Homothetic just intonation: Difference between revisions
Jump to navigation
Jump to search
mNo edit summary |
cent values updated |
||
| Line 1: | Line 1: | ||
Homothetic just intonation is | Homothetic just intonation is a kind of extended [[just intonation]] conceived by Sui-hin Mak. The term 'homothetic' refers to the [[wikipedia:Homothetic_center#Computing_homothetic_centers|homothetic formula]]. It aims at producing the pitches in between notes of an existing JI pitch collection. | ||
31-tone homothetic just scale generated by 11-limit JI: | 31-tone homothetic just scale generated by 11-limit JI: | ||
| Line 41: | Line 41: | ||
|- | |- | ||
|1201/990 | |1201/990 | ||
| | |334.482865 | ||
| | | | ||
|- | |- | ||
|977/792 | |977/792 | ||
| | |363.429758 | ||
| | | | ||
|- | |- | ||
|1223/968 | |1223/968 | ||
| | |404.814542 | ||
| | | | ||
|- | |- | ||
|281/220 | |281/220 | ||
| | |423.679928 | ||
| | | | ||
|- | |- | ||
|573/437 | |573/437 | ||
| | |469.082231 | ||
| | | | ||
|- | |- | ||
|511/376 | |511/376 | ||
| | |531.108755 | ||
| | | | ||
|- | |- | ||
|1107/800 | |1107/800 | ||
| | |562.299980 | ||
| | | | ||
|- | |- | ||
|99/70 | |99/70 | ||
| | |600.088324 | ||
| | | | ||
|- | |- | ||
|159/110 | |159/110 | ||
| | |637.827890 | ||
| | | | ||
|- | |- | ||
|761/517 | |761/517 | ||
| | |669.278608 | ||
| | | | ||
|- | |- | ||
|6001/3933 | |6001/3933 | ||
| | |731.487292 | ||
| | | | ||
|- | |- | ||
|1973/1260 | |1973/1260 | ||
| | |776.360667 | ||
| | | | ||
|- | |- | ||
|1219/770 | |1219/770 | ||
| | |795.321330 | ||
| | | | ||
|- | |- | ||
|981/605 | |981/605 | ||
| | |836.781593 | ||
| | | | ||
|- | |- | ||
|399/242 | |399/242 | ||
| | |865.658039 | ||
| | | | ||
|- | |- | ||
|[[27/16]] | |[[27/16]] | ||
| | |905.865003 | ||
| | | | ||
|- | |- | ||
|97/56 | |97/56 | ||
| | |951.069504 | ||
|semitwelve | |semitwelve | ||
|- | |- | ||
|3085/1748 | |3085/1748 | ||
| | |983.478365 | ||
| | | | ||
|- | |- | ||
|4429/2475 | |4429/2475 | ||
| | |1007.462966 | ||
| | | | ||
|- | |- | ||
|2191/1210 | |2191/1210 | ||
| | |1027.898924 | ||
| | | | ||
|- | |- | ||
|241/132 | |241/132 | ||
| | |1042.194260 | ||
| | | | ||
|- | |- | ||
|535/282 | |535/282 | ||
| | |1108.612475 | ||
| | | | ||
|- | |- | ||
Revision as of 12:42, 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. It aims at producing the pitches in between notes of an existing JI pitch collection.
31-tone homothetic just scale generated by 11-limit JI:
| frequency ratio | cents value | names |
|---|---|---|
| 1/1 | 0 | unison |
| 546/517 | 94.484004 | |
| 241/220 | 156.835547 | |
| 243/220 | 172.143348 | |
| 2213/1980 | 192.603625 | |
| 1981/1748 | 216.628435 | |
| 97/84 | 249.114503 | semifourth |
| 569/480 | 294.473096 | |
| 1201/990 | 334.482865 | |
| 977/792 | 363.429758 | |
| 1223/968 | 404.814542 | |
| 281/220 | 423.679928 | |
| 573/437 | 469.082231 | |
| 511/376 | 531.108755 | |
| 1107/800 | 562.299980 | |
| 99/70 | 600.088324 | |
| 159/110 | 637.827890 | |
| 761/517 | 669.278608 | |
| 6001/3933 | 731.487292 | |
| 1973/1260 | 776.360667 | |
| 1219/770 | 795.321330 | |
| 981/605 | 836.781593 | |
| 399/242 | 865.658039 | |
| 27/16 | 905.865003 | |
| 97/56 | 951.069504 | semitwelve |
| 3085/1748 | 983.478365 | |
| 4429/2475 | 1007.462966 | |
| 2191/1210 | 1027.898924 | |
| 241/132 | 1042.194260 | |
| 535/282 | 1108.612475 | |
| 2/1 | 1200 | octave |
Links
- Homothetic Just Intonation by Sui-hin Mak