Intervals of Negri-9 - Revision history

Overthink: correction

2026-04-13T22:07:30Z

correction

← Older revision		Revision as of 22:07, 13 April 2026
Line 114:		Line 114:
	\|-		\|-
	\| \| Major tetratone (M5.7)		\| \| Major tetratone (M5.7)
	\| \| ~~813~~.5		\| \| 823.3
	\| \| 8/5, 13/8		\| \| 8/5, 13/8
	\| \| -3		\| \| -3

Xenllium at 23:24, 23 June 2023

2023-06-23T23:24:06Z

← Older revision		Revision as of 23:24, 23 June 2023
Line 6:		Line 6:
	! \| Size*		! \| Size*
	! \| Ratio		! \| Ratio
	! \| Number of <br>~~Negri Generators~~		! \| Number of <br>generators
	! \| Comments		! \| Comments
	\|-		\|-
Line 176:		Line 176:

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

Xenllium at 23:22, 23 June 2023

2023-06-23T23:22:53Z

Show changes

Rperlner at 21:32, 24 April 2022

2022-04-24T21:32:36Z

← Older revision		Revision as of 21:32, 24 April 2022
Line 154:		Line 154:
	\| \| 16/9		\| \| 16/9
	\| \| 8		\| \| 8
	\| \| Also "Pythagorean ~~Minor~~ 7th"		\| \| Also "Pythagorean minor 7th"
	\|-		\|-
	\| \| Major seventh (M7)		\| \| Major seventh (M7)

Rperlner at 21:27, 24 April 2022

2022-04-24T21:27:41Z

← Older revision		Revision as of 21:27, 24 April 2022
Line 142:		Line 142:
	\|-		\|-
	\| \| Augmented semitwelfth (A6.5)		\| \| Augmented semitwelfth (A6.5)
	\| \| ~~948~~.9		\| \| 1017.8
	\| \| 9/5		\| \| 9/5
	\| \| -11		\| \| -11

Rperlner: Added some table entries and attribution of the naming system.

2022-04-24T21:26:03Z

Added some table entries and attribution of the naming system.

← Older revision		Revision as of 21:26, 24 April 2022
Line 1:		Line 1:
	This is one possible naming system for intervals of [[Negri\|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 [[Interseptimal\|intervals that divide 3-limit intervals exactly in half]] are referred to as "perfect" regardless of how commonly they occur in the MOS scale.		This is one possible naming system, suggested by [[Ray Perlner]], for intervals of [[Negri\|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 [[Interseptimal\|intervals that divide 3-limit intervals exactly in half]] are referred to as "perfect" regardless of how commonly they occur in the MOS scale.

	{\| class="wikitable"		{\| class="wikitable"
Line 43:		Line 43:
	\| \| 9/8		\| \| 9/8
	\| \| -8		\| \| -8
	\| \|		\| \| Also "major wholetone"
	\|-		\|-
	! colspan="4" \| [[Interseptimal\|Semifourths]]		! colspan="4" \| [[Interseptimal\|Semifourths]]
	! \|		! \|
			\|-
			\| \| Diminished semifourth (d2.5)
			\| \| 181.2
			\| \| 10/9
			\| \| 11
			\| \| Also "minor wholetone"
	\|-		\|-
	\| \| Perfect semifourth (P2.5)		\| \| Perfect semifourth (P2.5)
Line 129:		Line 135:
	\| \| Also "major sixth"		\| \| Also "major sixth"
	\|-		\|-
	\| \| Perfect ~~semifourth~~ (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)
			\| \| 948.9
			\| \| 9/5
			\| \| -11
			\| \| Also "just minor seventh"
	\|-		\|-
	! colspan="4" \| Sevenths		! colspan="4" \| Sevenths
Line 142:		Line 154:
	\| \| 16/9		\| \| 16/9
	\| \| 8		\| \| 8
	\| \|		\| \| Also "Pythagorean Minor 7th"
	\|-		\|-
	\| \| Major seventh (M7)		\| \| Major seventh (M7)
Line 148:		Line 160:
	\| \| 15/8~13/7~28/15~24/13		\| \| 15/8~13/7~28/15~24/13
	\| \| -1		\| \| -1
			\| \|
			\|-
			\| \| Augmented seventh (A7)
			\| \| 1144.3
			\| \| 48/25~27/14~49/25~63/32
			\| \| -10
	\| \|		\| \|
	\|-		\|-

Rperlner: Creating article. Intervals of Negri 9

2022-04-24T20:48:58Z

Creating article. Intervals of Negri 9

New page

This is one possible naming system for intervals of [[Negri|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 [[Interseptimal|intervals that divide 3-limit intervals exactly in half]] are referred to as "perfect" regardless of how commonly they occur in the MOS scale.

{| class="wikitable"
|-
! | Name
! | Size*
! | Ratio
! | No. of Negri Generators(~125.6¢)
! | Comments
|-
! colspan="4" | Unisons
! |
|-
| | Perfect unison (P1)
| | 0
| | 1/1
| | 0
| |
|-
| | Augmented unison (A1)
| | 69.9
| | 36/35~21/20~27/26
| | -9
| |
|-
! colspan="4" | Seconds
! |
|-
| | Diminished second (d2)
| | 55.7
| | 25/24~28/27~50/49~64/63
| | 10
| | "Negri[10] Chroma"
|-
| | Minor second (m2)
| | 125.6
| | 16/15~15/14~14/13~13/12
| | 1
| |
|-
| | Major second (M2)
| | 195.5
| | 9/8
| | -8
| |
|-
! colspan="4" | [[Interseptimal|Semifourths]]
! |
|-
| | Perfect semifourth (P2.5)
| | 251.1
| | 8/7~7/6~15/13
| | 2
| |
|-
| | Augmented semifourth (A2.5)
| | 321.0
| | 6/5
| | -7
| | Also "minor third"
|-
! colspan="4" | 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"
|-
! colspan="4" | Fourths
! |
|-
| | Perfect fourth (P4)
| | 502.3
| | 4/3
| | 4
| |
|-
| | Augmented fourth (A4)
| | 572.2
| | 7/5~18/13
| | -5
| |
|-
! colspan="4" | Fifths
! |
|-
| | Diminished fifth (d5)
| | 628.8
| | 10/7~13/9
| | 5
| | Also "supermajor fourth"
|-
| | Perfect fifth (P5)
| | 697.7
| | 3/2
| | -4
| |
|-
! colspan="4" | Tetratones
! |
|-
| | Minor tetratone (m5.7)
| | 753.4
| | 14/9~20/13
| | 6
| | Also "subminor sixth"
|-
| | Major tetratone (M5.7)
| | 813.5
| | 8/5
| | -3
| | Also "minor sixth"
|-
! colspan="4" | [[Interseptimal|Semitwelfths]]
! |
|-
| | diminished semitwelfth (d6.5)
| | 879.0
| | 5/3
| | 7
| | Also "major sixth"
|-
| | Perfect semifourth (P6.5)
| | 948.9
| | 7/4~12/7~26/15
| | -2
| | Also "supermajor sixth"
|-
! colspan="4" | Sevenths
! |
|-
| | Minor seventh (m7)
| | 1004.5
| | 16/9
| | 8
| |
|-
| | Major seventh (M7)
| | 1074.4
| | 15/8~13/7~28/15~24/13
| | -1
| |
|-
! colspan="4" | Octaves
! |
|-
| | Diminished octave (d8)
| | 1130.1
| | 35/18~40/21~52/27
| | 9
| |
|-
| | Perfect octave (P8)
| | 1200
| | 2/1
| | 0
| |
|-
| | Augmented octave (A8)
| | 1269.9
| | 72/35~21/10~27/13
| | -9
| |
|}
* In POTE 11-limit porcupine

[[Category:Negri]]

← Older revision		Revision as of 21:27, 24 April 2022
Line 142:		Line 142:
	\|-		\|-
	\| \| Augmented semitwelfth (A6.5)		\| \| Augmented semitwelfth (A6.5)
	\| \| ~~948~~.9		\| \| 1017.8
	\| \| 9/5		\| \| 9/5
	\| \| -11		\| \| -11