197edt

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197edt

198edt →

Prime factorization	197 (prime)
Step size	9.65459 ¢
Octave	124\197edt (1197.17 ¢)
Consistency limit	3
Distinct consistency limit	3

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 7 steps of 870edo.

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.

Harmonics

Approximation of harmonics in 197edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.83	+0.00	+3.99	+3.86	-2.83	+0.63	+1.16	+0.00	+1.03	+0.16	+3.99
	Relative (%)	-29.3	+0.0	+41.4	+40.0	-29.3	+6.5	+12.1	+0.0	+10.7	+1.6	+41.4
Steps (reduced)		124 (124)	197 (0)	249 (52)	289 (92)	321 (124)	349 (152)	373 (176)	394 (0)	413 (19)	430 (36)	446 (52)

Approximation of prime harmonics in 197edt

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-2.83	+0.00	+3.86	+0.63	+0.16	+0.59	-0.42	+0.11	-2.39	+1.80	+2.19
	Relative (%)	-29.3	+0.0	+40.0	+6.5	+1.6	+6.1	-4.4	+1.2	-24.8	+18.6	+22.7
Steps (reduced)		124 (124)	197 (0)	289 (92)	349 (152)	430 (36)	460 (66)	508 (114)	528 (134)	562 (168)	604 (13)	616 (25)

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