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Porcupine intervals: Difference between revisions

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This naming system names every interval of porcupine, not just Porcupine[7].
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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"
{| class="wikitable right-2 center-4"
|-
|-
! | Name
! Name
! | Size*
! Size*
! | Ratio
! Ratio
! | [[Fifthspan#Rank-2 temperaments|genspan]]
! [[Fifthspan #Rank-2 temperaments|Genspan]]
! | Comments
! Comments
|-
|-
! colspan="4" | Unisons
! colspan="4" | Unisons
! |
!  
|-
|-
| | Perfect unison (P1)
| Perfect unison (P1)
| | 0
| 0.0
| | 1/1
| 1/1
| | 0
| 0
| |  
|  
|-
|-
| | 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)|And other ratios, of course]]
|-
|-
! colspan="4" | Seconds
! colspan="4" | Seconds
! |
!  
|-
|-
| | Diminished second (d2)
| Diminished second (d2)
| | 101.6
| 101.6
| | 21/20~16/15
| 21/20~16/15
| | 8
| 8
| |  
|  
|-
|-
| | 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"
| Rather than "minor 2nd"
|-
|-
| | Augmented second (A2)
| Augmented second (A2)
| | 223.8
| 223.8
| | 9/8~8/7
| 9/8~8/7
| | -6
| -6
| | Rather than "major 2nd"
| Rather than "major 2nd"
|-
|-
| | Double-augmented second (AA2)
| Double-augmented second (AA2)
| | 284.9
| 284.9
| | Close to 13/11
| Close to 13/11
| | -13
| -13
| | Also "subminor third"
| Also "subminor third"
|-
|-
! colspan="4" | Thirds
! colspan="4" | Thirds
! |
!  
|-
|-
| | Diminished third (d3)
| Diminished third (d3)
| | 264.3
| 264.3
| | 7/6
| 7/6
| | 9
| 9
| | Also "supermajor second"
| Also "supermajor second"
|-
|-
| | Minor third (m3)
| Minor third (m3)
| | 325.4
| 325.4
| | 6/5~11/9
| 6/5~11/9
| | 2
| 2
| |
|  
|-
|-
| | Major third (M3)
| Major third (M3)
| | 386.5
| 386.5
| | 5/4
| 5/4
| | -5
| -5
| |
|  
|-
|-
| | Augmented third (A3)
| Augmented third (A3)
| | 447.6
| 447.6
| | 9/7 (close to 13/10)
| 9/7 (close to 13/10)
| | -12
| -12
| | Also "subminor fourth"
| Also "subminor fourth"
|-
|-
! colspan="4" | Fourths
! colspan="4" | Fourths
! |
!  
|-
|-
| | Diminished fourth (d4)
| Diminished fourth (d4)
| | 427.0
| 427.0
| | 14/11
| 14/11
| | 10
| 10
| | Also "supermajor third"
| Also "supermajor third"
|-
|-
| | Minor fourth (m4)
| Minor fourth (m4)
| | 488.1
| 488.1
| | 4/3
| 4/3
| | 3
| 3
| | Rather than "perfect fourth"
| Rather than "perfect fourth"
|-
|-
| | Major fourth (M4)
| Major fourth (M4)
| | 549.2
| 549.2
| | 11/8
| 11/8
| | -4
| -4
| |  
|  
|-
|-
| | Augmented fourth (A4)
| Augmented fourth (A4)
| | 610.3
| 610.3
| | 10/7
| 10/7
| | -11
| -11
| | Also "subminor fifth"
| Also "subminor fifth"
|-
|-
! colspan="4" | Fifths
! colspan="4" | Fifths
! |
!  
|-
|-
| | Diminished fifth (d5)
| Diminished fifth (d5)
| | 589.7
| 589.7
| | 7/5
| 7/5
| | 11
| 11
| | Also "supermajor fourth"
| Also "supermajor fourth"
|-
|-
| | Minor fifth (m5)
| Minor fifth (m5)
| | 650.8
| 650.8
| | 16/11
| 16/11
| | 4
| 4
| |  
|  
|-
|-
| | Major fifth (M5)
| Major fifth (M5)
| | 711.9
| 711.9
| | 3/2
| 3/2
| | -3
| -3
| | Rather than "perfect fifth"
| Rather than "perfect fifth"
|-
|-
| | Augmented fifth (A5)
| Augmented fifth (A5)
| | 773.0
| 773.0
| | 11/7
| 11/7
| | -10
| -10
| | Also "subminor sixth"
| Also "subminor sixth"
|-
|-
! colspan="4" | Sixths
! colspan="4" | Sixths
! |
!  
|-
|-
| | Diminished sixth (d6)
| Diminished sixth (d6)
| | 752.4
| 752.4
| | 14/9 (close to 20/13)
| 14/9 (close to 20/13)
| | 12
| 12
| | Also "supermajor fifth"
| Also "supermajor fifth"
|-
|-
| | Minor sixth (m6)
| Minor sixth (m6)
| | 813.5
| 813.5
| | 8/5
| 8/5
| | 5
| 5
| |
|  
|-
|-
| | Major sixth (M6)
| Major sixth (M6)
| | 874.6
| 874.6
| | 5/3
| 5/3
| | -2
| -2
| |
|  
|-
|-
| | Augmented sixth (A6)
| Augmented sixth (A6)
| | 935.7
| 935.7
| | 12/7
| 12/7
| | -9
| -9
| | Also "subminor seventh"
| Also "subminor seventh"
|-
|-
! colspan="4" | Sevenths
! colspan="4" | Sevenths
! |
!  
|-
|-
| | Double-diminished seventh (dd7)
| Double-diminished seventh (dd7)
| | 915.1
| 915.1
| | Close to 22/13
| Close to 22/13
| | 13
| 13
| | Also "supermajor sixth"
| Also "supermajor sixth"
|-
|-
| | Diminished seventh (d7)
| Diminished seventh (d7)
| | 976.2
| 976.2
| | 7/4~16/9
| 7/4~16/9
| | 6
| 6
| | Rather than "minor 7th"
| Rather than "minor 7th"
|-
|-
| | Perfect seventh (P7)
| Perfect seventh (P7)
| | 1037.3
| 1037.3
| | 9/5~11/6
| 9/5~11/6
| |  -1
|  -1
| | Rather than "major 7th"
| Rather than "major 7th"
|-
|-
| | Augmented seventh (A7)
| Augmented seventh (A7)
| | 1098.4
| 1098.4
| | 15/8
| 15/8
| | -8
| -8
| |  
|  
|-
|-
! colspan="4" | Octaves
! colspan="4" | Octaves
! |
!  
|-
|-
| | Diminished octave (d8)
| Diminished octave (d8)
| | 1138.9
| 1138.9
| | 21/11~35/18~160/81
| 21/11~35/18~160/81
| | 7
| 7
| |  
|  
|-
|-
| | Perfect octave (P8)
| Perfect octave (P8)
| | 1200
| 1200.0
| | 2/1
| 2/1
| | 0
| 0
| |  
|  
|-
|-
| | Augmented octave (A8)
| Augmented octave (A8)
| | 1261.1
| 1261.1
| | 81/40~45/22~33/16~25/12
| 81/40~45/22~33/16~25/12
| | -7
| -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]]
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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:Porcupine]]
[[Category:Todo:cleanup]]
[[Category:Todo:cleanup]]
Retrieved from "https://en.xen.wiki/w/Porcupine_intervals"