Homothetic just intonation

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

Links

• Homothetic Just Intonation by Sui-hin Mak