981edo

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981edo

982edo →

Prime factorization	32 × 109
Step size	1.22324 ¢
Fifth	574\981 (702.141 ¢)
Semitones (A1:m2)	94:73 (115 ¢ : 89.3 ¢)
Consistency limit	17
Distinct consistency limit	17

Theory

981edo is a good 13- and 17-limit system. It tempers out 2080/2079, 2401/2400, 2431/2430, 4096/4095, 4225/4224, 4375/4374, 4459/4455 and 4914/4913 in the 17-limit. It provides the optimal patent val for 13-limit ennealimmic, the rank-3 temperament tempering out 2080/2079, 2401/2400, and 4375/4374, and for 13-limit ennealimmia, which also tempers out 4096/4095.

Prime harmonics

Approximation of prime harmonics in 981edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.186	+0.231	-0.019	+0.364	-0.161	+0.243	-0.265	+0.472	+0.392	-0.081
	Relative (%)	+0.0	+15.2	+18.9	-1.5	+29.8	-13.1	+19.9	-21.7	+38.6	+32.1	-6.7
Steps (reduced)		981 (0)	1555 (574)	2278 (316)	2754 (792)	3394 (451)	3630 (687)	4010 (86)	4167 (243)	4438 (514)	4766 (842)	4860 (936)

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[1555 -981⟩	[⟨981 1555]]	-0.0586	0.0586	4.79
2.3.5	[1 -27 18⟩, [85 -17 -25⟩	[⟨981 1555 2278]]	-0.0722	0.0515	4.21
2.3.5.7	2401/2400, 4375/4374, [79 -25 -23 5⟩	[⟨981 1555 2278 2754]]	-0.0385	0.0562	4.59
2.3.5.7.11	2401/2400, 4375/4374, 131072/130977, 1771561/1771470	[⟨981 1555 2278 2754 3394]]	-0.0630	0.0545	4.46
2.3.5.7.11.13	2080/2079, 2401/2400, 4096/4095, 4375/4374, 1771561/1771470	[⟨981 1555 2278 2754 3394 3630]]	-0.0453	0.0636	5.20
2.3.5.7.11.13.17	2080/2079, 2401/2400, 2431/2430, 4096/4095, 4375/4374, 4914/4913	[⟨981 1555 2278 2754 3394 3630 4010]]	-0.0473	0.0591	4.83

Rank-2 temperaments

Periods per 8ve	Generator (Reduced)	Cents (Reduced)	Associated Ratio	Temperaments
9	258\981 (40\981)	315.60 (48.93)	6/5 (36/35)	Ennealimmal / ennealimmia