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Homothetic just intonation: Difference between revisions

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{| class="wikitable sortable"
{| class="wikitable sortable"
|+Octave-equivalent 31-tone homothetic just scale generated by 11-limit JI
|+ style="font-size: 105%;" | Octave-equivalent 31-tone homothetic just scale generated by 11-limit JI
|-
|-
! frequency
! Frequency ratio
ratio
! Cents
! cents
! Names
value
! names
|-
|-
|[[1/1]]
| [[1/1]] || 0 || unison
|0
|unison
|-
|-
|546/517
| 546/517 || 94.484004 || Large homothetic semitone
|94.484004
|large homothetic semitone
|-
|-
|241/220
| 241/220 || 156.835547 ||  
|156.835547
|
|-
|-
|243/220
| 243/220 || 172.143348 ||  
|172.143348
|
|-
|-
|2213/1980
| 2213/1980 || 192.603625 || Quasi-meantone
|192.603625
|quasi-meantone
|-
|-
|1981/1748
| 1981/1748 || 216.628435 ||  
|216.628435
|
|-
|-
|97/84
| 97/84 || 249.114503 || Homothetic semifourth
|249.114503
|homothetic semifourth
|-
|-
|569/480
| 569/480 || 294.473096 || Small homothetic supraminor third, quasi-Pythagorean minor third
|294.473096
|small homothetic supraminor third, quasi-Pythagorean minor third
|-
|-
|1201/990
| 1201/990 || 334.482865 || Large homothetic supraminor third
|334.482865
|large homothetic supraminor third
|-
|-
|977/792
| 977/792 || 363.429758 ||  
|363.429758
|
|-
|-
|1223/968
| 1223/968 || 404.814542 ||  
|404.814542
|
|-
|-
|281/220
| 281/220 || 423.679928 ||  
|423.679928
|
|-
|-
|573/437
| 573/437 || 469.082231 || Homothetic sub-fourth
|469.082231
|homothetic sub-fourth
|-
|-
|511/376
| 511/376 || 531.108755 || Homothetic acute fourth
|531.108755
|homothetic acute fourth
|-
|-
|1107/800
| 1107/800 || 562.299980 || Homothetic augmented fourth
|562.299980
|homothetic augmented fourth
|-
|-
|99/70
| 99/70 || 600.088324 || Quasi-tempered tritone
|600.088324
|quasi-tempered tritone
|-
|-
|159/110
| 159/110 || 637.827890 || Homothetic diminished fifth
|637.827890
|homothetic diminished fifth
|-
|-
|761/517
| 761/517 || 669.278608 || Homothetic quasi-catafifth
|669.278608
|homothetic quasi-catafifth
|-
|-
|6001/3933
| 6001/3933 || 731.487292 || Homothetic super-fifth
|731.487292
|homothetic super-fifth
|-
|-
|1973/1260
| 1973/1260 || 776.360667 ||  
|776.360667
|
|-
|-
|1219/770
| 1219/770 || 795.321330 ||  
|795.321330
|
|-
|-
|981/605
| 981/605 || 836.781593 ||  
|836.781593
|
|-
|-
|399/242
| 399/242 || 865.658039 ||  
|865.658039
|
|-
|-
|[[27/16]]
| [[27/16]] || 905.865003 || Pythagorean major sixth
|905.865003
|Pythagorean major sixth
|-
|-
|97/56
| 97/56 || 951.069504 || Homothetic semitwelve
|951.069504
|homothetic semitwelve
|-
|-
|3085/1748
| 3085/1748 || 983.478365 ||  
|983.478365
|
|-
|-
|4429/2475
| 4429/2475 || 1007.462966 || Quasi-meantone minor seventh
|1007.462966
|quasi-meantone minor seventh
|-
|-
|2191/1210
| 2191/1210 || 1027.898924 || Homothetic minor seventh
|1027.898924
|homothetic minor seventh
|-
|-
|241/132
| 241/132 || 1042.194260 || Homothetic neutral seventh
|1042.194260
|homothetic neutral seventh
|-
|-
|535/282
| 535/282 || 1108.612475 || Homothetic major seventh
|1108.612475
|homothetic major seventh
|-
|-
|[[2/1]]
| [[2/1]] || 1200 || [[Octave| octave]], [https://en.wikipedia.org/wiki/Diapason diapason]
|1200
|[[Octave|octave]], [https://en.wikipedia.org/wiki/Diapason diapason]
|}
|}


=Links=
== Links ==
* [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
[[Category:Just intonation]]
[[Category:Just intonation]]
[[Category:Math]]
[[Category:Math]]
[[Category:31-tone scales]]
[[Category:31-tone scales]]
Retrieved from "https://en.xen.wiki/w/Homothetic_just_intonation"