Porcupine intervals: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
m Cleanup
Made this page not plug one specific notation system
Line 1: Line 1:
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 7: Line 7:
{| class="wikitable right-2 center-4"
{| class="wikitable right-2 center-4"
|-
|-
! Name
!Name (zarlino)
! Name (heptatonic MOS)
! Size*
! Size*
! Ratio
! Ratio
Line 13: Line 14:
! Comments
! Comments
|-
|-
!
! colspan="4" | Unisons
! colspan="4" | Unisons
!  
!  
|-
|-
|Perfect unison (P1)
| Perfect unison (P1)
| Perfect unison (P1)
| 0.0
| 0.0
Line 22: Line 25:
|  
|  
|-
|-
|Augmented unison (A1)
| Augmented unison (A1)
| Augmented unison (A1)
| 61.1
| 61.1
Line 28: Line 32:
| [[Cluster temperament #porcupine(fish)|And other ratios, of course]]
| [[Cluster temperament #porcupine(fish)|And other ratios, of course]]
|-
|-
!
! colspan="4" | Seconds
! colspan="4" | Seconds
!  
!  
|-
|-
|Minor second (m2)
| Diminished second (d2)
| Diminished second (d2)
| 101.6
| 101.6
Line 37: Line 43:
|  
|  
|-
|-
|Neutral second (n2)
| Perfect second (P2)
| Perfect second (P2)
| 162.7
| 162.7
Line 43: Line 50:
| Rather than "minor 2nd"
| Rather than "minor 2nd"
|-
|-
|Major second (M2)
| Augmented second (A2)
| Augmented second (A2)
| 223.8
| 223.8
Line 49: Line 57:
| Rather than "major 2nd"
| Rather than "major 2nd"
|-
|-
|Augmented second (A2)
| Double-augmented second (AA2)
| Double-augmented second (AA2)
| 284.9
| 284.9
Line 55: Line 64:
| Also "subminor third"
| Also "subminor third"
|-
|-
!
! colspan="4" | Thirds
! colspan="4" | Thirds
!  
!  
|-
|-
|Wolf third (w3)
| Diminished third (d3)
| Diminished third (d3)
| 264.3
| 264.3
Line 64: Line 75:
| Also "supermajor second"
| Also "supermajor second"
|-
|-
|Minor third (m3)
| Minor third (m3)
| Minor third (m3)
| 325.4
| 325.4
Line 70: Line 82:
|  
|  
|-
|-
|Major third (M3)
| Major third (M3)
| Major third (M3)
| 386.5
| 386.5
Line 76: Line 89:
|  
|  
|-
|-
|Augmented third (A3)
| Augmented third (A3)
| Augmented third (A3)
| 447.6
| 447.6
Line 82: Line 96:
| Also "subminor fourth"
| Also "subminor fourth"
|-
|-
!
! colspan="4" | Fourths
! colspan="4" | Fourths
!  
!  
|-
|-
|Diminished fourth (d4)
| Diminished fourth (d4)
| Diminished fourth (d4)
| 427.0
| 427.0
Line 91: Line 107:
| Also "supermajor third"
| Also "supermajor third"
|-
|-
|Perfect fourth (P4)
| Minor fourth (m4)
| Minor fourth (m4)
| 488.1
| 488.1
Line 97: Line 114:
| Rather than "perfect fourth"
| Rather than "perfect fourth"
|-
|-
|Wolf fourth (w4)
| Major fourth (M4)
| Major fourth (M4)
| 549.2
| 549.2
Line 103: Line 121:
|  
|  
|-
|-
|Augmented fourth (A4)
| Augmented fourth (A4)
| Augmented fourth (A4)
| 610.3
| 610.3
Line 109: Line 128:
| Also "subminor fifth"
| Also "subminor fifth"
|-
|-
!
! colspan="4" | Fifths
! colspan="4" | Fifths
!  
!  
|-
|-
|Diminished fifth (d5)
| Diminished fifth (d5)
| Diminished fifth (d5)
| 589.7
| 589.7
Line 118: Line 139:
| Also "supermajor fourth"
| Also "supermajor fourth"
|-
|-
|Wolf fifth (w5)
| Minor fifth (m5)
| Minor fifth (m5)
| 650.8
| 650.8
Line 124: Line 146:
|  
|  
|-
|-
|Perfect fifth (P5)
| Major fifth (M5)
| Major fifth (M5)
| 711.9
| 711.9
Line 130: Line 153:
| Rather than "perfect fifth"
| Rather than "perfect fifth"
|-
|-
|Augmented fifth (A5)
| Augmented fifth (A5)
| Augmented fifth (A5)
| 773.0
| 773.0
Line 136: Line 160:
| Also "subminor sixth"
| Also "subminor sixth"
|-
|-
!
! colspan="4" | Sixths
! colspan="4" | Sixths
!  
!  
|-
|-
|Diminished sixth (d6)
| Diminished sixth (d6)
| Diminished sixth (d6)
| 752.4
| 752.4
Line 145: Line 171:
| Also "supermajor fifth"
| Also "supermajor fifth"
|-
|-
|Minor sixth (m6)
| Minor sixth (m6)
| Minor sixth (m6)
| 813.5
| 813.5
Line 151: Line 178:
|  
|  
|-
|-
|Major sixth (M6)
| Major sixth (M6)
| Major sixth (M6)
| 874.6
| 874.6
Line 157: Line 185:
|  
|  
|-
|-
|Wolf sixth (W6)
| Augmented sixth (A6)
| Augmented sixth (A6)
| 935.7
| 935.7
Line 163: Line 192:
| Also "subminor seventh"
| Also "subminor seventh"
|-
|-
!
! colspan="4" | Sevenths
! colspan="4" | Sevenths
!  
!  
|-
|-
|Diminished seventh (d7)
| Double-diminished seventh (dd7)
| Double-diminished seventh (dd7)
| 915.1
| 915.1
Line 172: Line 203:
| Also "supermajor sixth"
| Also "supermajor sixth"
|-
|-
|Minor seventh (m7)
| Diminished seventh (d7)
| Diminished seventh (d7)
| 976.2
| 976.2
Line 178: Line 210:
| Rather than "minor 7th"
| Rather than "minor 7th"
|-
|-
|Neutral seventh (n7)
| Perfect seventh (P7)
| Perfect seventh (P7)
| 1037.3
| 1037.3
Line 184: Line 217:
| Rather than "major 7th"
| Rather than "major 7th"
|-
|-
|Major seventh (M7)
| Augmented seventh (A7)
| Augmented seventh (A7)
| 1098.4
| 1098.4
Line 190: Line 224:
|  
|  
|-
|-
!
! colspan="4" | Octaves
! colspan="4" | Octaves
!  
!  
|-
|-
|Diminished octave (d8)
| Diminished octave (d8)
| Diminished octave (d8)
| 1138.9
| 1138.9
Line 199: Line 235:
|  
|  
|-
|-
|Perfect octave (P8)
| Perfect octave (P8)
| Perfect octave (P8)
| 1200.0
| 1200.0
Line 205: Line 242:
|  
|  
|-
|-
|Augmented octave (A8)
| Augmented octave (A8)
| Augmented octave (A8)
| 1261.1
| 1261.1

Revision as of 23:05, 24 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 (zarlino) Name (heptatonic MOS) Size* Ratio Genspan Comments
Unisons
Perfect unison (P1) Perfect unison (P1) 0.0 1/1 0
Augmented unison (A1) Augmented unison (A1) 61.1 81/80~36/35~33/32~25/24 -7 And other ratios, of course
Seconds
Minor second (m2) Diminished second (d2) 101.6 21/20~16/15 8
Neutral second (n2) Perfect second (P2) 162.7 12/11~11/10~10/9~35/32 1 Rather than "minor 2nd"
Major second (M2) Augmented second (A2) 223.8 9/8~8/7 -6 Rather than "major 2nd"
Augmented second (A2) Double-augmented second (AA2) 284.9 Close to 13/11 -13 Also "subminor third"
Thirds
Wolf third (w3) Diminished third (d3) 264.3 7/6 9 Also "supermajor second"
Minor third (m3) Minor third (m3) 325.4 6/5~11/9 2
Major third (M3) Major third (M3) 386.5 5/4 -5
Augmented third (A3) Augmented third (A3) 447.6 9/7 (close to 13/10) -12 Also "subminor fourth"
Fourths
Diminished fourth (d4) Diminished fourth (d4) 427.0 14/11 10 Also "supermajor third"
Perfect fourth (P4) Minor fourth (m4) 488.1 4/3 3 Rather than "perfect fourth"
Wolf fourth (w4) Major fourth (M4) 549.2 11/8 -4
Augmented fourth (A4) Augmented fourth (A4) 610.3 10/7 -11 Also "subminor fifth"
Fifths
Diminished fifth (d5) Diminished fifth (d5) 589.7 7/5 11 Also "supermajor fourth"
Wolf fifth (w5) Minor fifth (m5) 650.8 16/11 4
Perfect fifth (P5) Major fifth (M5) 711.9 3/2 -3 Rather than "perfect fifth"
Augmented fifth (A5) Augmented fifth (A5) 773.0 11/7 -10 Also "subminor sixth"
Sixths
Diminished sixth (d6) Diminished sixth (d6) 752.4 14/9 (close to 20/13) 12 Also "supermajor fifth"
Minor sixth (m6) Minor sixth (m6) 813.5 8/5 5
Major sixth (M6) Major sixth (M6) 874.6 5/3 -2
Wolf sixth (W6) Augmented sixth (A6) 935.7 12/7 -9 Also "subminor seventh"
Sevenths
Diminished seventh (d7) 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 Rather than "minor 7th"
Neutral seventh (n7) Perfect seventh (P7) 1037.3 9/5~11/6 -1 Rather than "major 7th"
Major seventh (M7) Augmented seventh (A7) 1098.4 15/8 -8
Octaves
Diminished octave (d8) Diminished octave (d8) 1138.9 21/11~35/18~160/81 7
Perfect octave (P8) Perfect octave (P8) 1200.0 2/1 0
Augmented octave (A8) 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=197531"