93edo

← 92edo

93edo

94edo →

Prime factorization	3 × 31
Step size	12.9032 ¢
Fifth	54\93 (696.774 ¢) (→ 18\31)
Semitones (A1:m2)	6:9 (77.42 ¢ : 116.1 ¢)
Dual sharp fifth	55\93 (709.677 ¢)
Dual flat fifth	54\93 (696.774 ¢) (→ 18\31)
Dual major 2nd	16\93 (206.452 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

Approximation of odd harmonics in 93edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-5.18	+0.78	-1.08	+2.54	+3.52	-1.82	-4.40	-1.73	-0.74	-6.26	+3.98
	Relative (%)	-40.2	+6.1	-8.4	+19.7	+27.3	-14.1	-34.1	-13.4	-5.7	-48.6	+30.9
Steps (reduced)		147 (54)	216 (30)	261 (75)	295 (16)	322 (43)	344 (65)	363 (84)	380 (8)	395 (23)	408 (36)	421 (49)

93 = 3 * 31, and 93 is a contorted 31 through the 7 limit. In the 11-limit the patent val tempers out 4000/3993 and in the 13-limit 144/143, 1188/1183 and 364/363. It provides the optimal patent val for the 11-limit prajapati and 13-limit kumhar temperaments, and the 11 and 13 limit 43&50 temperament. It is the 13th no-3s zeta peak edo.

Since 93edo has good approximations of 13th, 17th and 19th harmonics unlike 31edo (as 838.710 ¢, 103.226 ¢, and 296.774 ¢ respectively, octave-reduced), it also allows one to give a clearer harmonic identity to 31edo's excellent approximation of 13:17:19.

Scales

Meantone Chromatic

• 116.129
• 193.548
• 309.677
• 387.097
• 503.226
• 580.645
• 696.774
• 812.903
• 890.323
• 1006.452
• 1083.871
• 1200.000

Superpyth Chromatic

• 51.613
• 219.355
• 270.968
• 438.710
• 490.323
• 658.065
• 709.677
• 761.290
• 929.032
• 980.645
• 1148.387
• 1200.000

Superpyth Shailaja

• 270.968
• 709.677
• 761.290
• 980.645
• 1200.000

Superpyth Subminor Hexatonic

• 219.355
• 270.968
• 490.323
• 709.677
• 980.645
• 1200.000

Superpyth Subminor Pentatonic

• 270.968
• 490.323
• 709.677
• 980.645
• 1200.000

See Also

• 93edo and stretched hemififths