Porcupine intervals: Difference between revisions

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There's no accepted interval names for zarlino. Use ups and downs instead, which has real scores made in it. Formatting
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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 (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)
| Up minor second (^m2)
| Diminished second (d2)
| Diminished second (d2)
| 101.6
| 101.6
Line 43: Line 39:
|  
|  
|-
|-
|Neutral second (n2)
| Down major 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)
| Up major second (^M2)
| Double-augmented second (AA2)
| Double-augmented second (AA2)
| 284.9
| 284.9
Line 64: Line 60:
| 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
Line 75: Line 69:
| Also "supermajor second"
| Also "supermajor second"
|-
|-
|Minor third (m3)
| Up minor third (^m3)
| Minor third (m3)
| Minor third (m3)
| 325.4
| 325.4
Line 82: Line 76:
|  
|  
|-
|-
|Major third (M3)
| Down major third (vM3)
| Major third (M3)
| Major third (M3)
| 386.5
| 386.5
Line 89: Line 83:
|  
|  
|-
|-
|Augmented third (A3)
| Major third (M3)
| Augmented third (A3)
| Augmented third (A3)
| 447.6
| 447.6
Line 96: Line 90:
| 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
Line 107: Line 99:
| 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)
| Up fourth (^4)
| Major fourth (M4)
| Major fourth (M4)
| 549.2
| 549.2
Line 121: Line 113:
|  
|  
|-
|-
|Augmented fourth (A4)
| Down augmented fourth (vA4)
| Augmented fourth (A4)
| Augmented fourth (A4)
| 610.3
| 610.3
Line 128: Line 120:
| Also "subminor fifth"
| Also "subminor fifth"
|-
|-
!
! colspan="6" | Fifths
! colspan="4" | Fifths
!
|-
|-
|Diminished fifth (d5)
| Up diminished fifth (^d5)
| Diminished fifth (d5)
| Diminished fifth (d5)
| 589.7
| 589.7
Line 139: Line 129:
| Also "supermajor fourth"
| Also "supermajor fourth"
|-
|-
|Wolf fifth (w5)
| Down fifth (v5)
| Minor fifth (m5)
| Minor fifth (m5)
| 650.8
| 650.8
Line 146: Line 136:
|  
|  
|-
|-
|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
Line 160: Line 150:
| 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
Line 171: Line 159:
| Also "supermajor fifth"
| Also "supermajor fifth"
|-
|-
|Minor sixth (m6)
| Up minor sixth (^m6)
| Minor sixth (m6)
| Minor sixth (m6)
| 813.5
| 813.5
Line 178: Line 166:
|  
|  
|-
|-
|Major sixth (M6)
| Down major sixth (vM6)
| Major sixth (M6)
| Major sixth (M6)
| 874.6
| 874.6
Line 185: Line 173:
|  
|  
|-
|-
|Wolf sixth (W6)
| Major sixth (M6)
| Augmented sixth (A6)
| Augmented sixth (A6)
| 935.7
| 935.7
Line 192: Line 180:
| Also "subminor seventh"
| Also "subminor seventh"
|-
|-
!
! colspan="6" | Sevenths
! colspan="4" | Sevenths
!
|-
|-
|Diminished seventh (d7)
| Down minor seventh (vm7)
| Double-diminished seventh (dd7)
| Double-diminished seventh (dd7)
| 915.1
| 915.1
Line 203: Line 189:
| 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)
| Up minor 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)
| Down major seventh (vM7)
| Augmented seventh (A7)
| Augmented seventh (A7)
| 1098.4
| 1098.4
Line 224: Line 210:
|  
|  
|-
|-
!
! colspan="6" | Octaves
! colspan="4" | Octaves
!
|-
|-
|Diminished octave (d8)
| Down octave (v8)
| Diminished octave (d8)
| Diminished octave (d8)
| 1138.9
| 1138.9
Line 235: Line 219:
|  
|  
|-
|-
|Perfect octave (P8)
| Perfect octave (P8)
| Perfect octave (P8)
| Perfect octave (P8)
| 1200.0
| 1200.0
Line 242: Line 226:
|  
|  
|-
|-
|Augmented octave (A8)
| Up octave (^8)
| Augmented octave (A8)
| Augmented octave (A8)
| 1261.1
| 1261.1

Revision as of 11:42, 25 May 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
Up minor second (^m2) Diminished second (d2) 101.6 21/20~16/15 8
Down major 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
Up major 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"
Up minor third (^m3) Minor third (m3) 325.4 6/5~11/9 2
Down major 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
Up fourth (^4) Major fourth (M4) 549.2 11/8 -4
Down augmented fourth (vA4) Augmented fourth (A4) 610.3 10/7 -11 Also "subminor fifth"
Fifths
Up diminished 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"
Up minor sixth (^m6) Minor sixth (m6) 813.5 8/5 5
Down major 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
Down minor 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
Up minor seventh (^m7) Perfect seventh (P7) 1037.3 9/5~11/6 -1
Down major 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=197564"