17ed5/4

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17ed5/4

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Prime factorization	17 (prime)
Step size	22.7243 ¢
Octave	53\17ed5/4 (1204.39 ¢)
Twelfth	84\17ed5/4 (1908.84 ¢)
Consistency limit	6
Distinct consistency limit	6

17 equal divisions of 5/4 (abbreviated 17ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 17 equal parts of about 22.7 ¢ each. Each step represents a frequency ratio of (5/4)^1/17, or the 17th root of 5/4. It is related to 53edo, having the octave stretched by 4.39¢, but its patent val tunes some primes like 7, 13 and 19 flatter than 53edo

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	22.7
2	45.4
3	68.2	21/20, 23/22
4	90.9	17/16, 22/21, 24/23
5	113.6	16/15, 18/17
6	136.3	14/13, 15/14
7	159.1	11/10, 12/11, 23/21
8	181.8	10/9, 19/17, 21/19
9	204.5	9/8, 17/15
10	227.2	23/20
11	250	7/6, 8/7
12	272.7	13/11, 22/19
13	295.4	20/17
14	318.1	6/5
15	340.9	11/9, 17/14, 23/19
16	363.6	21/17
17	386.3	5/4

Harmonics

Approximation of harmonics in 17ed5/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.39	+6.89	+8.78	+8.78	+11.28	-5.62	-9.55	-8.95	-9.55	+7.24	-7.06
	Relative (%)	+19.3	+30.3	+38.6	+38.6	+49.6	-24.7	-42.0	-39.4	-42.0	+31.8	-31.0
Steps (reduced)		53 (2)	84 (16)	106 (4)	123 (4)	137 (1)	148 (12)	158 (5)	167 (14)	175 (5)	183 (13)	189 (2)

Approximation of harmonics in 17ed5/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-9.28	-1.23	-7.06	-5.17	+3.50	-4.56	-7.26	-5.17	+1.27	-11.10	+2.84
	Relative (%)	-40.8	-5.4	-31.0	-22.7	+15.4	-20.0	-32.0	-22.7	+5.6	-48.8	+12.5
Steps (reduced)		195 (8)	201 (14)	206 (2)	211 (7)	216 (12)	220 (16)	224 (3)	228 (7)	232 (11)	235 (14)	239 (1)

Music

Francium

• "you're used up" from have nice day (2025) – Spotify | Bandcamp | YouTube