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SKULO interval names: Difference between revisions

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i.e.,
i.e.,


19edo: P1 S1/sm2 m2 M2 SM2/sm3 m3 M3 SM3/s4 P4 A4 d5 P5 S5/sm6 m6 M6 SM6/sm7 m7 M7 SM7/s8 P8.
'''19edo''': P1 S1/sm2 m2 M2 SM2/sm3 m3 M3 SM3/s4 P4 A4 d5 P5 S5/sm6 m6 M6 SM6/sm7 m7 M7 SM7/s8 P8.


26edo: P1 S1 sm2 m2 M2 SM2 sm3 m3 M3 SM3 s4 P4 A4 SA4/sd5 d5 P5 S5 sm6 m6 M6 SM6 sm7 m7 M7 SM7 s8 P8.
'''26edo''': P1 S1 sm2 m2 M2 SM2 sm3 m3 M3 SM3 s4 P4 A4 SA4/sd5 d5 P5 S5 sm6 m6 M6 SM6 sm7 m7 M7 SM7 s8 P8.


These are meantone edos, wherein 81/80 is tempered out, so M3 ~ kM3 ~ 5/4, for example.
These are meantone edos, wherein 81/80 is tempered out, so M3 ~ kM3 ~ 5/4, for example.
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We can use K/k to label all the intervals of 10edo, 15edo, and 22edo, i.e.,
We can use K/k to label all the intervals of 10edo, 15edo, and 22edo, i.e.,


10edo: P1/m2 Km2/kM2 M2/m3 Km3/kM3 M3/P4 K4/k5 P5/m6 Km6/kM6 M6/m7 Km7/kM7 M7/P8.
'''10edo''': P1/m2 Km2/kM2 M2/m3 Km3/kM3 M3/P4 K4/k5 P5/m6 Km6/kM6 M6/m7 Km7/kM7 M7/P8.


15edo: P1/m2 Km2 kM2 M2/m3 Km3 kM3 M3/P4 K4 k5 P5/m6 Km6 kM6 M6/m7 Km7 kM7 M7/P8.
'''15edo''': P1/m2 Km2 kM2 M2/m3 Km3 kM3 M3/P4 K4 k5 P5/m6 Km6 kM6 M6/m7 Km7 kM7 M7/P8.


22edo: P1 m2 Km2 kM2 M2 m3 Km3 kM3 M3 P4 K4 kA4/Kd5 k5 P5 m6 Km6 kM6 M6 m7 Km7 kM7 M7 P8.
'''22edo''': P1 m2 Km2 kM2 M2 m3 Km3 kM3 M3 P4 K4 kA4/Kd5 k5 P5 m6 Km6 kM6 M6 m7 Km7 kM7 M7 P8.


64/63 is tempered out in these three edos, so M3 ~ SM3 ~ 9/7, for example.
64/63 is tempered out in these three edos, so M3 ~ SM3 ~ 9/7, for example.
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We can use U/u and N to give familiar labels to 17edo, or to label 10edo as a neutral system, i.e.,
We can use U/u and N to give familiar labels to 17edo, or to label 10edo as a neutral system, i.e.,


10edo: P1/m2 N2 M2/m3 N3 M3/P4 U4/u5 P5/m6 N6 M6/m7 N7 M7/P8.
'''10edo''': P1/m2 N2 M2/m3 N3 M3/P4 U4/u5 P5/m6 N6 M6/m7 N7 M7/P8.


17edo: P1 m2 N2 M2 m3 N3 M3 P4 U4 u5 m6 N6 M6 m7 N7 M7 P8.
'''17edo''': P1 m2 N2 M2 m3 N3 M3 P4 U4 u5 m6 N6 M6 m7 N7 M7 P8.


== SKU ==
== SKU ==
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We can use a combination of U/u and N and S/s to label 24edo, 31edo, 38edo, and 45edo.
We can use a combination of U/u and N and S/s to label 24edo, 31edo, 38edo, and 45edo.


24edo: P1 S1/U1/sm2 m2 N2 M2 SM2/sm3 m3 N3 M3 SM3/s4 P4 U4 A4/d5 u5 P5 S5/sm6 m6 N6 M6 SM6/sm7 m7 N7 M7 SM7/u8/s8 P8.
'''24edo''': P1 S1/U1/sm2 m2 N2 M2 SM2/sm3 m3 N3 M3 SM3/s4 P4 U4 A4/d5 u5 P5 S5/sm6 m6 N6 M6 SM6/sm7 m7 N7 M7 SM7/u8/s8 P8.


31edo: P1 S1/U1 sm2 m2 N2 M2 SM2 sm3 m3 N3 M3 SM3 s4 P4 U4 A4 d5 u5 P5 S5 sm6 m6 N6 M6 SM6 sm7 m7 N7 M7 SM7 s8/u8 P8.
'''31edo''': P1 S1/U1 sm2 m2 N2 M2 SM2 sm3 m3 N3 M3 SM3 s4 P4 U4 A4 d5 u5 P5 S5 sm6 m6 N6 M6 SM6 sm7 m7 N7 M7 SM7 s8/u8 P8.


38edo: P1 S1 A1 sm2 m2 N2 M2 SM2 A2/d3 sm3 m3 N3 M3 SM3 d4 s4 P4 U4 A4 SA4/sd5 d5 u5 P5 S5 A5 sm6 m6 N6 M6 SM6 A6/d7 sm7 m7 N7 M7 SM7 d8 s8 P8.
'''38edo''': P1 S1 A1 sm2 m2 N2 M2 SM2 A2/d3 sm3 m3 N3 M3 SM3 d4 s4 P4 U4 A4 SA4/sd5 d5 u5 P5 S5 A5 sm6 m6 N6 M6 SM6 A6/d7 sm7 m7 N7 M7 SM7 d8 s8 P8.


45edo: P1 S1/U1 uA1 A1 sm2 m2 n2 N2 M2 SM2 A2/d3 sm3 m3 n3 N3 M3 SM3 d4 s4 P4 U4 A4 SA4 sd5 d5 u5 P5 S5 A5 sm6 m6 n6 N6 M6 SM6 A6/d7 sm7 m7 n7 N7 M7 SM7 d8 Ud8 s8/u8 P8.
'''45edo''': P1 S1/U1 uA1 A1 sm2 m2 n2 N2 M2 SM2 A2/d3 sm3 m3 n3 N3 M3 SM3 d4 s4 P4 U4 A4 SA4 sd5 d5 u5 P5 S5 A5 sm6 m6 n6 N6 M6 SM6 A6/d7 sm7 m7 n7 N7 M7 SM7 d8 Ud8 s8/u8 P8.


We have to use chromatic interval names in 38edo and 45edo, like in many larger edos.
We have to use chromatic interval names in 38edo and 45edo, like in many larger edos.
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We can use a combination of K/k and S/s to label the intervals of 29edo, i.e.,
We can use a combination of K/k and S/s to label the intervals of 29edo, i.e.,


29edo: P1 K1/S1/sm2 m2 Km2 kM2 M2 SM2/sm3 m3 Km3 kM3 M3 SM3/s4 P4 K4 kA4/d5 A4/Kd5 k5 P5 S5/sm6 m6 Km6 kM6 M6 SM6/sm7 m7 Km7 kM7 M7 SM7/S8/k8 P8.
'''29edo''': P1 K1/S1/sm2 m2 Km2 kM2 M2 SM2/sm3 m3 Km3 kM3 M3 SM3/s4 P4 K4 kA4/d5 A4/Kd5 k5 P5 S5/sm6 m6 Km6 kM6 M6 SM6/sm7 m7 Km7 kM7 M7 SM7/S8/k8 P8.


We can use a combination of all the prefixes introduced so far to label the intervals of edos which do not temper out 64/63 or 81/80, i.e.,
We can use a combination of all the prefixes introduced so far to label the intervals of edos which do not temper out 64/63 or 81/80, i.e.,


34edo: P1 K1/S1/sm2 m2 Km2 N2 kM2 M2 SM2/sm3 m3 Km3 N3 kM3 M3 SM3/s4 P4 K4 U4/d5 kA4/Kd5 A4/u5 k5 P5 S5/sm6 m6 Km6 N6 kM6 M6 SM6/sm7 m7 Km7 N7 kM7 M7 SM7/k8/s8 P8.
'''34edo''': P1 K1/S1/sm2 m2 Km2 N2 kM2 M2 SM2/sm3 m3 Km3 N3 kM3 M3 SM3/s4 P4 K4 U4/d5 kA4/Kd5 A4/u5 k5 P5 S5/sm6 m6 Km6 N6 kM6 M6 SM6/sm7 m7 Km7 N7 kM7 M7 SM7/k8/s8 P8.


41edo: P1 K1/S1 U1/sm2 m2 Km2 N2 kM2 M2 SM2 sm3 m3 Km3 N3 kM3 M3 SM3 s4 P4 K4 U4 kA4 Kd5 u5 k5 P5 S5 sm6 m6 Km6 N6 kM6 M6 SM6 sm7 m7 Km7 N7 kM7 M7 SM7/u8 k8/s8 P8.
'''41edo''': P1 K1/S1 U1/sm2 m2 Km2 N2 kM2 M2 SM2 sm3 m3 Km3 N3 kM3 M3 SM3 s4 P4 K4 U4 kA4 Kd5 u5 k5 P5 S5 sm6 m6 Km6 N6 kM6 M6 SM6 sm7 m7 Km7 N7 kM7 M7 SM7/u8 k8/s8 P8.


46edo: P1 K1/S1 U1/sm2 m2 Km2 n2 N2 kM2 M2 SM2 sm3 m3 Km3 n3 N3 kM3 M3 SM3 s4 P4 K4 U4 uA4/d5 kA4/Kd5 A4/Ud5 SA4/u5 k5 P5 S5 sm6 m6 Km6 n6 N6 kM6 M6 SM6 sm7 m7 Km7 n7 N7 kM7 M7 SM7/u8 k8/s8 P8.
'''46edo''': P1 K1/S1 U1/sm2 m2 Km2 n2 N2 kM2 M2 SM2 sm3 m3 Km3 n3 N3 kM3 M3 SM3 s4 P4 K4 U4 uA4/d5 kA4/Kd5 A4/Ud5 SA4/u5 k5 P5 S5 sm6 m6 Km6 n6 N6 kM6 M6 SM6 sm7 m7 Km7 n7 N7 kM7 M7 SM7/u8 k8/s8 P8.


An astute reader, or a fan of 27edo, may be wondering what about 27edo? 27edo can be labelled using K/k and U/u (and N), though for 27edo this means using the 27e mapping, where 11/8 is mapped to it's second best approximation. 27e is generally preferred to 27p (patent 27edo, using the best approximation of 11/8 as well as the other primes in the 11-limit).
An astute reader, or a fan of 27edo, may be wondering what about 27edo? 27edo can be labelled using K/k and U/u (and N), though for 27edo this means using the 27e mapping, where 11/8 is mapped to it's second best approximation. 27e is generally preferred to 27p (patent 27edo, using the best approximation of 11/8 as well as the other primes in the 11-limit).
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