Interseptimal interval - Revision history

Overthink: /* Within a pentatonic framework */ link this page

2026-03-11T21:55:31Z

Within a pentatonic framework: link this page

← Older revision		Revision as of 21:55, 11 March 2026
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	=== Within a pentatonic framework ===		=== Within a pentatonic framework ===
	A pentatonic framework, as elucidated in Kite Giedraitis's [http://www.tallkite.com/AlternativeTunings.html Alternative Tuning guide], is far more amenable to interseptimal intervals than the traditional Western heptatonic framework.		A pentatonic framework, as elucidated in Kite Giedraitis's [http://www.tallkite.com/AlternativeTunings.html Alternative Tuning guide], is far more amenable to interseptimal intervals than the traditional Western heptatonic framework. Such a framework is also discussed on the page [[Pentatonic Functional Just System]].

	{\| class="wikitable"		{\| class="wikitable"
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	Interseptimal intervals are now easily named. However there are now hard-to-name "interpental" intervals which would be neutral intervals in the heptatonic framework, containing such ratios as 12/11, 11/9, etc. This is because interseptimal intervals are the neutral intervals with respect to the parent [[mos]] [[2L 3s]] of the diatonic mos [[5L 2s]].		Interseptimal intervals are now easily named. However there are now hard-to-name "interpental" intervals which would be neutral intervals in the heptatonic framework, containing such ratios as 12/11, 11/9, etc. This is because interseptimal intervals are the neutral intervals with respect to the parent [[mos]] [[2L 3s]] of the diatonic mos [[5L 2s]].

	So composing in a pentatonic framework may allow interseptimal intervals to play much more pivotal roles than usual.		Thus composing in a pentatonic framework may allow interseptimal intervals to play much more pivotal roles than usual.

	== Examples ==		== Examples ==

TallKite: /* "Plus" names */

2025-12-06T09:08:19Z

"Plus" names

← Older revision		Revision as of 09:08, 6 December 2025
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	* semifourth = plus-second (+2nd or +2)		* semifourth = plus-second (+2nd or +2)
	* semisixth = plus-third (+3rd or +3)		* semisixth = plus-third (+3rd or +3)
	* semioctave = plus-fourth (+4th or +4)
	* semitenth = plus-fifth (+5th or +5)		* semitenth = plus-fifth (+5th or +5)
	* semitwelfth = plus-sixth (+6th or +6)		* semitwelfth = plus-sixth (+6th or +6)

TallKite: /* Categorical and notational approaches */ added "plus" names

2025-12-06T03:37:09Z

Categorical and notational approaches: added "plus" names

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 * semitenth/cocytic = fifth-inter-sixth (5×6)
 * semitwelfth/ouranic = sixth-inter-seventh (6×7)
 === Decimal ordinal names ===

VectorGraphics: "super" and "sub" are JI-agnostic

2025-03-09T02:52:32Z

"super" and "sub" are JI-agnostic

← Older revision		Revision as of 02:52, 9 March 2025
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	While this does not give the interseptimals a single distinct ''notational'' name, it does reflect their ambiguity and flexibility with regards to the surrounding interval categories that many are so fond of. Furthermore, as both identities are exactly 12 notational fifths apart (i.e a direct analogue of the [[Pythagorean comma]]), composers can use a mechanism similar to the [[Color notation\|"po and qu" of Color Notation]], or the plus and minus accidentals (+/−) proposed in [[Rational Comma Notation (RCN)\|Rational Comma Notation]], to freely switch between the two identities.		While this does not give the interseptimals a single distinct ''notational'' name, it does reflect their ambiguity and flexibility with regards to the surrounding interval categories that many are so fond of. Furthermore, as both identities are exactly 12 notational fifths apart (i.e a direct analogue of the [[Pythagorean comma]]), composers can use a mechanism similar to the [[Color notation\|"po and qu" of Color Notation]], or the plus and minus accidentals (+/−) proposed in [[Rational Comma Notation (RCN)\|Rational Comma Notation]], to freely switch between the two identities.

	Alternatively, one can use the ''ultra-'' prefix for sharpening by ~50¢ and ''infra-'' for flattening by ~50{{c}}, analogous to ''super-'' and ''sub-'' for modifications by ~~[[64/63]] (in a [[12edo]]-related context such as [[36edo]], 33~~{{c}}).		Alternatively, one can use the ''ultra-'' prefix for sharpening by ~50¢ and ''infra-'' for flattening by ~50{{c}}, analogous to ''super-'' and ''sub-'' for modifications by ~30{{c}}.
	* semifourth/chthonic = ultramajor second, inframinor third		* semifourth/chthonic = ultramajor second, inframinor third
	* semisixth/naiadic = ultramajor third, infrafourth		* semisixth/naiadic = ultramajor third, infrafourth

ArrowHead294 at 13:48, 5 March 2025

2025-03-05T13:48:57Z

← Older revision		Revision as of 13:48, 5 March 2025
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	== Notes ==		== Notes ==
	<references group="note" />		<references group="note" />

			{{Navbox intervals}}

	[[Category:Interseptimal intervals\| ]]		[[Category:Interseptimal intervals\| ]]

ArrowHead294 at 13:48, 5 March 2025

2025-03-05T13:48:40Z

← Older revision		Revision as of 13:48, 5 March 2025
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	\|-		\|-
	! Interval		! Interval
	! ~~Cents~~		! Size<br />(cents)
	! Prime ~~Limit~~ (if applicable)		! Prime limit<br />(if applicable)
	\|-		\|-
	\| [[147/128]]		\| [[147/128]]
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	\|-		\|-
	! Interval		! Interval
	! ~~Cents Value~~		! Size<br />(cents)
	! Prime ~~Limit~~ (if applicable)		! Prime limit<br />(if applicable)
	\|-		\|-
	\| 5\[[88cET]] or 11\[[30edo\|30]]		\| 5\[[88cET]] or 11\[[30edo\|30]]
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	\|-		\|-
	! Interval		! Interval
	! ~~Cents Value~~		! Size<br />(cents)
	! Prime ~~Limit~~ (if applicable)		! Prime limit<br />(if applicable)
	\|-		\|-
	\| 5\[[13edt]]		\| 5\[[13edt]]
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	\|-		\|-
	! Interval		! Interval
	! ~~Cents Value~~		! Size<br />(cents)
	! Prime ~~Limit~~ (if applicable)		! Prime limit<br />(if applicable)
	\|-		\|-
	\| 18\[[23edo\|23]]		\| 18\[[23edo\|23]]

ArrowHead294 at 13:35, 5 March 2025

2025-03-05T13:35:10Z

Show changes

ArrowHead294: /* 5–min6 (semitenth/cocytic) */

2024-12-18T15:09:20Z

5–min6 (semitenth/cocytic)

← Older revision		Revision as of 15:09, 18 December 2024
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	! Prime Limit (if applicable)		! Prime Limit (if applicable)
	\|-		\|-
	\| 5\[[~~Bohlen-Pierce~~]]		\| 5\[[13edt]]
	\| 731.521		\| 731.521
	\| —		\| —

ArrowHead294 at 15:01, 18 December 2024

2024-12-18T15:01:04Z

Show changes

Lucius Chiaraviglio: Fix typo "Additionaly" --> "Additionally"

2024-08-03T08:47:09Z

Fix typo "Additionaly" --> "Additionally"

← Older revision		Revision as of 08:47, 3 August 2024
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	* Maj6–min7 – intermediate between [[12/7]] and [[7/4]] – 940¢–960¢		* Maj6–min7 – intermediate between [[12/7]] and [[7/4]] – 940¢–960¢

	~~Additionaly~~, there are also these 2 interseptimal regions near the unison and octave:		Additionally, there are also these 2 interseptimal regions near the unison and octave:
	* 1–min2 – intermediate between [[64/63]] and [[28/27]] – 40¢–60¢		* 1–min2 – intermediate between [[64/63]] and [[28/27]] – 40¢–60¢
	* Maj7-8 – intermediate between [[27/14]] and [[63/32]] – 1140¢–1160¢		* Maj7-8 – intermediate between [[27/14]] and [[63/32]] – 1140¢–1160¢