197edt

← 196edt

197edt

198edt →

Prime factorization	197 (prime)
Step size	9.65459¢
Octave	124\197edt (1197.17¢)
Consistency limit	2
Distinct consistency limit	2

197 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 197edt or 197ed3), is a nonoctave tuning system that divides the interval of 3/1 into 197 equal parts of about 9.65⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/197, or the 197th root of 3.

197edt can be described as approximately 124.293edo. This implies that each step of 197edt can be approximated by 3 steps of 373edo, 7 steps of 870edo, or 10 steps of 1243edo. In the 2.3.7.11.13.17.19 subgroup, these are represented by the 373g, 870df, and 1243g warted vals respectively.

It is a very strong no-twos, no-fives 19-limit system, though it additionally represents the interval of 5/4 very well, and the 8th harmonic decently. It supports mebsuta temperament, as well as various extensions thereof which slice the generator in thirds. Remarkably, it tempers out, and can be defined in this subgroup by tempering out, all the Don Page commas among the intervals 9/7, 11/9, 13/11, 17/13, 19/17, and 21/19, forming a complete tritave-spanning 7:9:11:13:17:19:21 heptad.

Harmonics

Approximation of prime harmonics in 197edt

Harmonic		2	3	5	7	11	13	17	19	23
Error	Absolute (¢)	-2.83	+0.00	+3.86	+0.63	+0.16	+0.59	-0.42	+0.11	-2.39
	Relative (%)	-29.3	+0.0	+40.0	+6.5	+1.6	+6.1	-4.4	+1.2	-24.8
Steps (reduced)		124 (124)	197 (0)	289 (92)	349 (152)	430 (36)	460 (66)	508 (114)	528 (134)	562 (168)

Approximation of odd harmonics in 197edt

Harmonic		25	27	29	31	33	35	37	39	41	43	45
Error	Absolute (¢)	-1.93	+0.00	+1.80	+2.19	+0.16	+4.49	-4.82	+0.59	+0.90	-4.32	+3.86
	Relative (%)	-20.0	+0.0	+18.6	+22.7	+1.6	+46.5	-49.9	+6.1	+9.3	-44.8	+40.0
Steps (reduced)		577 (183)	591 (0)	604 (13)	616 (25)	627 (36)	638 (47)	647 (56)	657 (66)	666 (75)	674 (83)	683 (92)

This page is a stub. You can help the Xenharmonic Wiki by expanding it.