User:MisterShafXen/17edf

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17edf

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Prime factorization	17 (prime)
Step size	41.2915 ¢
Octave	29\17edf (1197.45 ¢) (semiconvergent)
Twelfth	46\17edf (1899.41 ¢) (semiconvergent)
Consistency limit	6
Distinct consistency limit	6

17 equal divisions of the perfect fifth (abbreviated 17edf or 17ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 17 equal parts of about 41.3 ¢ each. Each step represents a frequency ratio of (3/2)^1/17, or the 17th root of 3/2.

Intervals

Steps	Cents	Approximate ratios	Note names (pseudo-diatonic)
0	0	1/1	C
1	41.3		^C
2	82.6	20/19, 22/21	Db
3	123.9	14/13	C#
4	165.2		vD
5	206.5	9/8	D
6	247.7	23/20	^D
7	289	13/11, 19/16	Eb
8	330.3	17/14, 23/19	D#
9	371.6	21/17, 26/21	vE
10	412.9	14/11, 19/15, 24/19	E
11	454.2	22/17	^E
12	495.5	4/3	F
13	536.8		^F
14	578.1		Gb
15	619.4		F#
16	660.7		vG
17	702	3/2	G
18	743.2	23/15, 26/17	^G
19	784.5	11/7	Ab
20	825.8	21/13	G#
21	867.1	28/17	vA
22	908.4	22/13, 27/16	A
23	949.7		^A
24	991	16/9	Bb
25	1032.3		A#
26	1073.6	13/7	vB
27	1114.9	19/10, 21/11	B
28	1156.2		^B
29	1197.5	2/1	C
30	1238.7		^C
31	1280		Db
32	1321.3	28/13	C#
33	1362.6		vD
34	1403.9	9/4	D

Commas

This tuning tempers out 45/44 in the 11-limit.

Harmonics

Approximation of prime harmonics in 17edf

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-2.5	-2.5	-19.8	+17.1	+19.1	+19.0	+8.7	-18.7	-19.1	-7.5	+0.9
	Relative (%)	-6.2	-6.2	-47.9	+41.4	+46.3	+45.9	+21.1	-45.2	-46.2	-18.1	+2.3
Steps (reduced)		29 (12)	46 (12)	67 (16)	82 (14)	101 (16)	108 (6)	119 (0)	123 (4)	131 (12)	141 (5)	144 (8)