Porcupine intervals - Revision history

TallKite at 07:26, 3 June 2025

2025-06-03T07:26:55Z

← Older revision		Revision as of 07:26, 3 June 2025
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	{\| class="wikitable right-3 center-5"		{\| class="wikitable right-3 center-5"
	\|-		\|-
	! Name (ups and downs)		! Name ([[Pergen\|ups and downs]])
	! Name (1L 6s (onyx))		! Name (1L 6s (onyx))
	! Size*		! Size*
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	! colspan="6" \| Seconds		! colspan="6" \| Seconds
	\|-		\|-
	\| ~~Up minor~~ second (^m2)		\| Upminor second (^m2)
	\| Diminished second (d2)		\| Diminished second (d2)
	\| 101.6		\| 101.6
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	\|		\|
	\|-		\|-
	\| ~~Down major~~ second (vM2)		\| Downmajor second (vM2)
	\| Perfect second (P2)		\| Perfect second (P2)
	\| 162.7		\| 162.7
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	\|		\|
	\|-		\|-
	\| ~~Up major~~ second (^M2)		\| Upmajor second (^M2)
	\| Double-augmented second (AA2)		\| Double-augmented second (AA2)
	\| 284.9		\| 284.9
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	\| Also "supermajor second"		\| Also "supermajor second"
	\|-		\|-
	\| ~~Up minor~~ third (^m3)		\| Upminor third (^m3)
	\| Minor third (m3)		\| Minor third (m3)
	\| 325.4		\| 325.4
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	\|		\|
	\|-		\|-
	\| ~~Down major~~ third (vM3)		\| Downmajor third (vM3)
	\| Major third (M3)		\| Major third (M3)
	\| 386.5		\| 386.5
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	\|		\|
	\|-		\|-
	\| ~~Up fourth~~ (^4)		\| Upfourth (^4)
	\| Major fourth (M4)		\| Major fourth (M4)
	\| 549.2		\| 549.2
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	\|		\|
	\|-		\|-
	\| ~~Down augmented~~ fourth (vA4)		\| Downaugmented fourth (vA4)
	\| Augmented fourth (A4)		\| Augmented fourth (A4)
	\| 610.3		\| 610.3
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	! colspan="6" \| Fifths		! colspan="6" \| Fifths
	\|-		\|-
	\| ~~Up diminished~~ fifth (^d5)		\| Updiminished fifth (^d5)
	\| Diminished fifth (d5)		\| Diminished fifth (d5)
	\| 589.7		\| 589.7
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	\| Also "supermajor fifth"		\| Also "supermajor fifth"
	\|-		\|-
	\| ~~Up minor~~ sixth (^m6)		\| Upminor sixth (^m6)
	\| Minor sixth (m6)		\| Minor sixth (m6)
	\| 813.5		\| 813.5
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	\|		\|
	\|-		\|-
	\| ~~Down major~~ sixth (vM6)		\| Downmajor sixth (vM6)
	\| Major sixth (M6)		\| Major sixth (M6)
	\| 874.6		\| 874.6
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	! colspan="6" \| Sevenths		! colspan="6" \| Sevenths
	\|-		\|-
	\| ~~Down minor~~ seventh (vm7)		\| Downminor seventh (vm7)
	\| Double-diminished seventh (dd7)		\| Double-diminished seventh (dd7)
	\| 915.1		\| 915.1
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	\|		\|
	\|-		\|-
	\| ~~Up minor~~ seventh (^m7)		\| Upminor seventh (^m7)
	\| Perfect seventh (P7)		\| Perfect seventh (P7)
	\| 1037.3		\| 1037.3
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	\|		\|
	\|-		\|-
	\| ~~Down major~~ seventh (vM7)		\| Downmajor seventh (vM7)
	\| Augmented seventh (A7)		\| Augmented seventh (A7)
	\| 1098.4		\| 1098.4

FloraC: There's no accepted interval names for zarlino. Use ups and downs instead, which has real scores made in it. Formatting

2025-05-25T11:42:04Z

There's no accepted interval names for zarlino. Use ups and downs instead, which has real scores made in it. Formatting

Show changes

VectorGraphics: Made this page not plug one specific notation system

2025-05-24T23:05:37Z

Made this page not plug one specific notation system

Show changes

FloraC: Cleanup

2025-04-20T12:10:10Z

Cleanup

Show changes

FloraC: This naming system names every interval of porcupine, not just Porcupine[7].

2025-04-20T12:06:52Z

This naming system names every interval of porcupine, not just Porcupine[7].

← Older revision		Revision as of 12:06, 20 April 2025
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	This is one possible naming and organization system for ~~the~~ intervals of ~~the~~ [[porcupine]][7] scale, or equivalently of the [[~~val\|~~val]] ~~<~~7 11 16\|.		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]] {{val\| 7 11 16 }}.

	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"

VectorGraphics at 09:04, 20 April 2025

2025-04-20T09:04:32Z

← Older revision		Revision as of 09:04, 20 April 2025
Line 1:		Line 1:
	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\|.		This is one possible naming and organization system for the intervals of the [[porcupine]][7] scale, or equivalently of the [[val\|val]] <7 11 16\|.

	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\|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.

VectorGraphics: the familiarity of the minor and major third intervals is not a coincidence

2025-04-20T09:03:41Z

the familiarity of the minor and major third intervals is not a coincidence

← Older revision		Revision as of 09:03, 20 April 2025
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	\| \| 6/5~11/9		\| \| 6/5~11/9
	\| \| 2		\| \| 2
	\| \| ~~Coincidentally familiar~~		\| \|
	\|-		\|-
	\| \| Major third (M3)		\| \| Major third (M3)
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	\| \| 5/4		\| \| 5/4
	\| \| -5		\| \| -5
	\| \| ~~Coincidentally familiar~~		\| \|
	\|-		\|-
	\| \| Augmented third (A3)		\| \| Augmented third (A3)
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	\| \| 8/5		\| \| 8/5
	\| \| 5		\| \| 5
	\| \| ~~Coincidentally familiar~~		\| \|
	\|-		\|-
	\| \| Major sixth (M6)		\| \| Major sixth (M6)
Line 155:		Line 155:
	\| \| 5/3		\| \| 5/3
	\| \| -2		\| \| -2
	\| \| ~~Coincidentally familiar~~		\| \|
	\|-		\|-
	\| \| Augmented sixth (A6)		\| \| Augmented sixth (A6)

TallKite: cleanup

2024-10-17T01:49:35Z

cleanup

← Older revision		Revision as of 01:49, 17 October 2024
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	! \| Size*		! \| Size*
	! \| Ratio		! \| Ratio
	! \| ~~No. of Porcupine Generators(~162.7¢)~~		! \| [[Fifthspan#Rank-2 temperaments\|genspan]]
	! \| Comments		! \| Comments
	\|-		\|-
Line 37:		Line 37:
	\| \|		\| \|
	\|-		\|-
	\| \| ~~Minor~~ second (m2)		\| \| 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"
	\|-		\|-
	\| \| ~~Major~~ second (M2)		\| \| Augmented second (A2)
	\| \| 223.8		\| \| 223.8
	\| \| 9/8~8/7		\| \| 9/8~8/7
	\| \| -6		\| \| -6
	\| \|		\| \| Rather than "major 2nd"
	\|-		\|-
	\| \| ~~Augmented~~ second (A2)		\| \| Double-augmented second (AA2)
	\| \| 284.9		\| \| 284.9
	\| \| Close to 13/11		\| \| Close to 13/11
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	! \|		! \|
	\|-		\|-
	\| \| ~~Diminished~~ seventh (d7)		\| \| Double-diminished seventh (dd7)
	\| \| 915.1		\| \| 915.1
	\| \| Close to 22/13		\| \| Close to 22/13
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	\| \| Also "supermajor sixth"		\| \| Also "supermajor sixth"
	\|-		\|-
	\| \| ~~Minor~~ seventh (m7)		\| \| Diminished seventh (d7)
	\| \| 976.2		\| \| 976.2
	\| \| 7/4~16/9		\| \| 7/4~16/9
	\| \| 6		\| \| 6
	\| \|		\| \| Rather than "minor 7th"
	\|-		\|-
	\| \| ~~Major~~ seventh (M7)		\| \| Perfect seventh (P7)
	\| \| 1037.3		\| \| 1037.3
	\| \| 9/5~11/6		\| \| 9/5~11/6
	\| \| -3		\| \| -1
	\| \|		\| \| Rather than "major 7th"
	\|-		\|-
	\| \| Augmented seventh (A7)		\| \| Augmented seventh (A7)
Line 211:		Line 211:
	\| \|		\| \|
	\|}		\|}
	* In POTE 11-limit porcupine		* In POTE 11-limit 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]]

Xenwolf: +cats

2020-10-25T10:50:25Z

+cats

← Older revision		Revision as of 10:50, 25 October 2020
Line 218:		Line 218:

	See also: [[Porcupine_Notation\|Porcupine Notation]]		See also: [[Porcupine_Notation\|Porcupine Notation]]

			[[Category:Porcupine]]

			[[Category:Todo:cleanup]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

← Older revision		Revision as of 09:03, 20 April 2025
Line 68:		Line 68:
	\| \| 6/5~11/9		\| \| 6/5~11/9
	\| \| 2		\| \| 2
	\| \| ~~Coincidentally familiar~~		\| \|
	\|-		\|-
	\| \| Major third (M3)		\| \| Major third (M3)
Line 74:		Line 74:
	\| \| 5/4		\| \| 5/4
	\| \| -5		\| \| -5
	\| \| ~~Coincidentally familiar~~		\| \|
	\|-		\|-
	\| \| Augmented third (A3)		\| \| Augmented third (A3)
Line 149:		Line 149:
	\| \| 8/5		\| \| 8/5
	\| \| 5		\| \| 5
	\| \| ~~Coincidentally familiar~~		\| \|
	\|-		\|-
	\| \| Major sixth (M6)		\| \| Major sixth (M6)
Line 155:		Line 155:
	\| \| 5/3		\| \| 5/3
	\| \| -2		\| \| -2
	\| \| ~~Coincidentally familiar~~		\| \|
	\|-		\|-
	\| \| Augmented sixth (A6)		\| \| Augmented sixth (A6)

← Older revision		Revision as of 01:49, 17 October 2024
Line 10:		Line 10:
	! \| Size*		! \| Size*
	! \| Ratio		! \| Ratio
	! \| ~~No. of Porcupine Generators(~162.7¢)~~		! \| [[Fifthspan#Rank-2 temperaments\|genspan]]
	! \| Comments		! \| Comments
	\|-		\|-
Line 37:		Line 37:
	\| \|		\| \|
	\|-		\|-
	\| \| ~~Minor~~ second (m2)		\| \| 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"
	\|-		\|-
	\| \| ~~Major~~ second (M2)		\| \| Augmented second (A2)
	\| \| 223.8		\| \| 223.8
	\| \| 9/8~8/7		\| \| 9/8~8/7
	\| \| -6		\| \| -6
	\| \|		\| \| Rather than "major 2nd"
	\|-		\|-
	\| \| ~~Augmented~~ second (A2)		\| \| Double-augmented second (AA2)
	\| \| 284.9		\| \| 284.9
	\| \| Close to 13/11		\| \| Close to 13/11
Line 166:		Line 166:
	! \|		! \|
	\|-		\|-
	\| \| ~~Diminished~~ seventh (d7)		\| \| Double-diminished seventh (dd7)
	\| \| 915.1		\| \| 915.1
	\| \| Close to 22/13		\| \| Close to 22/13
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	\| \| Also "supermajor sixth"		\| \| Also "supermajor sixth"
	\|-		\|-
	\| \| ~~Minor~~ seventh (m7)		\| \| Diminished seventh (d7)
	\| \| 976.2		\| \| 976.2
	\| \| 7/4~16/9		\| \| 7/4~16/9
	\| \| 6		\| \| 6
	\| \|		\| \| Rather than "minor 7th"
	\|-		\|-
	\| \| ~~Major~~ seventh (M7)		\| \| Perfect seventh (P7)
	\| \| 1037.3		\| \| 1037.3
	\| \| 9/5~11/6		\| \| 9/5~11/6
	\| \| -3		\| \| -1
	\| \|		\| \| Rather than "major 7th"
	\|-		\|-
	\| \| Augmented seventh (A7)		\| \| Augmented seventh (A7)
Line 211:		Line 211:
	\| \|		\| \|
	\|}		\|}
	* In POTE 11-limit porcupine		* In POTE 11-limit 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]]