44edo

← 43edo

44edo

45edo →

Prime factorization	22 × 11
Step size	27.2727¢
Fifth	26\44 (709.091¢) (→13\22)
Semitones (A1:m2)	6:2 (163.6¢ : 54.55¢)
Consistency limit	5
Distinct consistency limit	5

44 equal divisions of the octave (abbreviated 44edo or 44ed2), also called 44-tone equal temperament (44tet) or 44 equal temperament (44et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 44 equal parts of about 27.3 ¢ each. Each step represents a frequency ratio of 2^1/44, or the 44th root of 2.

Theory

44edo is a double of 22edo, to which it adds the ratios of 13, 19, and 23. While not the most accurate 2.3.5.7.11 tuning, 22edo is certainly a relatively compact one, and it's natural to extend it this way. The most practically useful of these additions is easily the 13th harmonic with its neutral intervals, but the 17th, 19th, and 23rd are not to be dismissed. In the 13-limit it supplies the optimal patent val for vigin temperament. The 2*44 subgroup of 44edo is 2.9.5.21.11.13.17.19.23, on which 44 tempers out the same commas as the patent val for 88edo.

Harmonics

Approximation of odd harmonics in 44edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	absolute (¢)	+7.1	-4.5	+13.0	-13.0	-5.9	+4.9	+2.6	+4.1	+2.5	-7.1	-1.0
	relative (%)	+26	-16	+48	-48	-21	+18	+10	+15	+9	-26	-4
Steps (reduced)		70 (26)	102 (14)	124 (36)	139 (7)	152 (20)	163 (31)	172 (40)	180 (4)	187 (11)	193 (17)	199 (23)

Subsets and supersets

44edo has subsets 2, 4, 11, 22.

One step of 44edo is very close (only 0.0086 cents sharp) to 64/63 (the septimal comma). Ruthenium temperament realizes this proximity through a regular temperament perspective, and it is supported by a large number of edos which are a multiple of 44 - for example 1012edo, 1848edo, and 2684edo.

Intervals

In 44edo, sharps and flats alter pitch by 6 EDOsteps. This means intervals can be notated with half sharps and half flats equal to 3 EDOsteps, in addition to ups and downs. The table below uses only sharps, flats, and ups and downs. When translating music from 22edo to 44edo, single ups and downs simply become double ups and downs (vEb in 22edo would be vvEb in 44edo).

Degrees	Cents	Ups and Downs Notation
0	0.000	Perfect 1sn	P1	D
1	27.273	Up 1sn	^1	^D
2	54.545	Minor 2nd	m2	Eb
3	81.818	Upminor 2nd	^m2	^Eb
4	109.091	Downmid 2nd	v~2	^^Eb
5	136.364	Mid 2nd	~2	vvvE, ^^^Eb
6	163.636	Upmid 2nd	^~2	vvE
7	190.909	Downmajor 2nd	vM2	vE
8	218.182	Major 2nd	M2	E
9	245.455	Upmajor 2nd, Downminor 3rd	^M2, vm3	^E, vF
10	272.727	Minor 3rd	m3	F
11	300.000	Upminor 3rd	^m3	^F
12	327.273	Downmid 3rd	v~3	^^F
13	354.545	Mid 3rd	~3	^^^F, vvvF#
14	381.818	Upmid 3rd	^~3	vvF#
15	409.091	Downmajor 3rd	vM3	vF#
16	436.364	Major 3rd	M3	F#
17	463.636	Upmajor 3rd, Down 4th	^M3, v4	^F#, vG
18	490.909	Perfect 4th	P4	G
19	518.182	Up 4th	^4	^G
20	545.455	Dim 5th, Downmid 4th	d5, v~4	Ab, ^^G
21	572.727	Mid 4th	~4	^^^G, vvvG#
22	600.000	Upmid 4th, Downmid 5th	^~4, v~5	vvG#, ^^Ab
23	627.273	Mid 5th	~5	vvvA, ^^^Ab
24	654.545	Aug 4th, Upmid 5th	A4, ^~5	G#, vvA
25	681.818	Down 5th	v5	vA
26	709.091	Perfect 5th	P5	A
27	736.364	Up 5th, Downminor 6th	^5, vm6	^A, vBb
28	763.636	Minor 6th	m6	Bb
29	790.909	Upminor 6th	^m6	^Bb
30	818.182	Downmid 6th	v~6	^^Bb
31	845.455	Mid 6th	~6	^^^Bb, vvvB
32	872.727	Upmid 6th	^~6	vvB
33	900.000	Downmajor 6th	vM6	vB
34	927.273	Major 6th	M6	B
35	954.545	Upmajor 6th, Downminor 7th	^M6, vm7	^B, vC
36	981.818	Minor 7th	m7	C
37	1009.091	Upminor 7th	^m7	^C
38	1036.364	Downmid 7th	v~7	^^C
39	1063.636	Mid 7th	~7	^^^C, vvvC#
40	1090.909	Upmid 7th	^~7	vvC#
41	1118.182	Downmajor 7th	vM7	vC#
42	1145.455	Major 7th	M7	C#
43	1172.727	Upmajor 7th, Down 8ve	^M7, v8	^C#, vD
44	1200.000	Perfect 8ve	P8	D

Instrument layouts

Lumatone mapping for 44edo

Skip fretting system 44 2 11