Mabilic - Revision history

Kili: linkoe

2026-06-01T18:55:47Z

linkoe

← Older revision		Revision as of 18:55, 1 June 2026
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	'''Mabilic''' is a rank-2 [[regular temperament]] based around the [[antidiatonic]] and [[armotonic]] scale structures. [[5/4\|5/2]] is split into three [[generators]] which are somewhat sharper than a fourth (~520-530 cents), five of which stack (octave-reduced) to make [[8/7]].		'''Mabilic''' is a rank-2 [[regular temperament]] based around the [[antidiatonic]] and [[armotonic]] scale structures. [[5/4\|5/2]] is split into three [[Generator\|generators]] which are somewhat sharper than a fourth (~520-530 cents), five of which stack (octave-reduced) to make [[8/7]].
	Mabilic in its basic form is a [[2.5.7 subgroup]] temperament, because 3 cannot be added without a high complexity or a significant loss of accuracy. Mabilic[7] or [9], Semabila[16], and Trismegistus[25] are reasonable forms.		Mabilic in its basic form is a [[2.5.7 subgroup]] temperament, because 3 cannot be added without a high complexity or a significant loss of accuracy. Mabilic[7] or [9], Semabila[16], and Trismegistus[25] are reasonable forms.

Vector at 19:04, 30 May 2026

2026-05-30T19:04:48Z

← Older revision		Revision as of 19:04, 30 May 2026
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	*** In fact, Semabila easily extends to the full 23-limit by finding 16/13 at 12 generators and 16/11 at 8 generators, which is not accurate at all in Trismegistus.		*** In fact, Semabila easily extends to the full 23-limit by finding 16/13 at 12 generators and 16/11 at 8 generators, which is not accurate at all in Trismegistus.
	* Mavila (best tuned around 522-528 cents), an exotemperament which sets the generator itself equal to 4/3, and somewhat functions as an opposite to [[Meantone]].		* Mavila (best tuned around 522-528 cents), an exotemperament which sets the generator itself equal to 4/3, and somewhat functions as an opposite to [[Meantone]].
			** Mavila and trismegistus can be considered co-structural temperaments.
	In Meantone, 4 fifths make a 5/4; in Mavila they make a [[6/5]].		In Meantone, 4 fifths make a 5/4; in Mavila they make a [[6/5]].

Overthink: /* Intervals */ + 10/9

2026-04-09T22:13:13Z

Intervals: + 10/9

← Older revision		Revision as of 22:13, 9 April 2026
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	\|'''8/7'''		\|'''8/7'''
	\|		\|
	\|		\|10/9
	\|		\|
	\|-		\|-

Inthar at 04:30, 9 March 2026

2026-03-09T04:30:18Z

← Older revision		Revision as of 04:30, 9 March 2026
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	* Semabila (best tuned around 530 cents) which finds [[4/3]] at 10 generators up, equating it to two 8/7s ([[Alpha-dicot\|Semaphore]] temperament).		* Semabila (best tuned around 530 cents) which finds [[4/3]] at 10 generators up, equating it to two 8/7s ([[Alpha-dicot\|Semaphore]] temperament).
	** Semabila also tunes the fifth to 25/17, finding 17 at 7 generators; then 8 generators may be assigned to 23/16. This is possible but less accurate in Trismegistus.		** Semabila also tunes the fifth to 25/17, finding 17 at 7 generators; then 8 generators may be assigned to 23/16. This is possible but less accurate in Trismegistus.
	*** In fact, ~~semabila~~ easily extends to the full 23-limit by finding 16/13 at 12 generators and 16/11 at 8 generators, which is not accurate at all in Trismegistus.		*** In fact, Semabila easily extends to the full 23-limit by finding 16/13 at 12 generators and 16/11 at 8 generators, which is not accurate at all in Trismegistus.
	* Mavila (best tuned around 522-528 cents), an exotemperament which sets the generator itself equal to 4/3, and somewhat functions as an opposite to [[Meantone]].		* Mavila (best tuned around 522-528 cents), an exotemperament which sets the generator itself equal to 4/3, and somewhat functions as an opposite to [[Meantone]].
	In Meantone, 4 fifths make a 5/4; in Mavila they make a [[6/5]].		In Meantone, 4 fifths make a 5/4; in Mavila they make a [[6/5]].

Inthar at 04:29, 9 March 2026

2026-03-09T04:29:31Z

← Older revision		Revision as of 04:29, 9 March 2026
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	'''Mabilic''' is a rank-2 [[regular temperament]] based around the [[antidiatonic]] scale ~~structure~~. [[5/4\|5/2]] is split into three [[generators]] which are somewhat sharper than a fourth (~520-530 cents), five of which stack (octave-reduced) to make [[8/7]].		'''Mabilic''' is a rank-2 [[regular temperament]] based around the [[antidiatonic]] and [[armotonic]] scale structures. [[5/4\|5/2]] is split into three [[generators]] which are somewhat sharper than a fourth (~520-530 cents), five of which stack (octave-reduced) to make [[8/7]].
	Mabilic in its basic form is a [[2.5.7 subgroup]] temperament, because 3 cannot be added without a high complexity or a significant loss of accuracy. Mabilic[7] or [9], Semabila[16], and Trismegistus[25] are reasonable forms.		Mabilic in its basic form is a [[2.5.7 subgroup]] temperament, because 3 cannot be added without a high complexity or a significant loss of accuracy. Mabilic[7] or [9], Semabila[16], and Trismegistus[25] are reasonable forms.

Inthar: /* Intervals */

2026-02-24T21:29:34Z

Intervals

← Older revision		Revision as of 21:29, 24 February 2026
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	{{Navbox regtemp}}		{{Navbox regtemp}}
			{{Cat\|temperaments}}

Vector at 21:27, 24 February 2026

2026-02-24T21:27:29Z

← Older revision		Revision as of 21:27, 24 February 2026
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	'''Mabilic''' is a rank-2 [[regular temperament]] based around the [[antidiatonic]] scale structure. [[5/4\|5/2]] is split into three [[generators]] which are somewhat sharper than a fourth (~520-530 cents), five of which stack (octave-reduced) to make [[8/7]].		'''Mabilic''' is a rank-2 [[regular temperament]] based around the [[antidiatonic]] scale structure. [[5/4\|5/2]] is split into three [[generators]] which are somewhat sharper than a fourth (~520-530 cents), five of which stack (octave-reduced) to make [[8/7]].
	Mabilic in its basic form is a [[2.5.7 subgroup]] temperament, because 3 cannot be added without a high complexity or a significant loss of accuracy.		Mabilic in its basic form is a [[2.5.7 subgroup]] temperament, because 3 cannot be added without a high complexity or a significant loss of accuracy. Mabilic[7] or [9], Semabila[16], and Trismegistus[25] are reasonable forms.

	{{Cat\|Temperaments}}		{{Cat\|Temperaments}}
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	* Semabila (best tuned around 530 cents) which finds [[4/3]] at 10 generators up, equating it to two 8/7s ([[Alpha-dicot\|Semaphore]] temperament).		* Semabila (best tuned around 530 cents) which finds [[4/3]] at 10 generators up, equating it to two 8/7s ([[Alpha-dicot\|Semaphore]] temperament).
	** Semabila also tunes the fifth to 25/17, finding 17 at 7 generators; then 8 generators may be assigned to 23/16. This is possible but less accurate in Trismegistus.		** Semabila also tunes the fifth to 25/17, finding 17 at 7 generators; then 8 generators may be assigned to 23/16. This is possible but less accurate in Trismegistus.
			*** In fact, semabila easily extends to the full 23-limit by finding 16/13 at 12 generators and 16/11 at 8 generators, which is not accurate at all in Trismegistus.
	* Mavila (best tuned around 522-528 cents), an exotemperament which sets the generator itself equal to 4/3, and somewhat functions as an opposite to [[Meantone]].		* Mavila (best tuned around 522-528 cents), an exotemperament which sets the generator itself equal to 4/3, and somewhat functions as an opposite to [[Meantone]].
	In Meantone, 4 fifths make a 5/4; in Mavila they make a [[6/5]].		In Meantone, 4 fifths make a 5/4; in Mavila they make a [[6/5]].
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	!Generators		!Generators
	!Tuning		!Tuning
	!Interpretation (2.3.5.7.17.19.23)		!Interpretation (2.3.5.7.19)
			!Interpretation (2...29)
	\|-		\|-
	\|0		\|0
	\|0		\|0
	\|1/1		\|1/1
			\|
	\|-		\|-
	\|1		\|1
	\|530		\|530
	\|19/14, 23/17, 34/25		\|19/14
			\|23/17, 34/25, 15/11
	\|-		\|-
	\|2		\|2
	\|1060		\|1060
	\|28/15, 64/35		\|28/15, 64/35
			\|
	\|-		\|-
	\|3		\|3
	\|390		\|390
	\|5/4, 19/15		\|5/4, 19/15
			\|14/11
	\|-		\|-
	\|4		\|4
	\|920		\|920
	\|32/19		\|32/19
			\|
	\|-		\|-
	\|5		\|5
	\|250		\|250
	\|7/6, 8/7		\|7/6, 8/7
			\|15/13
	\|-		\|-
	\|6		\|6
	\|780		\|780
	\|25/16, 19/12		\|25/16, 19/12
			\|
	\|-		\|-
	\|7		\|7
	\|110		\|110
	\|16/15, 17/16		\|16/15
			\|17/16
	\|-		\|-
	\|8		\|8
	\|640		\|640
	\|10/7, 23/16		\|10/7
			\|23/16, 16/11
	\|-		\|-
	\|9		\|9
	\|1170		\|1170
			\|
	\|		\|
	\|-		\|-
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	\|500		\|500
	\|4/3		\|4/3
			\|
	\|-		\|-
	\|11		\|11
	\|1030		\|1030
	\|34/19		\|
			\|34/19, 29/16, 20/11
	\|-		\|-
	\|12		\|12
	\|360		\|360
	\|		\|
			\|16/13
	\|-		\|-
	\|13		\|13
	\|890		\|890
	\|5/3		\|5/3
			\|
	\|-		\|-
	\|14		\|14
	\|220		\|220
			\|
	\|17/15		\|17/15
	\|-		\|-
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	\|750		\|750
	\|32/21		\|32/21
			\|20/13
	\|}		\|}

Vector at 21:12, 24 February 2026

2026-02-24T21:12:38Z

Show changes

Inthar at 23:06, 22 February 2026

2026-02-22T23:06:47Z

← Older revision		Revision as of 23:06, 22 February 2026
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	In Meantone, 4 fifths make a 5/4; in Mavila they make a [[6/5]].		In Meantone, 4 fifths make a 5/4; in Mavila they make a [[6/5]].

	In any tuning, the ~~sharp~~ generator may be identified wth 28/19. This produces an accurate 2.5.7.19 temperament, and justifies the generator as an imperfect fifth of 95/64 created by stacking 5/4 and 19/16.		In any tuning, the flat fifth generator may be identified wth 28/19. This produces an accurate 2.5.7.19 temperament, and justifies the generator as an imperfect fifth of 95/64 created by stacking 5/4 and 19/16.

	== Intervals ==		== Intervals ==

Vector at 11:36, 22 February 2026

2026-02-22T11:36:45Z

Show changes