Homothetic just intonation: Difference between revisions
Jump to navigation
Jump to search
cent values updated |
ratio names |
||
| Line 1: | Line 1: | ||
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. | 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 prime limit JI pitch collection. | ||
31-tone homothetic just scale generated by 11-limit JI: | Octave-equivalent 31-tone homothetic just scale generated by 11-limit JI: | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|- | |- | ||
| Line 14: | Line 14: | ||
|546/517 | |546/517 | ||
|94.484004 | |94.484004 | ||
| | |large homothetic semitone | ||
|- | |- | ||
|241/220 | |241/220 | ||
| Line 26: | Line 26: | ||
|2213/1980 | |2213/1980 | ||
|192.603625 | |192.603625 | ||
| | |quasi-meantone | ||
|- | |- | ||
|1981/1748 | |1981/1748 | ||
| Line 34: | Line 34: | ||
|97/84 | |97/84 | ||
|249.114503 | |249.114503 | ||
|semifourth | |homothetic semifourth | ||
|- | |- | ||
|569/480 | |569/480 | ||
|294.473096 | |294.473096 | ||
| | |small homothetic supraminor third, | ||
quasi-Pythagorean minor third | |||
|- | |- | ||
|1201/990 | |1201/990 | ||
|334.482865 | |334.482865 | ||
| | |large homothetic supraminor third | ||
|- | |- | ||
|977/792 | |977/792 | ||
| Line 58: | Line 60: | ||
|573/437 | |573/437 | ||
|469.082231 | |469.082231 | ||
| | |homothetic sub-fourth | ||
|- | |- | ||
|511/376 | |511/376 | ||
|531.108755 | |531.108755 | ||
| | |homothetic acute fourth | ||
|- | |- | ||
|1107/800 | |1107/800 | ||
|562.299980 | |562.299980 | ||
| | |homothetic augmented fourth | ||
|- | |- | ||
|99/70 | |99/70 | ||
|600.088324 | |600.088324 | ||
| | |quasi-tempered tritone | ||
|- | |- | ||
|159/110 | |159/110 | ||
|637.827890 | |637.827890 | ||
| | |homothetic diminished fifth | ||
|- | |- | ||
|761/517 | |761/517 | ||
|669.278608 | |669.278608 | ||
| | |homothetic quasi-catafifth | ||
|- | |- | ||
|6001/3933 | |6001/3933 | ||
|731.487292 | |731.487292 | ||
| | |homothetic super-fifth | ||
|- | |- | ||
|1973/1260 | |1973/1260 | ||
| Line 102: | Line 104: | ||
|[[27/16]] | |[[27/16]] | ||
|905.865003 | |905.865003 | ||
| | |Pythagorean major sixth | ||
|- | |- | ||
|97/56 | |97/56 | ||
|951.069504 | |951.069504 | ||
|semitwelve | |homothetic semitwelve | ||
|- | |- | ||
|3085/1748 | |3085/1748 | ||
| Line 114: | Line 116: | ||
|4429/2475 | |4429/2475 | ||
|1007.462966 | |1007.462966 | ||
| | |quasi-meantone minor seventh | ||
|- | |- | ||
|2191/1210 | |2191/1210 | ||
|1027.898924 | |1027.898924 | ||
| | |homothetic minor seventh | ||
|- | |- | ||
|241/132 | |241/132 | ||
|1042.194260 | |1042.194260 | ||
| | |homothetic neutral seventh | ||
|- | |- | ||
|535/282 | |535/282 | ||
|1108.612475 | |1108.612475 | ||
| | |homothetic major seventh | ||
|- | |- | ||
|[[2/1]] | |[[2/1]] | ||
Revision as of 13:15, 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 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 |
Links
- Homothetic Just Intonation by Sui-hin Mak