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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
Line 76: Line 83:
|  
|  
|-
|-
| Major third (M3)
| Augmented third (A3)
| Augmented third (A3)
| 447.6
| 447.6
Line 82: Line 90:
| 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
Line 91: Line 99:
| 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
Line 109: Line 120:
| 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
Retrieved from "https://en.xen.wiki/w/Porcupine_intervals"