47edf

← 46edf

47edf

48edf →

Prime factorization	47 (prime)
Step size	14.9352 ¢
Octave	80\47edf (1194.82 ¢)
Twelfth	127\47edf (1896.77 ¢)
Consistency limit	3
Distinct consistency limit	3

47EDF is the equal division of the just perfect fifth into 47 parts of 14.9352 cents each, corresponding to 80.3470 edo (similar to every third step of 241edo).

It is related to the microtemperament which tempers out |39 -39 -47 47> (1.82802 cents) in the 7-limit, which is supported by 482, 643, 1125, 1205, 1848, 2330, 2973, 3053, and 4178 EDOs.

Related regular temperaments

7-limit 1205&1848&2330

Comma: |39 -39 -47 47>

POTE generators: ~5/4 = 386.3319, ~3796875/3764768 = 14.9354

Mapping: [<1 1 0 0|, <0 47 0 39|, <0 0 1 1|]

EDOs: 80, 161, 482, 562, 643, 723, 1125, 1205, 1366, 1848, 2330, 2973, 3053, 4178, 6026

Harmonics

Approximation of harmonics in 47edf

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-5.18	-5.18	+4.57	+6.57	+4.57	+6.53	-0.61	+4.57	+1.39	+0.67	-0.61
	Relative (%)	-34.7	-34.7	+30.6	+44.0	+30.6	+43.7	-4.1	+30.6	+9.3	+4.5	-4.1
Steps (reduced)		80 (33)	127 (33)	161 (20)	187 (46)	208 (20)	226 (38)	241 (6)	255 (20)	267 (32)	278 (43)	288 (6)

contd.

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-4.77	+1.35	+1.39	-5.80	-6.21	-0.61	-4.61	-3.79	+1.35	-4.51	-6.79
	Relative (%)	-31.9	+9.0	+9.3	-38.8	-41.6	-4.1	-30.8	-25.4	+9.0	-30.2	-45.5
Steps (reduced)		297 (15)	306 (24)	314 (32)	321 (39)	328 (46)	335 (6)	341 (12)	347 (18)	353 (24)	358 (29)	363 (34)