Porcupine intervals: Difference between revisions

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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 (zarlino)
! Name ([[Pergen|ups and downs]])
! Name (heptatonic MOS)
! Name (1L 6s (onyx))
! Size*
! Size*
! Ratio
! Ratio
Line 14: Line 14:
! Comments
! Comments
|-
|-
!
! colspan="6" | Unisons
! colspan="4" | Unisons
!
|-
|-
|Perfect unison (P1)
| Perfect unison (P1)
| Perfect unison (P1)
| Perfect unison (P1)
| 0.0
| 0.0
Line 25: Line 23:
|  
|  
|-
|-
|Augmented unison (A1)
| 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="6" | Seconds
! colspan="4" | Seconds
!
|-
|-
|Minor second (m2)
| Upminor second (^m2)
| Diminished second (d2)
| Diminished second (d2)
| 101.6
| 101.6
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|  
|  
|-
|-
|Neutral second (n2)
| 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)
| 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"
|  
|-
|-
|Augmented second (A2)
| Upmajor second (^M2)
| Double-augmented second (AA2)
| Double-augmented second (AA2)
| 284.9
| 284.9
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| Also "subminor third"
| Also "subminor third"
|-
|-
!
! colspan="6" | Thirds
! colspan="4" | Thirds
!
|-
|-
|Wolf third (w3)
| Minor third (m3)
| Diminished third (d3)
| Diminished third (d3)
| 264.3
| 264.3
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| Also "supermajor second"
| Also "supermajor second"
|-
|-
|Minor third (m3)
| Upminor third (^m3)
| Minor third (m3)
| Minor third (m3)
| 325.4
| 325.4
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|  
|  
|-
|-
|Major third (M3)
| Downmajor third (vM3)
| Major third (M3)
| Major third (M3)
| 386.5
| 386.5
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|  
|  
|-
|-
|Augmented third (A3)
| Major third (M3)
| Augmented third (A3)
| Augmented third (A3)
| 447.6
| 447.6
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| Also "subminor fourth"
| Also "subminor fourth"
|-
|-
!
! colspan="6" | Fourths
! colspan="4" | Fourths
!
|-
|-
|Diminished fourth (d4)
| 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)
| Perfect fourth (P4)
| Minor fourth (m4)
| Minor fourth (m4)
| 488.1
| 488.1
| 4/3
| 4/3
| 3
| 3
| Rather than "perfect fourth"
|  
|-
|-
|Wolf fourth (w4)
| Upfourth (^4)
| Major fourth (M4)
| Major fourth (M4)
| 549.2
| 549.2
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|  
|  
|-
|-
|Augmented fourth (A4)
| Downaugmented fourth (vA4)
| Augmented fourth (A4)
| Augmented fourth (A4)
| 610.3
| 610.3
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| Also "subminor fifth"
| Also "subminor fifth"
|-
|-
!
! colspan="6" | Fifths
! colspan="4" | Fifths
!
|-
|-
|Diminished fifth (d5)
| Updiminished fifth (^d5)
| Diminished fifth (d5)
| Diminished fifth (d5)
| 589.7
| 589.7
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| Also "supermajor fourth"
| Also "supermajor fourth"
|-
|-
|Wolf fifth (w5)
| Down fifth (v5)
| Minor fifth (m5)
| Minor fifth (m5)
| 650.8
| 650.8
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|  
|  
|-
|-
|Perfect fifth (P5)
| Perfect fifth (P5)
| Major fifth (M5)
| Major fifth (M5)
| 711.9
| 711.9
| 3/2
| 3/2
| -3
| -3
| Rather than "perfect fifth"
|  
|-
|-
|Augmented fifth (A5)
| Up fifth (^5)
| Augmented fifth (A5)
| Augmented fifth (A5)
| 773.0
| 773.0
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| Also "subminor sixth"
| Also "subminor sixth"
|-
|-
!
! colspan="6" | Sixths
! colspan="4" | Sixths
!
|-
|-
|Diminished sixth (d6)
| Minor sixth (m6)
| Diminished sixth (d6)
| Diminished sixth (d6)
| 752.4
| 752.4
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| Also "supermajor fifth"
| Also "supermajor fifth"
|-
|-
|Minor sixth (m6)
| Upminor sixth (^m6)
| Minor sixth (m6)
| Minor sixth (m6)
| 813.5
| 813.5
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|  
|  
|-
|-
|Major sixth (M6)
| Downmajor sixth (vM6)
| Major sixth (M6)
| Major sixth (M6)
| 874.6
| 874.6
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|  
|  
|-
|-
|Wolf sixth (W6)
| Major sixth (M6)
| Augmented sixth (A6)
| Augmented sixth (A6)
| 935.7
| 935.7
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| Also "subminor seventh"
| Also "subminor seventh"
|-
|-
!
! colspan="6" | Sevenths
! colspan="4" | Sevenths
!
|-
|-
|Diminished seventh (d7)
| Downminor seventh (vm7)
| Double-diminished seventh (dd7)
| Double-diminished seventh (dd7)
| 915.1
| 915.1
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| Also "supermajor sixth"
| Also "supermajor sixth"
|-
|-
|Minor seventh (m7)
| 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"
|  
|-
|-
|Neutral seventh (n7)
| 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"
|  
|-
|-
|Major seventh (M7)
| Downmajor seventh (vM7)
| Augmented seventh (A7)
| Augmented seventh (A7)
| 1098.4
| 1098.4
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|  
|  
|-
|-
!
! colspan="6" | Octaves
! colspan="4" | Octaves
!
|-
|-
|Diminished octave (d8)
| Down octave (v8)
| Diminished octave (d8)
| Diminished octave (d8)
| 1138.9
| 1138.9
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|  
|  
|-
|-
|Perfect octave (P8)
| Perfect octave (P8)
| Perfect octave (P8)
| Perfect octave (P8)
| 1200.0
| 1200.0
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|  
|  
|-
|-
|Augmented octave (A8)
| 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"