Intervals of Negri-9: Difference between revisions

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Added some table entries and attribution of the naming system.
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Line 6: Line 6:
! | Size*
! | Size*
! | Ratio
! | Ratio
! | No. of Negri Generators(~125.6¢)
! | Number of <br>generators
! | Comments
! | Comments
|-
|-
! colspan="4" | Unisons
! colspan="5" | Unisons
! |
|-
|-
| | Perfect unison (P1)
| | Perfect unison (P1)
Line 20: Line 19:
| | Augmented unison (A1)
| | Augmented unison (A1)
| | 69.9
| | 69.9
| | 36/35~21/20~27/26
| | 21/20, 27/26, 36/35
| | -9
| | -9
| |  
| |  
|-
|-
! colspan="4" | Seconds
! colspan="5" | Seconds
! |
|-
|-
| | Diminished second (d2)
| | Diminished second (d2)
| | 55.7
| | 55.7
| | 25/24~28/27~50/49~64/63
| | 25/24, 28/27, 50/49, 64/63
| | 10
| | 10
| | "Negri[10] Chroma"
| | "Negri[10] Chroma"
Line 35: Line 33:
| | Minor second (m2)
| | Minor second (m2)
| | 125.6
| | 125.6
| | 16/15~15/14~14/13~13/12
| | 13/12, 14/13, 15/14, 16/15
| | 1
| | 1
| |  
| |  
Line 45: Line 43:
| | Also "major wholetone"
| | Also "major wholetone"
|-
|-
! colspan="4" | [[Interseptimal|Semifourths]]
! colspan="5" | [[Interseptimal|Semifourths]]
! |
|-
|-
| | Diminished semifourth (d2.5)
| | Diminished semifourth (d2.5)
Line 56: Line 53:
| | Perfect semifourth (P2.5)
| | Perfect semifourth (P2.5)
| | 251.1
| | 251.1
| | 8/7~7/6~15/13
| | 7/6, 8/7, 15/13
| | 2
| | 2
| |  
| |  
Line 66: Line 63:
| | Also "minor third"
| | Also "minor third"
|-
|-
! colspan="4" | Ditones
! colspan="5" | Ditones
! |
|-
|-
| | Minor ditone (m3.3)
| | Minor ditone (m3.3)
| | 376.7
| | 376.7
| | 5/4~16/13
| | 5/4, 16/13
| | 3
| | 3
| | Also "major third"
| | Also "major third"
Line 77: Line 73:
| | Major ditone (M3.3)
| | Major ditone (M3.3)
| | 446.6
| | 446.6
| | 9/7~13/10
| | 9/7, 13/10
| | -6
| | -6
| | Also "supermajor third"
| | Also "supermajor third"
|-
|-
! colspan="4" | Fourths
! colspan="5" | Fourths
! |
|-
|-
| | Perfect fourth (P4)
| | Perfect fourth (P4)
Line 92: Line 87:
| | Augmented fourth (A4)
| | Augmented fourth (A4)
| | 572.2
| | 572.2
| | 7/5~18/13
| | 7/5, 18/13
| | -5
| | -5
| |  
| |  
|-
|-
! colspan="4" | Fifths
! colspan="5" | Fifths
! |
|-
|-
| | Diminished fifth (d5)
| | Diminished fifth (d5)
| | 628.8
| | 628.8
| | 10/7~13/9
| | 10/7, 13/9
| | 5
| | 5
| | Also "supermajor fourth"
| | Also "supermajor fourth"
Line 111: Line 105:
| |  
| |  
|-
|-
! colspan="4" | Tetratones
! colspan="5" | Tetratones
! |
|-
|-
| | Minor tetratone (m5.7)
| | Minor tetratone (m5.7)
| | 753.4
| | 753.4
| | 14/9~20/13
| | 14/9, 20/13
| | 6
| | 6
| | Also "subminor sixth"
| | Also "subminor sixth"
Line 122: Line 115:
| | Major tetratone (M5.7)
| | Major tetratone (M5.7)
| | 813.5
| | 813.5
| | 8/5
| | 8/5, 13/8
| | -3
| | -3
| | Also "minor sixth"
| | Also "minor sixth"
|-
|-
! colspan="4" | [[Interseptimal|Semitwelfths]]
! colspan="5" | [[Interseptimal|Semitwelfths]]
! |
|-
|-
| | diminished semitwelfth (d6.5)
| | diminished semitwelfth (d6.5)
Line 137: Line 129:
| | Perfect semitwelfth (P6.5)
| | Perfect semitwelfth (P6.5)
| | 948.9
| | 948.9
| | 7/4~12/7~26/15
| | 7/4, 12/7, 26/15
| | -2
| | -2
| | Also "supermajor sixth"
| | Also "supermajor sixth"
|-
|-
| | Augmented semitwelfth (A6.5)
| | Augmented semitwelfth (A6.5)
| | 948.9
| | 1017.8
| | 9/5
| | 9/5
| | -11
| | -11
| | Also "just minor seventh"
| | Also "just minor seventh"
|-
|-
! colspan="4" | Sevenths
! colspan="5" | Sevenths
! |
|-
|-
| | Minor seventh (m7)
| | Minor seventh (m7)
Line 154: Line 145:
| | 16/9
| | 16/9
| | 8
| | 8
| | Also "Pythagorean Minor 7th"
| | Also "Pythagorean minor 7th"
|-
|-
| | Major seventh (M7)
| | Major seventh (M7)
| | 1074.4
| | 1074.4
| | 15/8~13/7~28/15~24/13
| | 13/7, 15/8, 24/13, 28/15
| | -1
| | -1
| |  
| |  
Line 164: Line 155:
| | Augmented seventh (A7)
| | Augmented seventh (A7)
| | 1144.3
| | 1144.3
| | 48/25~27/14~49/25~63/32
| | 27/14, 48/25, 49/25, 63/32
| | -10
| | -10
| |  
| |  
|-
|-
! colspan="4" | Octaves
! colspan="5" | Octaves
! |
|-
|-
| | Diminished octave (d8)
| | Diminished octave (d8)
| | 1130.1
| | 1130.1
| | 35/18~40/21~52/27
| | 35/18, 40/21, 52/27
| | 9
| | 9
| |  
| |  
Line 181: Line 171:
| | 2/1
| | 2/1
| | 0
| | 0
| |
|-
| | Augmented octave (A8)
| | 1269.9
| | 72/35~21/10~27/13
| | -9
| |  
| |  
|}
|}
* In POTE 11-limit porcupine
<nowiki>*</nowiki> In 2.3.5.7.13 subgroup POTE tuning


[[Category:Negri]]
[[Category:Negri]]
[[Category:Lists of intervals]]

Latest revision as of 23:24, 23 June 2023

This is one possible naming system, suggested by Ray Perlner, for intervals of negri temperament based on the negri[9] scale. The names of intervals are chosen to give intuition for those used to diatonic interval naming conventions, even when this results in a slight abuse of notation. For example, 3 step intervals are called "ditones", not because the true ditone of 81/64 would be rendered as such (this system would refer to the interval mapping to 81/64 as a doubly augmented semifourth), but because the "ditones" which appear naturally in the negri[9] MOS scale are either a little larger (major) or a little smaller (minor) than a true ditone. 3-limit intervals, and intervals that divide 3-limit intervals exactly in half are referred to as "perfect" regardless of how commonly they occur in the MOS scale.

Name Size* Ratio Number of
generators 		Comments
Unisons
Perfect unison (P1) 0 1/1 0
Augmented unison (A1) 69.9 21/20, 27/26, 36/35 -9
Seconds
Diminished second (d2) 55.7 25/24, 28/27, 50/49, 64/63 10 "Negri[10] Chroma"
Minor second (m2) 125.6 13/12, 14/13, 15/14, 16/15 1
Major second (M2) 195.5 9/8 -8 Also "major wholetone"
Semifourths
Diminished semifourth (d2.5) 181.2 10/9 11 Also "minor wholetone"
Perfect semifourth (P2.5) 251.1 7/6, 8/7, 15/13 2
Augmented semifourth (A2.5) 321.0 6/5 -7 Also "minor third"
Ditones
Minor ditone (m3.3) 376.7 5/4, 16/13 3 Also "major third"
Major ditone (M3.3) 446.6 9/7, 13/10 -6 Also "supermajor third"
Fourths
Perfect fourth (P4) 502.3 4/3 4
Augmented fourth (A4) 572.2 7/5, 18/13 -5
Fifths
Diminished fifth (d5) 628.8 10/7, 13/9 5 Also "supermajor fourth"
Perfect fifth (P5) 697.7 3/2 -4
Tetratones
Minor tetratone (m5.7) 753.4 14/9, 20/13 6 Also "subminor sixth"
Major tetratone (M5.7) 813.5 8/5, 13/8 -3 Also "minor sixth"
Semitwelfths
diminished semitwelfth (d6.5) 879.0 5/3 7 Also "major sixth"
Perfect semitwelfth (P6.5) 948.9 7/4, 12/7, 26/15 -2 Also "supermajor sixth"
Augmented semitwelfth (A6.5) 1017.8 9/5 -11 Also "just minor seventh"
Sevenths
Minor seventh (m7) 1004.5 16/9 8 Also "Pythagorean minor 7th"
Major seventh (M7) 1074.4 13/7, 15/8, 24/13, 28/15 -1
Augmented seventh (A7) 1144.3 27/14, 48/25, 49/25, 63/32 -10
Octaves
Diminished octave (d8) 1130.1 35/18, 40/21, 52/27 9
Perfect octave (P8) 1200 2/1 0

* In 2.3.5.7.13 subgroup POTE tuning

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