Semifourth-generated scales - Revision history

Ground at 00:28, 12 July 2026

2026-07-12T00:28:49Z

← Older revision		Revision as of 00:28, 12 July 2026
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	* '''Interseptimal''' or '''Semaphore''' is a 2.3.7 temperament that tempers out 49/48, often considered inaccurate.		* '''Interseptimal''' or '''Semaphore''' is a 2.3.7 temperament that tempers out 49/48, often considered inaccurate.
	* '''Island''' temperament is a 2.3.13/5 temperament that tempers out 676/675, equating the semifourth to 15/13.		* '''Island''' temperament is a 2.3.13/5 temperament that tempers out 676/675, equating the semifourth to 15/13.
	* ~~'''Intergan''' (short for Interganassismic, a superset of 12edo's 2.3.17.19 Ganassismic) is a proposed 19&24 2.3.(5).11.(13 or 13/5).17.19 temperament by~~ [[~~User:Ground~~]] ~~that seeks to cover all of the notable concordances generated by a meantone-range semifourth.~~		* [[Intergan]]

	== See also ==		== See also ==
	* [[Chthonic harmony]]		* [[Chthonic harmony]]
	* [[Semiquartal]]		* [[Semiquartal]]

Vector at 01:56, 2 June 2026

2026-06-02T01:56:44Z

← Older revision		Revision as of 01:56, 2 June 2026
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	{{problematic}}		{{problematic}}
			[[File:Semaphore5.png\|thumb\|Semaphore pentatonic]]
	'''Semifourth-generated scales''' are scales in tuning systems where two generators of approximately 250 cents in size stack to a perfect fourth, defining a temperament archetype called '''alpha-dicot''' or '''omega-dicot'''{{Adv\|, and notated [P8, P4/2] in pergen notation.}}		'''Semifourth-generated scales''' are scales in tuning systems where two generators of approximately 250 cents in size stack to a perfect fourth, defining a temperament archetype called '''alpha-dicot''' or '''omega-dicot'''{{Adv\|, and notated [P8, P4/2] in pergen notation.}}

Inthar: /* Temperaments */

2026-04-24T22:23:42Z

Temperaments

← Older revision		Revision as of 22:23, 24 April 2026
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	== Temperaments ==		== Temperaments ==
	Semifourth-generated temperaments have the edo join 5 & 9 (ignoring [[val#~~Warts~~\|warts]]).		Semifourth-generated temperaments have the edo join 5 & 9 (ignoring [[val#Wart notation\|warts]]).
	* '''Interseptimal''' or '''Semaphore''' is a 2.3.7 temperament that tempers out 49/48, often considered inaccurate.		* '''Interseptimal''' or '''Semaphore''' is a 2.3.7 temperament that tempers out 49/48, often considered inaccurate.
	* '''Island''' temperament is a 2.3.13/5 temperament that tempers out 676/675, equating the semifourth to 15/13.		* '''Island''' temperament is a 2.3.13/5 temperament that tempers out 676/675, equating the semifourth to 15/13.

Inthar: /* Temperaments */

2026-04-24T22:23:24Z

Temperaments

← Older revision		Revision as of 22:23, 24 April 2026
Line 9:		Line 9:

	== Temperaments ==		== Temperaments ==
	Semifourth-generated temperaments have the edo join 5 & 9 (ignoring warts).		Semifourth-generated temperaments have the edo join 5 & 9 (ignoring [[val#Warts\|warts]]).
	* '''Interseptimal''' or '''Semaphore''' is a 2.3.7 temperament that tempers out 49/48, often considered inaccurate.		* '''Interseptimal''' or '''Semaphore''' is a 2.3.7 temperament that tempers out 49/48, often considered inaccurate.
	* '''Island''' temperament is a 2.3.13/5 temperament that tempers out 676/675, equating the semifourth to 15/13.		* '''Island''' temperament is a 2.3.13/5 temperament that tempers out 676/675, equating the semifourth to 15/13.

Ground: /* Temperaments */

2026-04-24T02:33:05Z

Temperaments

← Older revision		Revision as of 02:33, 24 April 2026
Line 12:		Line 12:
	* '''Interseptimal''' or '''Semaphore''' is a 2.3.7 temperament that tempers out 49/48, often considered inaccurate.		* '''Interseptimal''' or '''Semaphore''' is a 2.3.7 temperament that tempers out 49/48, often considered inaccurate.
	* '''Island''' temperament is a 2.3.13/5 temperament that tempers out 676/675, equating the semifourth to 15/13.		* '''Island''' temperament is a 2.3.13/5 temperament that tempers out 676/675, equating the semifourth to 15/13.
	* '''Intergan''' (short for Interganassismic, a superset of 12edo's 2.3.17.19 Ganassismic) is a proposed 19&24 2.3.(5).11.(13).17.19 temperament by [[User:Ground]] that seeks to cover all of the notable concordances generated by a meantone-range semifourth.		* '''Intergan''' (short for Interganassismic, a superset of 12edo's 2.3.17.19 Ganassismic) is a proposed 19&24 2.3.(5).11.(13 or 13/5).17.19 temperament by [[User:Ground]] that seeks to cover all of the notable concordances generated by a meantone-range semifourth.

	== See also ==		== See also ==
	* [[Chthonic harmony]]		* [[Chthonic harmony]]
	* [[Semiquartal]]		* [[Semiquartal]]

Ground: /* Temperaments */

2026-04-24T02:32:26Z

Temperaments

← Older revision		Revision as of 02:32, 24 April 2026
Line 11:		Line 11:
	Semifourth-generated temperaments have the edo join 5 & 9 (ignoring warts).		Semifourth-generated temperaments have the edo join 5 & 9 (ignoring warts).
	* '''Interseptimal''' or '''Semaphore''' is a 2.3.7 temperament that tempers out 49/48, often considered inaccurate.		* '''Interseptimal''' or '''Semaphore''' is a 2.3.7 temperament that tempers out 49/48, often considered inaccurate.
	* '''Island''' temperament is a 2.3.15/13 temperament that tempers out 676/675, equating the semifourth to 15/13.		* '''Island''' temperament is a 2.3.13/5 temperament that tempers out 676/675, equating the semifourth to 15/13.
			* '''Intergan''' (short for Interganassismic, a superset of 12edo's 2.3.17.19 Ganassismic) is a proposed 19&24 2.3.(5).11.(13).17.19 temperament by [[User:Ground]] that seeks to cover all of the notable concordances generated by a meantone-range semifourth.

	== See also ==		== See also ==
	* [[Chthonic harmony]]		* [[Chthonic harmony]]
			* [[Semiquartal]]

Inthar: /* Temperaments */

2026-03-28T08:46:02Z

Temperaments

← Older revision		Revision as of 08:46, 28 March 2026
Line 10:		Line 10:
	== Temperaments ==		== Temperaments ==
	Semifourth-generated temperaments have the edo join 5 & 9 (ignoring warts).		Semifourth-generated temperaments have the edo join 5 & 9 (ignoring warts).
	* '''Interseptimal''' or '''Semaphore''' is a 2.3.7 temperament that tempers out 49/48~~. This is~~ often considered inaccurate.		* '''Interseptimal''' or '''Semaphore''' is a 2.3.7 temperament that tempers out 49/48, often considered inaccurate.
	* '''Island''' temperament is a 2.3.15/13 temperament that tempers out 676/675, equating the semifourth to 15/13.		* '''Island''' temperament is a 2.3.15/13 temperament that tempers out 676/675, equating the semifourth to 15/13.

	== See also ==		== See also ==
	* [[Chthonic harmony]]		* [[Chthonic harmony]]

Inthar: /* Temperaments */

2026-03-28T08:34:26Z

Temperaments

← Older revision		Revision as of 08:34, 28 March 2026
Line 9:		Line 9:

	== Temperaments ==		== Temperaments ==
			Semifourth-generated temperaments have the edo join 5 & 9 (ignoring warts).
	* '''Interseptimal''' or '''Semaphore''' is a 2.3.7 temperament that tempers out 49/48. This is often considered inaccurate.		* '''Interseptimal''' or '''Semaphore''' is a 2.3.7 temperament that tempers out 49/48. This is often considered inaccurate.
	* '''Island''' temperament is a 2.3.15/13 temperament that tempers out 676/675, equating the semifourth to 15/13.		* '''Island''' temperament is a 2.3.15/13 temperament that tempers out 676/675, equating the semifourth to 15/13.

	== See also ==		== See also ==
	* [[Chthonic harmony]]		* [[Chthonic harmony]]

Inthar at 08:33, 28 March 2026

2026-03-28T08:33:32Z

← Older revision		Revision as of 08:33, 28 March 2026
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	== Intervals and notation ==		== Intervals and notation ==
	Alpha-dicot notation is complicated as it conventionally requires either the introduction of new "hemi-Pythagorean" ordinals or the use of scales other than the standard diatonic scale. As such, there is no universally accepted convention. An intuitive option, if one that takes getting used to, is to use [https://en.xen.wiki/w/KISS_notation KISS] notation or [https://en.xen.wiki/w/Diamond-mos_notation diamond-mos] notation for 5L 4s.		Alpha-dicot notation is complicated as it conventionally requires either the introduction of new "hemi-Pythagorean" ordinals or the use of scales other than the standard diatonic scale. As such, there is no universally accepted convention. An intuitive option, if one that takes getting used to, is to use [https://en.xen.wiki/w/KISS_notation KISS] notation or [https://en.xen.wiki/w/Diamond-mos_notation diamond-mos] notation for 5L 4s.

			== Temperaments ==
			* '''Interseptimal''' or '''Semaphore''' is a 2.3.7 temperament that tempers out 49/48. This is often considered inaccurate.
			* '''Island''' temperament is a 2.3.15/13 temperament that tempers out 676/675, equating the semifourth to 15/13.

	== See also ==		== See also ==
	* [[Chthonic harmony]]		* [[Chthonic harmony]]

Overthink: link and spaces

2026-03-22T22:49:29Z

link and spaces

← Older revision		Revision as of 22:49, 22 March 2026
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	'''Semifourth-generated scales''' are scales in tuning systems where two generators of approximately 250 cents in size stack to a perfect fourth, defining a temperament archetype called '''alpha-dicot''' or '''omega-dicot'''{{Adv\|, and notated [P8, P4/2] in pergen notation.}}		'''Semifourth-generated scales''' are scales in tuning systems where two generators of approximately 250 cents in size stack to a perfect fourth, defining a temperament archetype called '''alpha-dicot''' or '''omega-dicot'''{{Adv\|, and notated [P8, P4/2] in pergen notation.}}

	The semifourth-generated scales are characteristically 4L 1s, semiquartal (~~5L4s~~), and ~~5L9s~~. 4L 1s is structurally significant because it is the [[Equipentatonic\|equal trichordal pentatonic]].		The semifourth-generated scales are characteristically 4L 1s, [[semiquartal]] (5L 4s), and 5L 9s. 4L 1s is structurally significant because it is the [[Equipentatonic\|equal trichordal pentatonic]].

	== Intervals and notation ==		== Intervals and notation ==