Porcupine intervals: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
This naming system names every interval of porcupine, not just Porcupine[7].
m Cleanup
Line 5: Line 5:
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]]
Line 217: Line 217:
[[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]]

Revision as of 12:10, 20 April 2025

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 ⟨7 11 16].

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 Size* Ratio Genspan Comments
Unisons
Perfect unison (P1) 0.0 1/1 0
Augmented unison (A1) 61.1 81/80~36/35~33/32~25/24 -7 And other ratios, of course
Seconds
Diminished second (d2) 101.6 21/20~16/15 8
Perfect second (P2) 162.7 12/11~11/10~10/9~35/32 1 Rather than "minor 2nd"
Augmented second (A2) 223.8 9/8~8/7 -6 Rather than "major 2nd"
Double-augmented second (AA2) 284.9 Close to 13/11 -13 Also "subminor third"
Thirds
Diminished third (d3) 264.3 7/6 9 Also "supermajor second"
Minor third (m3) 325.4 6/5~11/9 2
Major third (M3) 386.5 5/4 -5
Augmented third (A3) 447.6 9/7 (close to 13/10) -12 Also "subminor fourth"
Fourths
Diminished fourth (d4) 427.0 14/11 10 Also "supermajor third"
Minor fourth (m4) 488.1 4/3 3 Rather than "perfect fourth"
Major fourth (M4) 549.2 11/8 -4
Augmented fourth (A4) 610.3 10/7 -11 Also "subminor fifth"
Fifths
Diminished fifth (d5) 589.7 7/5 11 Also "supermajor fourth"
Minor fifth (m5) 650.8 16/11 4
Major fifth (M5) 711.9 3/2 -3 Rather than "perfect fifth"
Augmented fifth (A5) 773.0 11/7 -10 Also "subminor sixth"
Sixths
Diminished sixth (d6) 752.4 14/9 (close to 20/13) 12 Also "supermajor fifth"
Minor sixth (m6) 813.5 8/5 5
Major sixth (M6) 874.6 5/3 -2
Augmented sixth (A6) 935.7 12/7 -9 Also "subminor seventh"
Sevenths
Double-diminished seventh (dd7) 915.1 Close to 22/13 13 Also "supermajor sixth"
Diminished seventh (d7) 976.2 7/4~16/9 6 Rather than "minor 7th"
Perfect seventh (P7) 1037.3 9/5~11/6 -1 Rather than "major 7th"
Augmented seventh (A7) 1098.4 15/8 -8
Octaves
Diminished octave (d8) 1138.9 21/11~35/18~160/81 7
Perfect octave (P8) 1200.0 2/1 0
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=193246"