In this article, we will cover the various flavors of 13-limit intervals. We consider intervals that differ by a pythagorean interval to have the same flavor. The flavor of an interval depends on the primes higher than 3 in its prime factorization.
The flavors of intervals
We first look at the pythagorean intervals:
Pythagorean (wa)
| Cents
|
Ratio
|
FJS Name
|
Color name
|
| 0.000
|
1/1
|
P1
|
wa 1sn
|
| 90.225
|
256/243
|
m2
|
sawa 2nd
|
| 203.910
|
9/8
|
M2
|
wa 2nd
|
| 294.135
|
32/27
|
m3
|
wa 3rd
|
| 407.820
|
81/64
|
M3
|
lawa 3rd
|
| 498.045
|
4/3
|
P4
|
wa 4th
|
| 588.270
|
1024/729
|
d5
|
sawa 5th
|
| 611.730
|
729/512
|
A4
|
lawa 4th
|
| 701.955
|
3/2
|
P5
|
wa 5th
|
| 792.180
|
128/81
|
m6
|
sawa 6th
|
| 905.865
|
27/16
|
M6
|
wa 6th
|
| 996.090
|
16/9
|
m7
|
wa 7th
|
| 1109.775
|
243/128
|
M7
|
lawa 7th
|
| 1200.000
|
2/1
|
P8
|
wa 8ve
|
We then look at intervals of 5:
Classical (yo, gu)
| Cents
|
Ratio
|
FJS Name
|
Color name
|
| 21.506
|
81/80
|
P15
|
gu 1sn
|
| 111.731
|
16/15
|
m25
|
gu 2nd
|
| 182.404
|
10/9
|
M25
|
yo 2nd
|
| 315.641
|
6/5
|
m35
|
gu 3rd
|
| 386.314
|
5/4
|
M35
|
yo 3rd
|
| 519.551
|
27/20
|
P45
|
gu 4th
|
| 590.224
|
45/32
|
A45
|
yo 4th
|
| 609.776
|
64/45
|
d55
|
gu 5th
|
| 680.449
|
40/27
|
P55
|
yo 5th
|
| 813.686
|
8/5
|
m65
|
gu 6th
|
| 884.359
|
5/3
|
M65
|
yo 6th
|
| 1017.596
|
9/5
|
m75
|
gu 7th
|
| 1088.269
|
15/8
|
M75
|
yo 7th
|
| 1178.494
|
160/81
|
P85
|
yo 8ve
|