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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|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*
! | No. of Porcupine Generators(~162.7¢)
! 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
|  
|-
|-
| | Minor second (m2)
| 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
| |  
| 1
|  
|-
|-
| | Major second (M2)
| Major second (M2)
| | 223.8
| Augmented second (A2)
| | 9/8~8/7
| 223.8
| | -6
| 9/8~8/7
| |  
| -6
|  
|-
|-
| | Augmented second (A2)
| 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
! |
|-
|-
| | Diminished seventh (d7)
| 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"
|-
|-
| | Minor seventh (m7)
| Minor seventh (m7)
| | 976.2
| Diminished seventh (d7)
| | 7/4~16/9
| 976.2
| | 6
| 7/4~16/9
| |  
| 6
|  
|-
|-
| | Major seventh (M7)
| Upminor seventh (^m7)
| | 1037.3
| Perfect seventh (P7)
| | 9/5~11/6
| 1037.3
| | -3
| 9/5~11/6
| |  
| -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
* 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]]
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[[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:Todo:cleanup]]
Retrieved from "https://en.xen.wiki/w/Porcupine_intervals"