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SKULO interval names: Difference between revisions

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SKULO names are the successor to [[SHEFKHED interval names]]. SKULO is an [[Extended-diatonic interval names|extended-diatonic]] system, wherein prefixes are added for sub-chroma alterations from standard Pythagorean diatonic intervals.
SKULO interval names are the successor to [[FKH Extended-diatonic Interval Names]]. SKULO is an [[Extended-diatonic interval names|extended-diatonic]] system, wherein prefixes are added for sub-chroma alterations from standard Pythagorean diatonic intervals. SKULO also exists as a notation system based on a Pythagorean scale on a diatonic staff, with accidentals based on the letters representing the alterations. SKULO interval names observe diatonic interval arithmetic and follow the ''well-ordered'' interval naming scheme, wherein for the interval names of a tuning system no larger interval is named with reference to a smaller interval class.


S signals the septimal intervals, altering a Pythagorean interval by the septimal or Archytas comma, [[64/63]].
S signals the septimal intervals, altering a Pythagorean interval by the septimal or Archytas comma, [[64/63]].
Line 52: Line 52:
== SKU ==
== SKU ==
{| class="wikitable"
{| class="wikitable"
|+Basic SKU extended diatonic intervals
|+Basic SKU extended-diatonic intervals
!Short-form
!Short-form
!Mid-form
!Long-form
!Long-form
!JI interval represented
!JI interval represented
|-
|-
|P1
|P1
|prf 1st
|perfect unison
|perfect unison
|1/1
|1/1
|-
|-
|K1
|K1
|k-wde 1st
|komma-wide/comma-wide unison
|komma-wide/comma-wide unison
|81/80
|81/80
|-
|-
|S1
|S1
|sup 1st
|super unison
|super unison
|64/63
|64/63
|-
|-
|U1
|U1
|ubr 1st
|uber unison
|uber unison
|33/32
|33/32
|-
|(kkA1)
|(klassisch/classic augmented unison)
|(25/24)
|-
|kA1
|komma-narrow/comma-narrow augmented unison
|135/128
|-
|A1
|augmented unison
|2187/2048
|-
|SA1
|super augmented unison
|243/224
|-
|-
|sm2
|sm2
|sub-min 2nd
|subminor second
|subminor second
|28/27
|28/27
|-
|-
|m2
|m2
|min 2nd
|minor second
|minor second
|256/243
|256/243
|-
|-
|Km2
|Km2
|kla-min 2nd
|klassisch/classic minor second
|klassisch/classic minor second
|16/15
|16/15
|-
|-
|Um2/n2
|Um2/n2
|ubr-min 2nd / lsr-ntl 2nd
|uber minor second / lesser neutral second
|uber minor second / lesser neutral second
|88/81
|88/81
|-
|-
|uM2/N2
|uM2/N2
|unt-maj 2nd / gtr-ntl 2nd
|unter major second  / greater neutral second
|unter major second  / greater neutral second
|12/11
|12/11
|-
|-
|kM2
|kM2
|k-nrw 2nd
|komma-narrow/comma narrow major second, klassisch/classic major second
|komma-narrow/comma narrow major second
|10/9
|10/9
|-
|-
|M2
|M2
|maj 2nd
|major second
|major second
|9/8
|9/8
|-
|-
|SM2
|SM2
|sup-maj 2nd
|supermajor second
|supermajor second
|8/7
|8/7
|-
|-
|sm3
|sm3
|sub-min 3rd
|subminor third
|subminor third
|7/6
|7/6
|-
|-
|m3
|m3
|min 3rd
|minor third
|minor third
|32/27
|32/27
|-
|-
|Km3
|Km3
|kla-min 3rd
|klassisch/classic minor third
|klassisch/classic minor third
|6/5
|6/5
|-
|-
|Um3/n3
|Um3/n3
|ubr-min 3rd / lsr-ntl 3rd
|uber minor third / lesser neutral third
|uber minor third / lesser neutral third
|11/9
|11/9
|-
|-
|uM3/N3
|uM3/N3
|unt-maj 3rd / gtr-ntl 3rd
|unter major third / greater neutral third
|unter major third / greater neutral third
|27/22
|27/22
|-
|-
|kM3
|kM3
|kla-maj 3rd
|klassisch/classic major third
|klassisch/classic major third
|5/4
|5/4
|-
|-
|M3
|M3
|maj 3rd
|major third
|major third
|81/64
|81/64
|-
|-
|SM3
|SM3
|sup-maj 3rd
|supermajor third
|supermajor third
|9/7
|9/7
|-
|-
|s4
|s4
|sub 4th
|sub fourth
|sub fourth
|21/16
|21/16
|-
|-
|P4
|P4
|prf 4th
|perfect fourth
|perfect fourth
|4/3
|4/3
|-
|-
|K4
|K4
|k-wde 4th
|komma-wide/comma-wide fourth
|komma-wide/comma-wide fourth
|27/20
|27/20
|-
|-
|U4
|U4
|ubr 4th (/ lsr-ntl 4th)
|uber fourth (/ lesser neutral fourth)
|uber fourth (/ lesser neutral fourth)
|11/8
|11/8
|-
|-
|uA4
|uA4
|unt-aug 4th (/ gtr-ntl 4th)
|unter augmented fourth (/ greater neutral fourth)
|unter augmented fourth (/ greater neutral fourth)
|243/176
|243/176
|-
|(kkA4)
|(klassisch/classic augmented fourth)
|(25/18)
|-
|-
|kA4
|kA4
|kla-aug 4th
|komma-narrow/comma-narrow augmented fourth
|klassisch/classic augmented fourth
|45/32
|45/32
|-
|-
|A4
|A4
|aug 4th
|augmented fourth
|augmented fourth
|729/512
|729/512
|-
|-
|SA4
|SA4
|sup-aug 4th
|super augmented fourth
|super augmented fourth
|81/56
|81/56
|-
|-
|sd5
|sd5
|sub-dim 5th
|sub diminished fifth
|sub diminished fifth
|112/81
|112/81
|-
|-
|d5
|d5
|dim 5th
|diminished fifth
|diminished fifth
|1024/729
|1024/729
|-
|-
|Kd5
|Kd5
|kla-dim 5th
|komma-wide/comma-wide diminished fifth
|klassisch/classic diminished fifth
|64/45
|64/45
|-
|(KKd5)
|(klassich/classic diminished fifth)
|(36/25)
|-
|-
|Ud5
|Ud5
|ubr-dim 5th (/lsr-ntl 5th)
|uber diminished fifth (/lesser neutral fifth)
|uber diminished fifth (/lesser neutral fifth)
|352/243
|352/243
|-
|-
|u5
|u5
|unt 5th (/gtr-ntl 5th)
|unter fifth (/greater neutral fifth)
|unter fifth (/greater neutral fifth)
|16/11
|16/11
|-
|-
|k5
|k5
|k-nrw 5th
|komma-narrow/comma-narrow fifth
|komma-narrow/comma-narrow fifth
|40/27
|40/27
|-
|-
|P5
|P5
|prf 5th
|perfect fifth
|perfect fifth
|3/2
|3/2
|-
|-
|S5
|S5
|sup 5th
|super fifth
|super fifth
|32/21
|32/21
|-
|-
|sm6
|sm6
|sub-min 6th
|subminor sixth
|subminor sixth
|14/9
|14/9
|-
|-
|m6
|m6
|min 6th
|minor sixth
|minor sixth
|128/81
|128/81
|-
|-
|Km6
|Km6
|kla-min 6th
|klassisch/classic minor sixth
|klassisch/classic minor sixth
|8/5
|8/5
|-
|-
|Um6/n6
|Um6/n6
|ubr-min 6th / lsr-ntl 6th
|uber minor sixth / lesser neutral sixth
|uber minor sixth / lesser neutral sixth
|44/27
|44/27
|-
|-
|uM6/N6
|uM6/N6
|unt-maj 6th / gtr-ntl 6th
|unter major sixth / greater neutral sixth
|unter major sixth / greater neutral sixth
|18/11
|18/11
|-
|-
|kM6
|kM6
|kla-maj 6th
|klassisch/classic major sixth
|klassisch/classic major sixth
|5/3
|5/3
|-
|-
|M6
|M6
|maj 6th
|major sixth
|major sixth
|27/16
|27/16
|-
|-
|SM6
|SM6
|sup-maj 6th
|supermajor sixth
|supermajor sixth
|12/7
|12/7
|-
|-
|sm7
|sm7
|sub-min 7th
|subminor seventh
|subminor seventh
|7/4
|7/4
|-
|-
|m7
|m7
|min 7th
|minor seventh
|minor seventh
|16/9
|16/9
|-
|-
|Km7
|Km7
|kla-min 7th
|komma-wide/comma-wide minor seventh / klassisch/classic minor seventh
|komma-wide/comma-wide minor seventh / klassisch/classic minor seventh
|9/5
|9/5
|-
|-
|Um7/n7
|Um7/n7
|ubr-min 7th / lsr-ntl 7th
|uber minor seventh / lesser neutral seventh
|uber minor seventh / lesser neutral seventh
|11/6
|11/6
|-
|-
|uM7/N7
|uM7/N7
|unt-maj 7th / gtr-ntl 7th
|unter minor seventh / greater neutral seventh
|unter minor seventh / greater neutral seventh
|81/44
|81/44
|-
|-
|kM7
|kM7
|kla-maj 7th
|klassisch/classic major seventh
|klassisch/classic major seventh
|15/8
|15/8
|-
|-
|M7
|M7
|maj 7th
|major seventh
|major seventh
|243/128
|243/128
|-
|-
|SM7
|SM7
|sup-maj 7th
|supermajor seventh
|supermajor seventh
|27/14
|27/14
|-
|sd8
|sub diminished octave
|448/243
|-
|d8
|diminished octave
|4096/2187
|-
|Kd8
|komma-wide/comma-wide diminished octave
|256/135
|-
|(KKd8)
|(klassisch/classic diminished octave)
|48/25
|-
|-
|u8
|u8
|unt 8ve
|unter octave
|unter octave
|64/33
|64/33
|-
|-
|s8
|s8
|sub 8ve
|sub octave
|sub octave
|63/32
|63/32
|-
|-
|k8
|k8
|k-nrw 8ve
|komma-narrow/comma-narrow octave
|komma-narrow/comma-narrow octave
|160/81
|160/81
|-
|-
|P8
|P8
|pft 8ve
|perfect octave
|perfect octave
|2/1
|2/1
Line 358: Line 341:
'''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/d5 Kd5/A4 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.
Line 446: Line 429:


'''10edo:''' P1 Tm2/tM2 SM2/sm3 Tm3/tM3 SM3/s4 T4/t5 S5/sm6 Tm6/tM6 SM6/sm7 Tm7/tM7 P8.
'''10edo:''' P1 Tm2/tM2 SM2/sm3 Tm3/tM3 SM3/s4 T4/t5 S5/sm6 Tm6/tM6 SM6/sm7 Tm7/tM7 P8.
'''15edo:''' P1 Km2 kM2 SM2/sm3 Km3 kM3 SM3/s4 K4 k5 S5/sm6 Km6 kM6 SM6/sm7 Km7 kM7 P8.


'''27edo:''' P1 sm2 Km2 Tm2/tM2 kM2 SM2 sm3 Km3 Tm3/tM3 kM3 SM3 P4 K4 T4 t5 k5 P5 sm6 Km6 tM6/Tm6 kM6 SM6 sm7 Km7 Tm7/tM7 kM7 SM7 P8.
'''27edo:''' P1 sm2 Km2 Tm2/tM2 kM2 SM2 sm3 Km3 Tm3/tM3 kM3 SM3 P4 K4 T4 t5 k5 P5 sm6 Km6 tM6/Tm6 kM6 SM6 sm7 Km7 Tm7/tM7 kM7 SM7 P8.
Line 472: Line 457:
|1
|1
|54.55
|54.55
|minor second / comma-wide unison
|minor 2nd, comma-wide unison, (classic augmented unison)
|m2/K1
|m2, K1, (kkA1)
|256/243, 81/80
|256/243, 81/80, (25/24)
|sub minor second / uber unison
|subminor 2nd, uber unison
|sm2/U1
|sm2, U1
|28/27, 33/32
|28/27, 33/32
|-
|-
|2
|2
|109.09
|109.09
|classic minor second
|classic minor 2nd, comma-narrow augmented unison
|Km2
|Km2, kA1,
|16/15
|16/15, 135/128
|lesser neutral second
|lesser neutral 2nd, unter augmented unison
|n2
|n2, uA1
|88/81
|88/81, 729/704
|-
|-
|3
|3
|163.64
|163.64
|classic major second
|classic/comma-narrow major 2nd, augmented unison
|kM2
|kM2, A1
|10/9
|10/9, 2187/2048
|greater neutral second
|greater neutral 2nd, super augmented unison,
|N2
|N2, SA1
|12/11
|12/11, 243/224
|-
|-
|4
|4
|218.18
|218.18
|major second
|major 2nd
|M2
|M2
|9/8
|9/8
|super major second
|supermajor 2nd
|SM2
|SM2
|8/7
|8/7
Line 508: Line 493:
|5
|5
|272.73
|272.73
|minor third
|minor 3rd
|m3
|m3
|32/27
|32/27
|super minor third
|subminor 3rd
|sm3
|sm3
|7/6
|7/6
Line 517: Line 502:
|6
|6
|327.27
|327.27
|classic minor third
|classic minor 3rd
|Km3
|Km3
|6/5
|6/5
|lesser neutral third
|lesser neutral 3rd
|n3
|n3
|11/9
|11/9
Line 526: Line 511:
|7
|7
|381.82
|381.82
|classic major third
|classic major 3rd
|kM3
|kM3
|5/4
|5/4
|greater neutral third
|greater neutral 3rd
|N3
|N3
|27/22
|27/22
Line 535: Line 520:
|8
|8
|436.36
|436.36
|major third
|major 3rd
|M3
|M3
|81/64
|81/64
|super major third
|supermajor 3rd
|SM3
|SM3
|9/7
|9/7
Line 544: Line 529:
|9
|9
|490.91
|490.91
|perfect fourth
|perfect 4th
|P4
|P4
|4/3
|4/3
|sub fourth
|sub 4th
|s4
|s4
|21/16
|21/16
Line 553: Line 538:
|10
|10
|545.45
|545.45
|comma-wide fourth
|comma-wide 4th, (classic augmented 4th), diminished 5th
|K4
| K4, (kkA4), d5
|27/20
|27/20, (25/18), 729/512
|uber fourth
|uber 4th / lesser neutral 4th, sub diminished 5th
|U4
| U4/n4, sd5
|11/8
|11/8, 112/81
|-
|-
|11
|11
|600
|600
|classic augmented fourth
|comma-narrow augmented 4th, comma-wide diminished 5th
classic diminished fifth
|kA4, Kd5
|kA4
|45/32, 64/45
Kd5
|unter augmented 4th / greater neutral 4th, uber diminished 5th / lesser neutral 5th
|45/32
|uA4/N4, Ud5/n5
64/45
|243/176, 352/243
|unter augmented fourth
uber diminished fifth
|uA4
Ud5
|243/176
352/243
|-
|-
|12
|12
|654.55
|654.55
|comma-narrow fifth
|comma-narrow 5th, (classic diminished 5th), augmented 4th
|k5
|k5, (KKd5), A4
|40/27
|40/27, (32/25), 1024/729
|unter fifth
|unter 5th / greater neutral 5th, super augmented 4th
|u5
|u5/N5, SA4
|16/11
|16/11, 81/56
|-
|-
|13
|13
|709.09
|709.09
|perfect fifth
|perfect 5th
|P5
|P5
|3/2
|3/2
|super fifth
|super 5th
|S5
|S5
|32/21
|32/21
Line 595: Line 574:
|14
|14
|763.64
|763.64
|minor sixth
|minor 6th
|m6
|m6
|128/81
|128/81
|sub minor sixth
|subminor 6th
|sm6
|sm6
|14/9
|14/9
Line 604: Line 583:
|15
|15
|818.18
|818.18
|classic minor sixth
|classic minor 6th
|Km6
|Km6
|8/5
|8/5
|less neutral sixth
|lesser neutral 6th
|n6
|n6
|44/27
|44/27
Line 613: Line 592:
|16
|16
|872.73
|872.73
|classic major sixth
|classic major 6th
|kM6
|kM6
|5/3
|5/3
|greater neutral sixth
|greater neutral 6th
|N6
|N6
|18/11
|18/11
Line 622: Line 601:
|17
|17
|927.27
|927.27
|major sixth
|major 6th
|M6
|M6
|27/16
|27/16
|super major sixth
|supermajor 6th
|SM6
|SM6
|12/7
|12/7
Line 631: Line 610:
|18
|18
|981.82
|981.82
|minor seventh
|minor 7th
|m7
|m7
|16/9
|16/9
|sub minor seventh
|subminor 7th
|sm7
|sm7
|7/4
|7/4
Line 640: Line 619:
|19
|19
|1036.36
|1036.36
|classic minor seventh
|classic/comma-wide minor 7th, diminished 8ve
|Km7
|Km7, d8
|9/5
|9/5, 4096/2187
|lesser neutral seventh
| lesser neutral 7th, super diminished 8ve
|n7
|n7, sd8
|11/6
|11/6, 448/243
|-
|-
|20
|20
|1090.91
|1090.91
|classic major seventh
|classic major 7th, comma-wide diminished 8ve
|kM7
|kM7, Kd8
|15/8
|15/8, 256/135
|greater neutral seventh
|greater neutral 7th, unter diminished 8ve
|N7
|N7, ud8
|81/44
| 81/44, 1408/729
|-
|-
|21
|21
|1145.45
|1145.45
|major seventh / comma-narrow octave
|major 7th, comma-narrow 8ve, (classic diminished 8ve)
|M7 / k8
|M7, k8, (KKd8)
|243/128, 160/81
|243/128 , 160/81, (48/25)
|super major seventh / unter octave
|supermajor 7th, unter 8ve
|SM7/k8
|SM7, u8
|27/14, 64/33
|27/14, 64/33
|-
|-
|22
|22
|1200
|1200
|perfect octave
|perfect 8ve
|P8
|P8
|2/1
|2/1
|sub octave
|sub 8ve
|s8
|s8
|2/1, 63/32
|63/32
|}
|}


== WOFED interval names ==
==WOFED interval names ==
Well-ordered, functional, extended diatonic interval names.
Well-ordered, functional, extended diatonic interval names.


Line 685: Line 664:


'''94edo:''' P1 L1/R1 K1/S1 O1/H1 U1/hm2 uA1/sm2 oA1/lm2 kA1/m2 rA1/Rm2 A1/Km2 LA1/Om2 SA1/n2 N2 oM2 kM2 rM2 M2 LM2 SM2 HM2 hm3 sm3 lm3 m3 Rm3 Km3 Om3 n3 N3 oM3 kM3 rM3 M3 LM3 SM3 HM3 h4 s4 l4 P4 R4 K4 O4 U4/hd5 uA4/sd5 oA4/ld5 kA4/d5 rA4/Rd5 A4/Kd5 LA4/Od5 SA4/Ud5 HA4/u5 o5 k5 r5 P5 L5 S5 H5 hm6 sm6 lm6 m6 Rm6 Km6 Om6 n6 N6 oM6 kM6 rM6 M6 LM6 SM6 HM6 hm7 sm7 lm7 m7 Rm7 Km7 Om7 n7 N7/sd8 oM7/ld8 kM7/d8 rM7/Rd8 M7/Kd8 LM7/Od8 SM7/Ud8 HM7/u8 o8/h8 k8/s8 l8/r8 P8.
'''94edo:''' P1 L1/R1 K1/S1 O1/H1 U1/hm2 uA1/sm2 oA1/lm2 kA1/m2 rA1/Rm2 A1/Km2 LA1/Om2 SA1/n2 N2 oM2 kM2 rM2 M2 LM2 SM2 HM2 hm3 sm3 lm3 m3 Rm3 Km3 Om3 n3 N3 oM3 kM3 rM3 M3 LM3 SM3 HM3 h4 s4 l4 P4 R4 K4 O4 U4/hd5 uA4/sd5 oA4/ld5 kA4/d5 rA4/Rd5 A4/Kd5 LA4/Od5 SA4/Ud5 HA4/u5 o5 k5 r5 P5 L5 S5 H5 hm6 sm6 lm6 m6 Rm6 Km6 Om6 n6 N6 oM6 kM6 rM6 M6 LM6 SM6 HM6 hm7 sm7 lm7 m7 Rm7 Km7 Om7 n7 N7/sd8 oM7/ld8 kM7/d8 rM7/Rd8 M7/Kd8 LM7/Od8 SM7/Ud8 HM7/u8 o8/h8 k8/s8 l8/r8 P8.
With the addition of R/r, we can also label the intervals of 87edo where R=1, K=S=2, O=T=H=3, and U=4, with A=8 and m2=6, though R/r needs to be used in both directions.
[[Category:Interval naming]]
[[Category:Interval naming]]
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