventh |
| 2/1 | 1200 | octave, diapason |
Links
- Homothetic Just Intonation by Sui-hin Mak