Porcupine intervals: Difference between revisions

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This is one possible naming and organization system for intervals of [[Porcupine|porcupine]] temperament. It's 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|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.


In [[15edo|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"
{| class="wikitable right-3 center-5"
|-
|-
! | Name
! Name ([[Pergen|ups and downs]])
! | Size*
! Name (1L 6s (onyx))
! | Ratio
! Size*
! | [[Fifthspan#Rank-2 temperaments|genspan]]
! Ratio
! | Comments
! [[Fifthspan #Rank-2 temperaments|Genspan]]
! Comments
|-
|-
! colspan="4" | Unisons
! colspan="6" | Unisons
! |
|-
|-
| | Perfect unison (P1)
| Perfect unison (P1)
| | 0
| Perfect unison (P1)
| | 1/1
| 0.0
| | 0
| 1/1
| |  
| 0
|  
|-
|-
| | Augmented unison (A1)
| Up unison (^1)
| | 61.1
| Augmented unison (A1)
| | 81/80~36/35~33/32~25/24
| 61.1
| | -7
| 81/80~36/35~33/32~25/24
| | [[Cluster_temperament#porcupine(fish)|And other ratios, of course]]
| -7
| [[Cluster temperament #porcupine(fish)|Among other ratios]]
|-
|-
! colspan="4" | Seconds
! colspan="6" | Seconds
! |
|-
|-
| | Diminished second (d2)
| Upminor second (^m2)
| | 101.6
| Diminished second (d2)
| | 21/20~16/15
| 101.6
| | 8
| 21/20~16/15
| |  
| 8
|  
|-
|-
| | Perfect second (P2)
| Downmajor second (vM2)
| | 162.7
| Perfect second (P2)
| | 12/11~11/10~10/9~35/32
| 162.7
| | 1
| 12/11~11/10~10/9~35/32
| | Rather than "minor 2nd"
| 1
|  
|-
|-
| | Augmented second (A2)
| Major second (M2)
| | 223.8
| Augmented second (A2)
| | 9/8~8/7
| 223.8
| | -6
| 9/8~8/7
| | Rather than "major 2nd"
| -6
|  
|-
|-
| | Double-augmented second (AA2)
| Upmajor second (^M2)
| | 284.9
| Double-augmented second (AA2)
| | Close to 13/11
| 284.9
| | -13
| Close to 13/11
| | Also "subminor third"
| -13
| Also "subminor third"
|-
|-
! colspan="4" | Thirds
! colspan="6" | Thirds
! |
|-
|-
| | Diminished third (d3)
| Minor third (m3)
| | 264.3
| Diminished third (d3)
| | 7/6
| 264.3
| | 9
| 7/6
| | Also "supermajor second"
| 9
| Also "supermajor second"
|-
|-
| | Minor third (m3)
| Upminor third (^m3)
| | 325.4
| Minor third (m3)
| | 6/5~11/9
| 325.4
| | 2
| 6/5~11/9
| | Coincidentally familiar
| 2
|  
|-
|-
| | Major third (M3)
| Downmajor third (vM3)
| | 386.5
| Major third (M3)
| | 5/4
| 386.5
| | -5
| 5/4
| | Coincidentally familiar
| -5
|  
|-
|-
| | Augmented third (A3)
| Major third (M3)
| | 447.6
| Augmented third (A3)
| | 9/7 (close to 13/10)
| 447.6
| | -12
| 9/7 (close to 13/10)
| | Also "subminor fourth"
| -12
| Also "subminor fourth"
|-
|-
! colspan="4" | Fourths
! colspan="6" | Fourths
! |
|-
|-
| | Diminished fourth (d4)
| Down fourth (v4)
| | 427.0
| Diminished fourth (d4)
| | 14/11
| 427.0
| | 10
| 14/11
| | Also "supermajor third"
| 10
| Also "supermajor third"
|-
|-
| | Minor fourth (m4)
| Perfect fourth (P4)
| | 488.1
| Minor fourth (m4)
| | 4/3
| 488.1
| | 3
| 4/3
| | Rather than "perfect fourth"
| 3
|  
|-
|-
| | Major fourth (M4)
| Upfourth (^4)
| | 549.2
| Major fourth (M4)
| | 11/8
| 549.2
| | -4
| 11/8
| |  
| -4
|  
|-
|-
| | Augmented fourth (A4)
| Downaugmented fourth (vA4)
| | 610.3
| Augmented fourth (A4)
| | 10/7
| 610.3
| | -11
| 10/7
| | Also "subminor fifth"
| -11
| Also "subminor fifth"
|-
|-
! colspan="4" | Fifths
! colspan="6" | Fifths
! |
|-
|-
| | Diminished fifth (d5)
| Updiminished fifth (^d5)
| | 589.7
| Diminished fifth (d5)
| | 7/5
| 589.7
| | 11
| 7/5
| | Also "supermajor fourth"
| 11
| Also "supermajor fourth"
|-
|-
| | Minor fifth (m5)
| Down fifth (v5)
| | 650.8
| Minor fifth (m5)
| | 16/11
| 650.8
| | 4
| 16/11
| |  
| 4
|  
|-
|-
| | Major fifth (M5)
| Perfect fifth (P5)
| | 711.9
| Major fifth (M5)
| | 3/2
| 711.9
| | -3
| 3/2
| | Rather than "perfect fifth"
| -3
|  
|-
|-
| | Augmented fifth (A5)
| Up fifth (^5)
| | 773.0
| Augmented fifth (A5)
| | 11/7
| 773.0
| | -10
| 11/7
| | Also "subminor sixth"
| -10
| Also "subminor sixth"
|-
|-
! colspan="4" | Sixths
! colspan="6" | Sixths
! |
|-
|-
| | Diminished sixth (d6)
| Minor sixth (m6)
| | 752.4
| Diminished sixth (d6)
| | 14/9 (close to 20/13)
| 752.4
| | 12
| 14/9 (close to 20/13)
| | Also "supermajor fifth"
| 12
| Also "supermajor fifth"
|-
|-
| | Minor sixth (m6)
| Upminor sixth (^m6)
| | 813.5
| Minor sixth (m6)
| | 8/5
| 813.5
| | 5
| 8/5
| | Coincidentally familiar
| 5
|  
|-
|-
| | Major sixth (M6)
| Downmajor sixth (vM6)
| | 874.6
| Major sixth (M6)
| | 5/3
| 874.6
| | -2
| 5/3
| | Coincidentally familiar
| -2
|  
|-
|-
| | Augmented sixth (A6)
| Major sixth (M6)
| | 935.7
| Augmented sixth (A6)
| | 12/7
| 935.7
| | -9
| 12/7
| | Also "subminor seventh"
| -9
| Also "subminor seventh"
|-
|-
! colspan="4" | Sevenths
! colspan="6" | Sevenths
! |
|-
|-
| | Double-diminished seventh (dd7)
| Downminor seventh (vm7)
| | 915.1
| Double-diminished seventh (dd7)
| | Close to 22/13
| 915.1
| | 13
| Close to 22/13
| | Also "supermajor sixth"
| 13
| Also "supermajor sixth"
|-
|-
| | Diminished seventh (d7)
| Minor seventh (m7)
| | 976.2
| Diminished seventh (d7)
| | 7/4~16/9
| 976.2
| | 6
| 7/4~16/9
| | Rather than "minor 7th"
| 6
|  
|-
|-
| | Perfect seventh (P7)
| Upminor seventh (^m7)
| | 1037.3
| Perfect seventh (P7)
| | 9/5~11/6
| 1037.3
| |  -1
| 9/5~11/6
| | Rather than "major 7th"
|  -1
|  
|-
|-
| | Augmented seventh (A7)
| Downmajor seventh (vM7)
| | 1098.4
| Augmented seventh (A7)
| | 15/8
| 1098.4
| | -8
| 15/8
| |  
| -8
|  
|-
|-
! colspan="4" | Octaves
! colspan="6" | Octaves
! |
|-
|-
| | Diminished octave (d8)
| Down octave (v8)
| | 1138.9
| Diminished octave (d8)
| | 21/11~35/18~160/81
| 1138.9
| | 7
| 21/11~35/18~160/81
| |  
| 7
|  
|-
|-
| | Perfect octave (P8)
| Perfect octave (P8)
| | 1200
| Perfect octave (P8)
| | 2/1
| 1200.0
| | 0
| 2/1
| |  
| 0
|  
|-
|-
| | Augmented octave (A8)
| Up octave (^8)
| | 1261.1
| Augmented octave (A8)
| | 81/40~45/22~33/16~25/12
| 1261.1
| | -7
| 81/40~45/22~33/16~25/12
| |  
| -7
|  
|}
|}
* In POTE 11-limit porcupine, where the generator is ~162.7¢.
* In cents, 11-limit POTE tuning of porcupine, where the generator is ~162.7¢.


[[File:porcupine_interval_matrix_pote.png|alt=porcupine_interval_matrix_pote.png|porcupine_interval_matrix_pote.png]]
[[File:porcupine_interval_matrix_pote.png|alt=porcupine_interval_matrix_pote.png|porcupine_interval_matrix_pote.png]]
Line 217: Line 239:
[[File:porcupine_interval_matrix_22edo.png|alt=porcupine_interval_matrix_22edo.png|porcupine_interval_matrix_22edo.png]]
[[File:porcupine_interval_matrix_22edo.png|alt=porcupine_interval_matrix_22edo.png|porcupine_interval_matrix_22edo.png]]


See also: [[Porcupine_Notation|Porcupine Notation]]
== See also ==
* [[Porcupine notation]]


[[Category:Porcupine]]
[[Category:Porcupine]]
[[Category:Todo:cleanup]]
[[Category:Todo:cleanup]]

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"