67edo

← 66edo

67edo

68edo →

Prime factorization	67 (prime)
Step size	17.9104 ¢
Fifth	39\67 (698.507 ¢)
Semitones (A1:m2)	5:6 (89.55 ¢ : 107.5 ¢)
Consistency limit	3
Distinct consistency limit	3

Theory

67edo tempers out 81/80, supporting meantone, with a tuning which is slightly sharp of 1/6-comma (the tuning favored by Mozart and contemporaries, though they suggested the flatter & composite 55edo as an approximation). It is indistinguishable from 4/25=0.16-comma meantone. In the 7-limit the patent val tempers out 1029/1024 and 1728/1715, so that it supports mothra. In the 11-limit it tempers out 176/175 and 540/539, supporting mosura, an alternative 11-limit mothra. In the 13-limit it tempers out 144/143 and 196/195, supporting 13-limit mosura. It tempers out the orgonisma, and on the 2.7.11 subgroup it supports the orgone temperament.

It is a promising tuning which has, as many relatively large equal temperaments do, a variety of tonal resources: it is the first edo to have both meantone and an orgone temperament (26edo could be called meantone, but it is more of a flattone). It has relatively good approximations of the 3rd, 7th, 11th, 13th, 15th, 17th harmonics, although the 5th, 9th, and 19th as well as certain higher ones are workable as well. 33 + 34 can be used to construct this temperament explaining some of its properties. It does well on the 2.3.7.11.13.17.23.31.37.41 subgroup.

Prime harmonics

Approximation of prime harmonics in 67edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31	37	41
Error	Absolute (¢)	+0.00	-3.45	+7.72	-1.66	+3.91	+1.26	+2.51	+6.96	-1.41	-8.68	+1.23	-0.60	+0.79
	Relative (%)	+0.0	-19.2	+43.1	-9.3	+21.8	+7.1	+14.0	+38.9	-7.9	-48.5	+6.9	-3.3	+4.4
Steps (reduced)		67 (0)	106 (39)	156 (22)	188 (54)	232 (31)	248 (47)	274 (6)	285 (17)	303 (35)	325 (57)	332 (64)	349 (14)	359 (24)

Subsets and supersets

67edo is the 19th prime edo, following 61edo and before 71edo.

Intervals

Steps	Cents	Approximate ratios	Ups and downs notation
0	0	1/1	D
1	17.9		^D, E♭♭
2	35.8		^^D, ^E♭♭
3	53.7	31/30, 32/31, 33/32, 34/33, 35/34	vvD♯, ^^E♭♭
4	71.6	24/23	vD♯, vvE♭
5	89.6	20/19	D♯, vE♭
6	107.5	17/16, 33/31	^D♯, E♭
7	125.4	14/13, 29/27	^^D♯, ^E♭
8	143.3		vvD𝄪, ^^E♭
9	161.2	11/10, 23/21, 34/31	vD𝄪, vvE
10	179.1	31/28	D𝄪, vE
11	197		E
12	214.9	17/15, 26/23	^E, F♭
13	232.8	8/7	^^E, ^F♭
14	250.7	15/13, 22/19	vvE♯, ^^F♭
15	268.7	7/6	vE♯, vvF
16	286.6	13/11, 33/28	E♯, vF
17	304.5	31/26	F
18	322.4		^F, G♭♭
19	340.3	28/23	^^F, ^G♭♭
20	358.2	16/13	vvF♯, ^^G♭♭
21	376.1	36/29	vF♯, vvG♭
22	394		F♯, vG♭
23	411.9	19/15, 33/26	^F♯, G♭
24	429.9		^^F♯, ^G♭
25	447.8	22/17	vvF𝄪, ^^G♭
26	465.7	17/13	vF𝄪, vvG
27	483.6		F𝄪, vG
28	501.5	4/3	G
29	519.4	23/17, 31/23	^G, A♭♭
30	537.3	15/11	^^G, ^A♭♭
31	555.2	11/8, 29/21	vvG♯, ^^A♭♭
32	573.1	32/23	vG♯, vvA♭
33	591	31/22	G♯, vA♭
34	609		^G♯, A♭
35	626.9	23/16, 33/23	^^G♯, ^A♭
36	644.8	16/11	vvG𝄪, ^^A♭
37	662.7	22/15	vG𝄪, vvA
38	680.6	34/23	G𝄪, vA
39	698.5	3/2	A
40	716.4		^A, B♭♭
41	734.3	26/17	^^A, ^B♭♭
42	752.2	17/11	vvA♯, ^^B♭♭
43	770.1		vA♯, vvB♭
44	788.1	30/19	A♯, vB♭
45	806	35/22	^A♯, B♭
46	823.9	29/18	^^A♯, ^B♭
47	841.8	13/8	vvA𝄪, ^^B♭
48	859.7	23/14	vA𝄪, vvB
49	877.6		A𝄪, vB
50	895.5		B
51	913.4	22/13	^B, C♭
52	931.3	12/7	^^B, ^C♭
53	949.3	19/11, 26/15	vvB♯, ^^C♭
54	967.2	7/4	vB♯, vvC
55	985.1	23/13, 30/17	B♯, vC
56	1003		C
57	1020.9		^C, D♭♭
58	1038.8	20/11, 31/17	^^C, ^D♭♭
59	1056.7	35/19	vvC♯, ^^D♭♭
60	1074.6	13/7	vC♯, vvD♭
61	1092.5	32/17	C♯, vD♭
62	1110.4	19/10	^C♯, D♭
63	1128.4	23/12	^^C♯, ^D♭
64	1146.3	31/16, 33/17	vvC𝄪, ^^D♭
65	1164.2		vC𝄪, vvD
66	1182.1		C𝄪, vD
67	1200	2/1	D

Scales

Mos scales

• Meantone[5]: 11 11 17 11 17
• Meantone[7]: 11 11 6 11 11 11 6
• Barbados[5], Bustling Docks (original/default tuning): 14 14 11 14 14

Modmos scales

• Cavernous (original/default tuning): 14 14 11 21 7
• Formicarium (original/default tuning): 14 7 18 14 14
• Negri Blues (original/default tuning): 14 14 3 8 14 14
• Negri Blues Septatonic (original/default tuning): 14 14 3 8 11 3 14
• Negri Blues Octatonic (original/default tuning): 7 14 7 11 7 11 3 7
• Understory (original/default tuning): 14 7 18 7 21
• Meantone Ionian Pentatonic: 22 6 11 22 6
• Meantone Minor Melodic: 11 6 11 11 11 11 6
• Meantone Minor Harmonic: 11 6 11 11 6 16 6
• Meantone Minor Hexatonic: 11 6 11 11 17 11
• Meantone Dorian Harmonic: 11 6 16 6 11 6 11
• Meantone Mixolydian Pentatonic: 22 6 11 17 11
• Meantone Phrygian Dominant: 6 16 6 11 6 11 11
• Meantone Phrygian Dominant Hexatonic: 6 16 6 11 6 22
• Meantone Phrygian Dominant Pentatonic: 22 6 11 6 22
• Meantone Phrygian Pentatonic: 6 11 22 6 22
• Meantone Double Harmonic: 6 16 6 11 6 16 6

Blues scales

• Lost spirit (approximated from 31edo): 17 11 6 5 13 4 11
• Blackened skies (approximated from 72edo): 18 10 5 6 5 18 5
• Blues Aeolian Hexatonic: 17 11 6 5 6 22
• Blues Aeolian Pentatonic I: 17 11 11 6 22
• Blues Aeolian Pentatonic II: 17 22 6 11 11
• Blues Bright Double Harmonic: 6 16 6 11 6 11 6 5
• Blues Dark Double Harmonic: 11 6 11 6 5 6 16 6
• Blues Dorian Hexatonic: 17 11 11 11 6 11
• Blues Dorian Pentatonic: 17 22 11 6 11
• Blues Dorian Septatonic: 17 11 6 5 11 6 11
• Blues Harmonic Hexatonic: 11 6 11 11 22 6
• Blues Harmonic Septatonic: 17 11 6 5 6 11 5 6
• Blues Leading: 17 11 6 5 17 6 5
• Blues Minor: 17 11 6 5 17 11
• Blues Minor Maj7: 17 11 6 5 22 6
• Blues Pentachordal: 11 6 11 5 6 28
• Greyed Skies (approximated from 91edo): 17 11 5 6 6 17 5
• Akebono I: 11 6 11 11 17
• Augmented: 17 6 16 6 16 6
• Dominant Pentatonic: 11 11 17 17 11
• Hirajoshi: 11 6 12 6 22
• Javanese Pentachordal: 6 11 17 4 29

Others

• Approximation of Pelog lima: 6 10 22 7 22
• Arcade (approximated from 32afdo): 22 4 13 15 13
• Cosmic (approximated from 32afdo): 29 10 6 11 11
• Mechanical (approximated from 16afdo): 17 5 17 15 13
• Moonbeam (approximated from 16afdo): 11 6 12 22 6
• Springwater (approximated from 8afdo): 11 11 17 15 13
• Volcanic (approximated from 16afdo): 6 16 17 15 13
• Deja Vu (approximated from 101afdo): 18 21 6 12 10
• Freeway (approximated from 6afdo): 15 12 11 11 9 8
• Mushroom (approximated from 30afdo): 15 12 11 4 24
• Underpass (approximated from 10afdo): 18 21 12 6 10
• Sourgummy (approximated from 51afdo): 14 12 14 14 13
• Bubblegum/Cola (approximated from 60afdo/99afdo): 14 13 13 13 14
• Spearmint/Whitechocolate (approximated from 62afdo/90afdo): 13 14 13 14 13
• Lemonade (approximated from 79afdo): 14 13 13 14 13
• Candycorn (approximated from 91afdo): 11 12 11 10 12 11
• Trailmix (approximated from 97afdo): 11 11 11 12 11 11
• Liquorice (approximated from 101afdo): 11 11 12 10 12 11
• Apple Mint (approximated from 80afdo): 9 11 9 9 10 9 10

Music

• Beginning of a piece in 67 tone, Peter Kosmorsky ^{[dead link]}
• 67edo Negri8 MODMOS Improvisation, Budjarn Lambeth