SKULO interval names: Difference between revisions

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'''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.

== K/k, komma-wide/komma-narrow, klassisch intervals ==

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|88/81

|-

|uM2/n2

|uM2/N2

|unt-maj 2nd / gtr-ntl 2nd

|unter major second / greater neutral second

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'''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) because it has lower 11-limit error overall:

'''27edo''': P1 K1/m2 U1/Km2 N2 kM2 M2 m3 Km3 N3 kM3 M3 P4 K4/d5 U4/Kd5 kA4/u5 A4/k5 P5 m6 Km6 N6 kM6 M6 m7 Km7 N7 kM7/u8 M7/k8 P8.

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O alters by 45/44, the undecimal 1/5th tone, where oM2 is 11/10, and Om3 is 40/33.

== L/l, Large/little ==

=== L/l, Large/little ===

A capital 'L' signals alteration upward by 896/891, and a lower case 'u' signals alteration downward by 896/891. The alteration is typically applied upward for positive Pythagorean intervals, and downward for negative Pythagorean intervals.

14/11 is a large major third, LM3, and 11/7 is a little minor sixth, lm6.

== O/o, On/off, oceanic ==

=== O/o, On/off, oceanic ===

A capital 'O' signals alteration upward by 45/44, and a lower case 'o' signals alteration downward by 45/44. The alteration is typically applied downward for positive Pythagorean intervals, and upward for negative Pythagorean intervals.

11/10 is an off major second, or oceanic major second, oM2, and 40/33 is an on minor third, or oceanic minor third, Om3.

[[Category:Interval naming]]

@@ Line 22: / Line 22: @@
 '''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.
 == K/k, komma-wide/komma-narrow, klassisch intervals ==
@@ Line 98: / Line 98: @@
 |88/81
 |-
-|uM2/n2
+|uM2/N2
 |unt-maj 2nd / gtr-ntl 2nd
 |unter major second  / greater neutral second
@@ Line 362: / Line 362: @@
 '''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) because it has lower 11-limit error overall:
 '''27edo''': P1 K1/m2 U1/Km2 N2 kM2 M2 m3 Km3 N3 kM3 M3 P4 K4/d5 U4/Kd5 kA4/u5 A4/k5 P5 m6 Km6 N6 kM6 M6 m7 Km7 N7 kM7/u8 M7/k8 P8.
@@ Line 373: / Line 373: @@
 O alters by 45/44, the undecimal 1/5th tone, where oM2 is 11/10, and Om3 is 40/33.
-== L/l, Large/little ==
+=== L/l, Large/little ===
 A capital 'L' signals alteration upward by 896/891, and a lower case 'u' signals alteration downward by 896/891. The alteration is typically applied upward for positive Pythagorean intervals, and downward for negative Pythagorean intervals.
 /11 is a large major third, LM3, and 11/7 is a little minor sixth, lm6.
-== O/o, On/off, oceanic ==
+=== O/o, On/off, oceanic ===
 A capital 'O' signals alteration upward by 45/44, and a lower case 'o' signals alteration downward by 45/44. The alteration is typically applied downward for positive Pythagorean intervals, and upward for negative Pythagorean intervals.
 /10 is an off major second, or oceanic major second, oM2, and 40/33 is an on minor third, or oceanic minor third, Om3.
 [[Category:Interval naming]]