7-Limit Intervals
7-limit, 81-odd-limit intervals.
| Interval Class
|
Wa Intervals
|
Yo/Gu Intervals
|
Zo/Ru Intervals
|
Ruyo/Zogu Intervals
|
Yoyo/Gugu Intervals
|
Zozo/Ruru Intervals
|
Zoyo/Rugu Intervals
|
Biruyo/Bizogu Intervals
|
| Traditional Name
|
Fifthspan
|
Ratio
|
Cent
|
Ratio
|
Cent
|
Ratio
|
Cent
|
Ratio
|
Cent
|
Ratio
|
Cent
|
Ratio
|
Cent
|
Ratio
|
Cent
|
Ratio
|
Cent
|
| ?
|
+12
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
50/49
|
34.976
|
| Perfect 1sn
|
0
|
1/1
|
0
|
81/80
|
21.506
|
64/63
|
27.264
|
|
|
|
|
|
|
36/35
|
48.770
|
|
|
| Augmented 1sn
|
+7
|
|
|
|
|
|
|
15/14
|
119.443
|
25/24
|
70.672
|
54/49
|
168.213
|
|
|
|
|
| Minor 2nd
|
-5
|
|
|
16/15
|
111.731
|
28/27
|
62.961
|
21/20
|
84.467
|
27/25
|
133.238
|
49/48
|
35.697
|
|
|
|
|
| Major 2nd
|
+2
|
9/8
|
203.910
|
10/9
|
182.404
|
8/7
|
231.174
|
|
|
|
|
|
|
|
|
|
|
| Augmented 2nd
|
+9
|
|
|
|
|
|
|
|
|
75/64
|
274.582
|
|
|
|
|
|
|
| Minor 3rd
|
-3
|
32/27
|
294.135
|
6/5
|
315.641
|
7/6
|
266.871
|
|
|
|
|
|
|
|
|
|
|
| Major 3rd
|
+4
|
81/64
|
407.820
|
5/4
|
386.313
|
9/7
|
435.084
|
80/63
|
413.578
|
|
|
64/49
|
462.348
|
|
|
|
|
| Diminished 4th
|
-8
|
|
|
|
|
|
|
56/45
|
378.602
|
32/25
|
427.373
|
|
|
|
|
|
|
| Perfect 4th
|
-1
|
4/3
|
498.045
|
27/20
|
519.551
|
21/16
|
470.781
|
|
|
|
|
|
|
35/27
|
449.275
|
|
|
| Augmented 4th
|
+6
|
|
|
45/32
|
590.224
|
81/56
|
638.994
|
10/7
|
617.488
|
|
|
|
|
|
|
|
|
| Diminshed 5th
|
-6
|
|
|
64/45
|
609.776
|
112/81
|
561.006
|
7/5
|
582.512
|
|
|
|
|
|
|
|
|
| Perfect 5th
|
+1
|
3/2
|
701.955
|
40/27
|
680.449
|
32/21
|
729.219
|
|
|
|
|
|
|
54/35
|
750.725
|
|
|
| Augmented 5th
|
+8
|
|
|
|
|
|
|
45/28
|
821.398
|
25/16
|
772.627
|
|
|
|
|
|
|
| Minor 6th
|
-4
|
128/81
|
792.180
|
8/5
|
813.687
|
14/9
|
764.916
|
63/40
|
786.422
|
|
|
49/32
|
737.652
|
|
|
|
|
| Major 6th
|
+3
|
27/16
|
905.865
|
5/3
|
884.339
|
12/7
|
933.129
|
|
|
|
|
|
|
|
|
|
|
| Diminished 7th
|
-9
|
|
|
|
|
|
|
|
|
128/75
|
925.418
|
|
|
|
|
|
|
| Minor 7th
|
-2
|
16/9
|
996.090
|
9/5
|
1017.596
|
7/4
|
968.826
|
|
|
|
|
|
|
|
|
|
|
| Major 7th
|
+5
|
|
|
15/8
|
1088.269
|
27/14
|
1131.039
|
40/21
|
1115.533
|
50/27
|
1066.762
|
96/49
|
1164.303
|
|
|
|
|
| Diminished 8ve
|
-7
|
|
|
|
|
|
|
28/15
|
1080.557
|
48/25
|
1129.328
|
49/27
|
1031.787
|
|
|
|
|
| Perfect 8ve
|
0
|
2/1
|
1200
|
160/81
|
1178.494
|
63/32
|
1172.736
|
|
|
|
|
|
|
35/18
|
1151.230
|
|
|
| Diminished 9th
|
-12
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
49/25
|
1165.028
|
Intervals of 87edo
| #
|
Cents
|
Approximated Ratios
|
Ups and Downs Notation
|
Solfege
|
| 0
|
0.000
|
1/1
|
D
|
|
| 1
|
13.793
|
126/125, 100/99, 91/90
|
^D
|
|
| 2
|
27.586
|
81/80, 64/63, 49/48, 55/54, 65/64
|
^^D
|
|
| 3
|
41.379
|
50/49, 45/44
|
^^^D/vvvEb
|
|
| 4
|
55.172
|
28/27, 36/35, 33/32
|
vvEb
|
|
| 5
|
68.966
|
25/24, 27/26, 26/25
|
vEb
|
|
| 6
|
82.759
|
21/20, 22/21
|
Eb
|
|
| 7
|
96.552
|
35/33
|
^Eb
|
|
| 8
|
110.345
|
16/15
|
^^Eb
|
|
| 9
|
124.138
|
15/14, 14/13
|
^^^Eb
|
|
| 10
|
137.931
|
13/12
|
^^^^Eb
|
|
| 11
|
151.724
|
12/11
|
vvvvE
|
|
| 12
|
165.517
|
11/10
|
vvvE
|
|
| 13
|
179.310
|
10/9
|
vvE
|
|
| 14
|
193.103
|
28/25
|
vE
|
|
| 15
|
206.897
|
9/8
|
E
|
|
| 16
|
220.690
|
25/22
|
^E
|
|
| 17
|
234.483
|
8/7
|
^^E
|
|
| 18
|
248.276
|
15/13
|
^^^E/vvvF
|
|
| 19
|
262.089
|
7/6
|
vvF
|
|
| 20
|
275.862
|
75/64
|
vF
|
|
| 21
|
289.655
|
33/28, 13/11
|
F
|
|
| 22
|
303.448
|
25/21, 105/88
|
^F
|
|
| 23
|
317.241
|
6/5
|
^^F
|
|
| 24
|
331.034
|
63/52
|
^^^F
|
|
| 25
|
344.828
|
11/9, 39/32
|
^^^^F
|
|
| 26
|
358.621
|
27/22, 16/13
|
vvvvF#
|
|
| 27
|
372.414
|
26/21
|
vvvF#
|
|
| 28
|
386.207
|
5/4
|
vvF#
|
|
| 29
|
400.000
|
63/50, 44/35
|
vF#
|
|
| 30
|
413.793
|
14/11, 33/26
|
F#
|
|
| 31
|
427.586
|
32/25
|
^F#
|
|
| 32
|
441.379
|
9/7
|
^^F#
|
|
| 33
|
455.172
|
13/10
|
^^^F#/vvvG
|
|
| 34
|
468.966
|
21/16
|
vvG
|
|
| 35
|
482.759
|
33/25
|
vG
|
|
| 36
|
496.552
|
4/3
|
G
|
|
| 37
|
510.345
|
75/56
|
^G
|
|
| 38
|
524.138
|
27/20
|
^^G
|
|
| 39
|
537.931
|
15/11
|
^^^G
|
|
| 40
|
551.724
|
11/8
|
^^^^G
|
|
| 41
|
565.517
|
18/13
|
vvvvG#, vAb
|
|
| 42
|
579.310
|
7/5, 39/28
|
vvvG#, Ab
|
|
| 43
|
593.103
|
45/32
|
vvG#, ^Ab
|
|