| Prime factorization
|
3 × 17
|
| Step size
|
23.5294 ¢
|
| Fifth
|
30\51 (705.882 ¢) (→ 10\17)
|
| Semitones (A1:m2)
|
6:3 (141.2 ¢ : 70.59 ¢)
|
| Consistency limit
|
3
|
| Distinct consistency limit
|
3
|
Theory
Script error: No such module "primes_in_edo".
51-EDO divides the octave into 51 equal parts of 23.529 cents each, which is about the size of the Pythagorean comma (even though this comma itself is mapped to a different interval). It tempers out 250/243 in the 5-limit, 225/224 and 2401/2400 in the 7-limit, and 55/54 and 100/99 in the 11-limit. It is the optimal patent val for sonic, the rank three temperament tempering out 250/243, 55/54 and 100/99, and also for the rank four temperament tempering out 55/54. It provides an alternative tuning to 22edo for porcupine temperament, with a nice fifth but a rather flat major third, and the optimal patent val for 7 and 11-limit porky temperament, which is sonic plus 225/224.
Intervals
| Degrees
|
Cents
|
Ups and Downs Notation
|
| 0
|
0.000
|
Perfect 1sn
|
P1
|
D
|
| 1
|
23.529
|
Up 1sn
|
^1
|
^D
|
| 2
|
47.059
|
Downminor 2nd
|
vm2
|
vEb
|
| 3
|
70.588
|
Minor 2nd
|
m2
|
Eb
|
| 4
|
94.118
|
Upminor 2nd
|
^m2
|
^Eb
|
| 5
|
117.647
|
Downmid 2nd
|
v~2
|
^^Eb
|
| 6
|
141.176
|
Mid 2nd
|
~2
|
vvvE, ^^^Eb
|
| 7
|
164.706
|
Upmid 2nd
|
^~2
|
vvE
|
| 8
|
188.235
|
Downmajor 2nd
|
vM2
|
vE
|
| 9
|
211.765
|
Major 2nd
|
M2
|
E
|
| 10
|
235.294
|
Upmajor 2nd
|
^M2
|
^E
|
| 11
|
258.824
|
Downminor 3rd
|
vm3
|
vF
|
| 12
|
282.353
|
Minor 3rd
|
m3
|
F
|
| 13
|
305.882
|
Upminor 3rd
|
^m3
|
^F
|
| 14
|
329.412
|
Downmid 3rd
|
v~3
|
^^F
|
| 15
|
352.941
|
Mid 3rd
|
~3
|
^^^F, vvvF#
|
| 16
|
376.471
|
Upmid 3rd
|
^~3
|
vvF#
|
| 17
|
400.000
|
Downmajor 3rd
|
vM3
|
vF#
|
| 18
|
423.529
|
Major 3rd
|
M3
|
F#
|
| 19
|
447.509
|
Upmajor 3rd
|
^M3
|
^F#
|
| 20
|
470.588
|
Down 4th
|
v4
|
vG
|
| 21
|
494.118
|
Perfect 4th
|
P4
|
G
|
| 22
|
517.647
|
Up 4th
|
^1
|
^G
|
| 23
|
541.176
|
Downdim 5th
|
vd5
|
vAb
|
| 24
|
564.706
|
Dim 5th
|
d5
|
Ab
|
| 25
|
588.235
|
Updim 5th
|
^d5
|
^Ab
|
| 26
|
611.765
|
Downaug 4th
|
vA4
|
vG#
|
| 27
|
635.294
|
Aug 4th
|
A4
|
G#
|
| 28
|
658.824
|
Upaug 4th
|
^A4
|
^G#
|
| 29
|
682.353
|
Down 5th
|
v5
|
vA
|
| 30
|
705.882
|
Perfect 5th
|
P5
|
A
|
| 31
|
729.412
|
Up 5th
|
^5
|
^A
|
| 32
|
752.941
|
Downminor 6th
|
vm6
|
vBb
|
| 33
|
776.471
|
Minor 6th
|
m6
|
Bb
|
| 34
|
800.000
|
Upminor 6th
|
^m6
|
^Bb
|
| 35
|
823.529
|
Downmid 6th
|
v~6
|
^^Bb
|
| 36
|
847.059
|
Mid 6th
|
~6
|
vvvB, ^^^Bb
|
| 37
|
870.588
|
Upmid 6th
|
^~6
|
vvB
|
| 38
|
894.118
|
Downmajor 6th
|
vM6
|
vB
|
| 39
|
917.647
|
Major 6th
|
M6
|
B
|
| 40
|
941.176
|
Upmajor 6th
|
^M6
|
^B
|
| 41
|
964.706
|
Downminor 7th
|
vm7
|
vC
|
| 42
|
988.235
|
Minor 7th
|
m7
|
C
|
| 43
|
1011.765
|
Upminor 7th
|
^m7
|
^C
|
| 44
|
1035.294
|
Downmid 7th
|
v~7
|
^^C
|
| 45
|
1058.824
|
Mid 7th
|
~7
|
^^^C, vvvC#
|
| 46
|
1082.353
|
Upmid 7th
|
^~7
|
vvC#
|
| 47
|
1105.882
|
Downmajor 7th
|
vM7
|
vC#
|
| 48
|
1129.412
|
Major 7th
|
M7
|
C#
|
| 49
|
1152.941
|
Upmajor 7th
|
^M7
|
^C#
|
| 50
|
1176.471
|
Down 8ve
|
v8
|
vD
|
| 51
|
1200.000
|
Perfect 8ve
|
P8
|
D
|