Porcupine intervals: Difference between revisions

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This is one possible naming and organization system for intervals of [[porcupine]] temperament. It is based on the Porcupine[7] scale, or equivalently on the [[val]] {{val| 7 11 16 }}.
These are the intervals found in porcupine temperament.


In [[22edo]], all the neighboring intervals on this chart that are shown as about 20 cents apart are actually the same. For example, the augmented third (9/7) and the diminished fourth (14/11) are both the same interval (8\22) in 22edo. This corresponds to 99/98 being tempered out in 22edo.
In [[22edo]], all the neighboring intervals on this chart that are shown as about 20 cents apart are actually the same. For example, the augmented third (9/7) and the diminished fourth (14/11) are both the same interval (8\22) in 22edo. This corresponds to 99/98 being tempered out in 22edo.
Line 5: Line 5:
In [[15edo]], on the other hand, the intervals that are shown as about 40 cents apart are actually the same. For example, the augmented third (9/7), is now the same as a '''minor''' fourth (4/3) rather than a diminished one. That is because 28/27 is tempered out in 15edo.
In [[15edo]], on the other hand, the intervals that are shown as about 40 cents apart are actually the same. For example, the augmented third (9/7), is now the same as a '''minor''' fourth (4/3) rather than a diminished one. That is because 28/27 is tempered out in 15edo.


{| class="wikitable right-2 center-4"
{| class="wikitable right-3 center-5"
|-
|-
! Name
! Name ([[Pergen|ups and downs]])
! Name (1L 6s (onyx))
! Size*
! Size*
! Ratio
! Ratio
Line 13: Line 14:
! Comments
! Comments
|-
|-
! colspan="4" | Unisons
! colspan="6" | Unisons
!
|-
|-
| Perfect unison (P1)
| Perfect unison (P1)
| Perfect unison (P1)
| 0.0
| 0.0
Line 22: Line 23:
|  
|  
|-
|-
| Up unison (^1)
| Augmented unison (A1)
| Augmented unison (A1)
| 61.1
| 61.1
| 81/80~36/35~33/32~25/24
| 81/80~36/35~33/32~25/24
| -7
| -7
| [[Cluster temperament #porcupine(fish)|And other ratios, of course]]
| [[Cluster temperament #porcupine(fish)|Among other ratios]]
|-
|-
! colspan="4" | Seconds
! colspan="6" | Seconds
!
|-
|-
| Upminor second (^m2)
| Diminished second (d2)
| Diminished second (d2)
| 101.6
| 101.6
Line 37: Line 39:
|  
|  
|-
|-
| Downmajor second (vM2)
| Perfect second (P2)
| Perfect second (P2)
| 162.7
| 162.7
| 12/11~11/10~10/9~35/32
| 12/11~11/10~10/9~35/32
| 1
| 1
| Rather than "minor 2nd"
|  
|-
|-
| Major second (M2)
| Augmented second (A2)
| Augmented second (A2)
| 223.8
| 223.8
| 9/8~8/7
| 9/8~8/7
| -6
| -6
| Rather than "major 2nd"
|  
|-
|-
| Upmajor second (^M2)
| Double-augmented second (AA2)
| Double-augmented second (AA2)
| 284.9
| 284.9
Line 55: Line 60:
| Also "subminor third"
| Also "subminor third"
|-
|-
! colspan="4" | Thirds
! colspan="6" | Thirds
!
|-
|-
| Minor third (m3)
| Diminished third (d3)
| Diminished third (d3)
| 264.3
| 264.3
Line 64: Line 69:
| Also "supermajor second"
| Also "supermajor second"
|-
|-
| Upminor third (^m3)
| Minor third (m3)
| Minor third (m3)
| 325.4
| 325.4
Line 70: Line 76:
|  
|  
|-
|-
| Downmajor third (vM3)
| Major third (M3)
| Major third (M3)
| 386.5
| 386.5
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|  
|  
|-
|-
| Major third (M3)
| Augmented third (A3)
| Augmented third (A3)
| 447.6
| 447.6
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| Also "subminor fourth"
| Also "subminor fourth"
|-
|-
! colspan="4" | Fourths
! colspan="6" | Fourths
!
|-
|-
| Down fourth (v4)
| Diminished fourth (d4)
| Diminished fourth (d4)
| 427.0
| 427.0
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| Also "supermajor third"
| Also "supermajor third"
|-
|-
| Perfect fourth (P4)
| Minor fourth (m4)
| Minor fourth (m4)
| 488.1
| 488.1
| 4/3
| 4/3
| 3
| 3
| Rather than "perfect fourth"
|  
|-
|-
| Upfourth (^4)
| Major fourth (M4)
| Major fourth (M4)
| 549.2
| 549.2
Line 103: Line 113:
|  
|  
|-
|-
| Downaugmented fourth (vA4)
| Augmented fourth (A4)
| Augmented fourth (A4)
| 610.3
| 610.3
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| Also "subminor fifth"
| Also "subminor fifth"
|-
|-
! colspan="4" | Fifths
! colspan="6" | Fifths
!
|-
|-
| Updiminished fifth (^d5)
| Diminished fifth (d5)
| Diminished fifth (d5)
| 589.7
| 589.7
Line 118: Line 129:
| Also "supermajor fourth"
| Also "supermajor fourth"
|-
|-
| Down fifth (v5)
| Minor fifth (m5)
| Minor fifth (m5)
| 650.8
| 650.8
Line 124: Line 136:
|  
|  
|-
|-
| Perfect fifth (P5)
| Major fifth (M5)
| Major fifth (M5)
| 711.9
| 711.9
| 3/2
| 3/2
| -3
| -3
| Rather than "perfect fifth"
|  
|-
|-
| Up fifth (^5)
| Augmented fifth (A5)
| Augmented fifth (A5)
| 773.0
| 773.0
Line 136: Line 150:
| Also "subminor sixth"
| Also "subminor sixth"
|-
|-
! colspan="4" | Sixths
! colspan="6" | Sixths
!
|-
|-
| Minor sixth (m6)
| Diminished sixth (d6)
| Diminished sixth (d6)
| 752.4
| 752.4
Line 145: Line 159:
| Also "supermajor fifth"
| Also "supermajor fifth"
|-
|-
| Upminor sixth (^m6)
| Minor sixth (m6)
| Minor sixth (m6)
| 813.5
| 813.5
Line 151: Line 166:
|  
|  
|-
|-
| Downmajor sixth (vM6)
| Major sixth (M6)
| Major sixth (M6)
| 874.6
| 874.6
Line 157: Line 173:
|  
|  
|-
|-
| Major sixth (M6)
| Augmented sixth (A6)
| Augmented sixth (A6)
| 935.7
| 935.7
Line 163: Line 180:
| Also "subminor seventh"
| Also "subminor seventh"
|-
|-
! colspan="4" | Sevenths
! colspan="6" | Sevenths
!
|-
|-
| Downminor seventh (vm7)
| Double-diminished seventh (dd7)
| Double-diminished seventh (dd7)
| 915.1
| 915.1
Line 172: Line 189:
| Also "supermajor sixth"
| Also "supermajor sixth"
|-
|-
| Minor seventh (m7)
| Diminished seventh (d7)
| Diminished seventh (d7)
| 976.2
| 976.2
| 7/4~16/9
| 7/4~16/9
| 6
| 6
| Rather than "minor 7th"
|  
|-
|-
| Upminor seventh (^m7)
| Perfect seventh (P7)
| Perfect seventh (P7)
| 1037.3
| 1037.3
| 9/5~11/6
| 9/5~11/6
|  -1
|  -1
| Rather than "major 7th"
|  
|-
|-
| Downmajor seventh (vM7)
| Augmented seventh (A7)
| Augmented seventh (A7)
| 1098.4
| 1098.4
Line 190: Line 210:
|  
|  
|-
|-
! colspan="4" | Octaves
! colspan="6" | Octaves
!
|-
|-
| Down octave (v8)
| Diminished octave (d8)
| Diminished octave (d8)
| 1138.9
| 1138.9
Line 199: Line 219:
|  
|  
|-
|-
| Perfect octave (P8)
| Perfect octave (P8)
| Perfect octave (P8)
| 1200.0
| 1200.0
Line 205: Line 226:
|  
|  
|-
|-
| Up octave (^8)
| Augmented octave (A8)
| Augmented octave (A8)
| 1261.1
| 1261.1

Latest revision as of 07:26, 3 June 2025

These are the intervals found in porcupine temperament.

In 22edo, all the neighboring intervals on this chart that are shown as about 20 cents apart are actually the same. For example, the augmented third (9/7) and the diminished fourth (14/11) are both the same interval (8\22) in 22edo. This corresponds to 99/98 being tempered out in 22edo.

In 15edo, on the other hand, the intervals that are shown as about 40 cents apart are actually the same. For example, the augmented third (9/7), is now the same as a minor fourth (4/3) rather than a diminished one. That is because 28/27 is tempered out in 15edo.

Name (ups and downs) Name (1L 6s (onyx)) Size* Ratio Genspan Comments
Unisons
Perfect unison (P1) Perfect unison (P1) 0.0 1/1 0
Up unison (^1) Augmented unison (A1) 61.1 81/80~36/35~33/32~25/24 -7 Among other ratios
Seconds
Upminor second (^m2) Diminished second (d2) 101.6 21/20~16/15 8
Downmajor second (vM2) Perfect second (P2) 162.7 12/11~11/10~10/9~35/32 1
Major second (M2) Augmented second (A2) 223.8 9/8~8/7 -6
Upmajor second (^M2) Double-augmented second (AA2) 284.9 Close to 13/11 -13 Also "subminor third"
Thirds
Minor third (m3) Diminished third (d3) 264.3 7/6 9 Also "supermajor second"
Upminor third (^m3) Minor third (m3) 325.4 6/5~11/9 2
Downmajor third (vM3) Major third (M3) 386.5 5/4 -5
Major third (M3) Augmented third (A3) 447.6 9/7 (close to 13/10) -12 Also "subminor fourth"
Fourths
Down fourth (v4) Diminished fourth (d4) 427.0 14/11 10 Also "supermajor third"
Perfect fourth (P4) Minor fourth (m4) 488.1 4/3 3
Upfourth (^4) Major fourth (M4) 549.2 11/8 -4
Downaugmented fourth (vA4) Augmented fourth (A4) 610.3 10/7 -11 Also "subminor fifth"
Fifths
Updiminished fifth (^d5) Diminished fifth (d5) 589.7 7/5 11 Also "supermajor fourth"
Down fifth (v5) Minor fifth (m5) 650.8 16/11 4
Perfect fifth (P5) Major fifth (M5) 711.9 3/2 -3
Up fifth (^5) Augmented fifth (A5) 773.0 11/7 -10 Also "subminor sixth"
Sixths
Minor sixth (m6) Diminished sixth (d6) 752.4 14/9 (close to 20/13) 12 Also "supermajor fifth"
Upminor sixth (^m6) Minor sixth (m6) 813.5 8/5 5
Downmajor sixth (vM6) Major sixth (M6) 874.6 5/3 -2
Major sixth (M6) Augmented sixth (A6) 935.7 12/7 -9 Also "subminor seventh"
Sevenths
Downminor seventh (vm7) Double-diminished seventh (dd7) 915.1 Close to 22/13 13 Also "supermajor sixth"
Minor seventh (m7) Diminished seventh (d7) 976.2 7/4~16/9 6
Upminor seventh (^m7) Perfect seventh (P7) 1037.3 9/5~11/6 -1
Downmajor seventh (vM7) Augmented seventh (A7) 1098.4 15/8 -8
Octaves
Down octave (v8) Diminished octave (d8) 1138.9 21/11~35/18~160/81 7
Perfect octave (P8) Perfect octave (P8) 1200.0 2/1 0
Up octave (^8) Augmented octave (A8) 1261.1 81/40~45/22~33/16~25/12 -7
  • In cents, 11-limit POTE tuning of porcupine, where the generator is ~162.7¢.

porcupine_interval_matrix_pote.png

porcupine_interval_matrix_22edo.png

See also

Retrieved from "https://en.xen.wiki/index.php?title=Porcupine_intervals&oldid=198554"