41ed4

← 39ed4

41ed4

43ed4 →

Prime factorization	41 (prime)
Step size	58.5366¢
Octave	21\41ed4 (1229.27¢)
Twelfth	32\41ed4 (1873.17¢)
Consistency limit	1
Distinct consistency limit	1

41ed4 is the equal division of the double octave into 41 parts of 58.54 cents each, corresponding to 20.5edo or every second step of 41edo.

The Kite Guitar (see also KiteGuitar.com and Kite Tuning) is a guitar fretting using every other step of 41edo, i.e. 41ed4 or "20½-edo". However, the interval between two adjacent open strings is always an odd number of 41-edosteps. Thus each string only covers 41ed4, but the full edo can be found on every pair of adjacent strings.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	58.537	30/29
2	117.073
3	175.61	21/19
4	234.146
5	292.683	13/11
6	351.22
7	409.756	19/15
8	468.293	17/13
9	526.829	23/17
10	585.366	7/5
11	643.902
12	702.439
13	760.976
14	819.512
15	878.049
16	936.585	12/7
17	995.122
18	1053.659	11/6
19	1112.195
20	1170.732
21	1229.268
22	1287.805
23	1346.341
24	1404.878
25	1463.415
26	1521.951	12/5, 29/12
27	1580.488	5/2
28	1639.024
29	1697.561
30	1756.098
31	1814.634
32	1873.171
33	1931.707
34	1990.244	19/6
35	2048.78
36	2107.317
37	2165.854	7/2
38	2224.39
39	2282.927
40	2341.463
41	2400

Harmonics

Approximation of harmonics in 41ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+29.3	-28.8	+0.0	+23.4	+0.5	+26.3	+29.3	+1.0	-5.8	+4.8	-28.8
	Relative (%)	+50.0	-49.2	+0.0	+40.0	+0.8	+44.9	+50.0	+1.7	-10.0	+8.2	-49.2
Steps (reduced)		21 (21)	32 (32)	41 (0)	48 (7)	53 (12)	58 (17)	62 (21)	65 (24)	68 (27)	71 (30)	73 (32)

Approximation of harmonics in 41ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+8.3	-3.0	-5.3	+0.0	+12.1	-28.3	-4.8	+23.4	-2.5	-24.5	+15.6
	Relative (%)	+14.1	-5.1	-9.1	+0.0	+20.7	-48.3	-8.3	+40.0	-4.3	-41.8	+26.7
Steps (reduced)		76 (35)	78 (37)	80 (39)	82 (0)	84 (2)	85 (3)	87 (5)	89 (7)	90 (8)	91 (9)	93 (11)