2.5.7 subgroup - Revision history

Inthar: /* JI scales */

2026-07-17T02:55:45Z

JI scales

← Older revision		Revision as of 02:55, 17 July 2026
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	== JI scales ==		== JI scales ==
	The fundamental 2.5.7 [[aberrismic]] scale is ~~prelembic~~ or citro3s (4L2m3s, L = 28/25, m = 35/32, s = 50/49). It is the JI preimage of Lemba[6], or soft citric, via adding three 50/49 steps.		The fundamental 2.5.7 [[aberrismic]] scale is prejubilic or citro3s (4L2m3s, L = 28/25, m = 35/32, s = 50/49). It is the JI preimage of Lemba[6], or soft citric, via adding three 50/49 steps.
	* Achiral: LsmLsLmsL (28/25 8/7 5/4 7/5 10/7 8/5 7/4 25/14 2/1)		* Achiral: LsmLsLmsL (28/25 8/7 5/4 7/5 10/7 8/5 7/4 25/14 2/1)
	* Right-handed: sLmLsLmsL (50/49 8/7 5/4 7/5 10/7 8/5 7/4 25/14 2/1)		* Right-handed: sLmLsLmsL (50/49 8/7 5/4 7/5 10/7 8/5 7/4 25/14 2/1)

Inthar: /* JI scales */

2026-07-13T17:55:11Z

JI scales

← Older revision		Revision as of 17:55, 13 July 2026
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	== JI scales ==		== JI scales ==
	The fundamental 2.5.7 [[aberrismic]] scale is prelembic or citro3s (4L2m3s, L = 28/25, m = 35/32, s = 50/49). It is the JI preimage of Lemba[6], or citric, via adding three 50/49 steps.		The fundamental 2.5.7 [[aberrismic]] scale is prelembic or citro3s (4L2m3s, L = 28/25, m = 35/32, s = 50/49). It is the JI preimage of Lemba[6], or soft citric, via adding three 50/49 steps.
	* Achiral: LsmLsLmsL (28/25 8/7 5/4 7/5 10/7 8/5 7/4 25/14 2/1)		* Achiral: LsmLsLmsL (28/25 8/7 5/4 7/5 10/7 8/5 7/4 25/14 2/1)
	* Right-handed: sLmLsLmsL (50/49 8/7 5/4 7/5 10/7 8/5 7/4 25/14 2/1)		* Right-handed: sLmLsLmsL (50/49 8/7 5/4 7/5 10/7 8/5 7/4 25/14 2/1)
	* Left-handed: LsmLsLmLs (28/25 8/7 5/4 7/5 10/7 8/5 7/4 49/25 2/1)		* Left-handed: LsmLsLmLs (28/25 8/7 5/4 7/5 10/7 8/5 7/4 49/25 2/1)
	~~It sounds like soft [[citric]] (4L2s) with aberrismas.~~

	Didacus tempering sets L = m + s. 37edo equates 49/40 to 16/13.		Didacus tempering sets L = m + s. 37edo equates 49/40 to 16/13.

Inthar: /* JI scales */

2026-07-13T17:54:11Z

JI scales

← Older revision		Revision as of 17:54, 13 July 2026
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	== JI scales ==		== JI scales ==
	The fundamental 2.5.7 [[aberrismic]] scale is prelembic ~~(tentative name)~~ or citro3s (4L2m3s, L = 28/25, m = 35/32, s = 50/49). It is the JI preimage of Lemba[6], or citric, via adding three 50/49 steps.		The fundamental 2.5.7 [[aberrismic]] scale is prelembic or citro3s (4L2m3s, L = 28/25, m = 35/32, s = 50/49). It is the JI preimage of Lemba[6], or citric, via adding three 50/49 steps.
	* Achiral: LsmLsLmsL (28/25 8/7 5/4 7/5 10/7 8/5 7/4 25/14 2/1)		* Achiral: LsmLsLmsL (28/25 8/7 5/4 7/5 10/7 8/5 7/4 25/14 2/1)
	* Right-handed: sLmLsLmsL (50/49 8/7 5/4 7/5 10/7 8/5 7/4 25/14 2/1)		* Right-handed: sLmLsLmsL (50/49 8/7 5/4 7/5 10/7 8/5 7/4 25/14 2/1)

Inthar: /* JI scales */

2026-07-13T17:53:55Z

JI scales

← Older revision		Revision as of 17:53, 13 July 2026
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	== JI scales ==		== JI scales ==
	The fundamental 2.5.7 [[aberrismic]] scale is 4L2m3s, L = 28/25, m = 35/32, s = 50/49:		The fundamental 2.5.7 [[aberrismic]] scale is prelembic (tentative name) or citro3s (4L2m3s, L = 28/25, m = 35/32, s = 50/49). It is the JI preimage of Lemba[6], or citric, via adding three 50/49 steps.
	* Achiral: LsmLsLmsL (28/25 8/7 5/4 7/5 10/7 8/5 7/4 25/14 2/1)		* Achiral: LsmLsLmsL (28/25 8/7 5/4 7/5 10/7 8/5 7/4 25/14 2/1)
	* Right-handed: sLmLsLmsL (50/49 8/7 5/4 7/5 10/7 8/5 7/4 25/14 2/1)		* Right-handed: sLmLsLmsL (50/49 8/7 5/4 7/5 10/7 8/5 7/4 25/14 2/1)
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	\|25/14		\|25/14
	\|}		\|}

	== Tempered scales ==		== Tempered scales ==
	=== [[Didacus]][6] ===		=== [[Didacus]][6] ===

Inthar: /* Temperaments */

2026-06-07T08:02:40Z

Temperaments

← Older revision		Revision as of 08:02, 7 June 2026
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	* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].		* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].
	{{Cat\|JI groups}}		{{Cat\|JI groups}}
	* [[Sidewalk]] ({{e\|21}} & {{e\|46}}): Generated by a neominor third, two of which make 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. Accurately extends to primes 11, 13, 17, and 23.		* [[Sidewalk]] ({{e\|21}} & {{e\|46}}): Generated by a neominor third, two of which make a flattened 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. Accurately extends to primes 11, 13, 17, and 23.

Inthar: /* Temperaments */

2026-06-07T03:35:04Z

Temperaments

← Older revision		Revision as of 03:35, 7 June 2026
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	== Temperaments ==		== Temperaments ==
	Common rank-2 temperaments in 2.5.7 (i.e. temperaments that interpret intervals as 2.5.7 JI ratios):		Common rank-2 temperaments in 2.5.7 (i.e. temperaments that interpret intervals as 2.5.7 JI ratios):
	* [[Didacus]] ({{e\|25}} & {{e\|31}}): Best accuracy-simplicity tradeoff. Generates 5L1s generated by ~28/25.		* [[Didacus]] ({{e\|25}} & {{e\|31}}): Best accuracy-simplicity tradeoff among 2.5.7 temperaments. Generates 5L1s generated by ~28/25.
	* [[Mabilic]] ({{e\|16}} & {{e\|25}}): generated by a flat armotonic fifth around 672 cents.
	* [[Jubilismic]] ({{e\|16}} & {{e\|22}}): Less accurate, identifying 7/5 and 10/7. Has [[citric]] (4L2s, LLsLLs) MOS scales (L/s = 3/2 in 16edo, L/s = 4/3 in 22edo).		* [[Jubilismic]] ({{e\|16}} & {{e\|22}}): Less accurate, identifying 7/5 and 10/7. Has [[citric]] (4L2s, LLsLLs) MOS scales (L/s = 3/2 in 16edo, L/s = 4/3 in 22edo).
			* [[Mabilic]] ({{e\|16}} & {{e\|25}}): Generated by a flat armotonic fifth around 672 cents.
	* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].		* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].
	{{Cat\|JI groups}}		{{Cat\|JI groups}}
	* [[Sidewalk]] ({{e\|21}} & {{e\|46}}): ~~generated~~ by a neominor third, two of which make 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. Accurately extends to primes 11, 13, 17, and 23.		* [[Sidewalk]] ({{e\|21}} & {{e\|46}}): Generated by a neominor third, two of which make 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. Accurately extends to primes 11, 13, 17, and 23.

Inthar: /* Temperaments */

2026-06-07T03:33:58Z

Temperaments

← Older revision		Revision as of 03:33, 7 June 2026
Line 364:		Line 364:
	Common rank-2 temperaments in 2.5.7 (i.e. temperaments that interpret intervals as 2.5.7 JI ratios):		Common rank-2 temperaments in 2.5.7 (i.e. temperaments that interpret intervals as 2.5.7 JI ratios):
	* [[Didacus]] ({{e\|25}} & {{e\|31}}): Best accuracy-simplicity tradeoff. Generates 5L1s generated by ~28/25.		* [[Didacus]] ({{e\|25}} & {{e\|31}}): Best accuracy-simplicity tradeoff. Generates 5L1s generated by ~28/25.
			* [[Mabilic]] ({{e\|16}} & {{e\|25}}): generated by a flat armotonic fifth around 672 cents.
	* [[Jubilismic]] ({{e\|16}} & {{e\|22}}): Less accurate, identifying 7/5 and 10/7. Has [[citric]] (4L2s, LLsLLs) MOS scales (L/s = 3/2 in 16edo, L/s = 4/3 in 22edo).		* [[Jubilismic]] ({{e\|16}} & {{e\|22}}): Less accurate, identifying 7/5 and 10/7. Has [[citric]] (4L2s, LLsLLs) MOS scales (L/s = 3/2 in 16edo, L/s = 4/3 in 22edo).
	* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].		* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].
	{{Cat\|JI groups}}		{{Cat\|JI groups}}
	* [[Sidewalk]] ({{e\|21}} & {{e\|46}}): generated by a neominor third, two of which make 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. Accurately extends to primes 11, 13, 17, and 23.		* [[Sidewalk]] ({{e\|21}} & {{e\|46}}): generated by a neominor third, two of which make 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. Accurately extends to primes 11, 13, 17, and 23.

Inthar: /* Temperaments */

2026-06-07T03:32:39Z

Temperaments

← Older revision		Revision as of 03:32, 7 June 2026
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	* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].		* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].
	{{Cat\|JI groups}}		{{Cat\|JI groups}}
	* [[Sidewalk]] ({{e\|21}} & {{e\|46}}): generated by a neominor third, two of which make 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. ~~Noted for accurately extending~~ to primes 11, 13, 17, and 23.		* [[Sidewalk]] ({{e\|21}} & {{e\|46}}): generated by a neominor third, two of which make 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. Accurately extends to primes 11, 13, 17, and 23.

Inthar: /* Temperaments */

2026-06-07T03:32:09Z

Temperaments

← Older revision		Revision as of 03:32, 7 June 2026
Line 367:		Line 367:
	* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].		* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].
	{{Cat\|JI groups}}		{{Cat\|JI groups}}
	* [[Sidewalk]] ({{e\|21}} & {{e\|25}}): generated by a neominor third, two of which make 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. Noted for accurately extending to primes 11, 13, 17, and 23.		* [[Sidewalk]] ({{e\|21}} & {{e\|46}}): generated by a neominor third, two of which make 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. Noted for accurately extending to primes 11, 13, 17, and 23.

Inthar: /* Temperaments */

2026-06-07T03:30:51Z

Temperaments

← Older revision		Revision as of 03:30, 7 June 2026
Line 367:		Line 367:
	* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].		* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].
	{{Cat\|JI groups}}		{{Cat\|JI groups}}
			* [[Sidewalk]] ({{e\|21}} & {{e\|25}}): generated by a neominor third, two of which make 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. Noted for accurately extending to primes 11, 13, 17, and 23.

← Older revision		Revision as of 08:02, 7 June 2026
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	* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].		* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].
	{{Cat\|JI groups}}		{{Cat\|JI groups}}
	* [[Sidewalk]] ({{e\|21}} & {{e\|46}}): Generated by a neominor third, two of which make 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. Accurately extends to primes 11, 13, 17, and 23.		* [[Sidewalk]] ({{e\|21}} & {{e\|46}}): Generated by a neominor third, two of which make a flattened 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. Accurately extends to primes 11, 13, 17, and 23.

← Older revision		Revision as of 03:35, 7 June 2026
Line 363:		Line 363:
	== Temperaments ==		== Temperaments ==
	Common rank-2 temperaments in 2.5.7 (i.e. temperaments that interpret intervals as 2.5.7 JI ratios):		Common rank-2 temperaments in 2.5.7 (i.e. temperaments that interpret intervals as 2.5.7 JI ratios):
	* [[Didacus]] ({{e\|25}} & {{e\|31}}): Best accuracy-simplicity tradeoff. Generates 5L1s generated by ~28/25.		* [[Didacus]] ({{e\|25}} & {{e\|31}}): Best accuracy-simplicity tradeoff among 2.5.7 temperaments. Generates 5L1s generated by ~28/25.
	* [[Mabilic]] ({{e\|16}} & {{e\|25}}): generated by a flat armotonic fifth around 672 cents.
	* [[Jubilismic]] ({{e\|16}} & {{e\|22}}): Less accurate, identifying 7/5 and 10/7. Has [[citric]] (4L2s, LLsLLs) MOS scales (L/s = 3/2 in 16edo, L/s = 4/3 in 22edo).		* [[Jubilismic]] ({{e\|16}} & {{e\|22}}): Less accurate, identifying 7/5 and 10/7. Has [[citric]] (4L2s, LLsLLs) MOS scales (L/s = 3/2 in 16edo, L/s = 4/3 in 22edo).
			* [[Mabilic]] ({{e\|16}} & {{e\|25}}): Generated by a flat armotonic fifth around 672 cents.
	* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].		* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].
	{{Cat\|JI groups}}		{{Cat\|JI groups}}
	* [[Sidewalk]] ({{e\|21}} & {{e\|46}}): ~~generated~~ by a neominor third, two of which make 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. Accurately extends to primes 11, 13, 17, and 23.		* [[Sidewalk]] ({{e\|21}} & {{e\|46}}): Generated by a neominor third, two of which make 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. Accurately extends to primes 11, 13, 17, and 23.

← Older revision		Revision as of 03:33, 7 June 2026
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	Common rank-2 temperaments in 2.5.7 (i.e. temperaments that interpret intervals as 2.5.7 JI ratios):		Common rank-2 temperaments in 2.5.7 (i.e. temperaments that interpret intervals as 2.5.7 JI ratios):
	* [[Didacus]] ({{e\|25}} & {{e\|31}}): Best accuracy-simplicity tradeoff. Generates 5L1s generated by ~28/25.		* [[Didacus]] ({{e\|25}} & {{e\|31}}): Best accuracy-simplicity tradeoff. Generates 5L1s generated by ~28/25.
			* [[Mabilic]] ({{e\|16}} & {{e\|25}}): generated by a flat armotonic fifth around 672 cents.
	* [[Jubilismic]] ({{e\|16}} & {{e\|22}}): Less accurate, identifying 7/5 and 10/7. Has [[citric]] (4L2s, LLsLLs) MOS scales (L/s = 3/2 in 16edo, L/s = 4/3 in 22edo).		* [[Jubilismic]] ({{e\|16}} & {{e\|22}}): Less accurate, identifying 7/5 and 10/7. Has [[citric]] (4L2s, LLsLLs) MOS scales (L/s = 3/2 in 16edo, L/s = 4/3 in 22edo).
	* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].		* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].
	{{Cat\|JI groups}}		{{Cat\|JI groups}}
	* [[Sidewalk]] ({{e\|21}} & {{e\|46}}): generated by a neominor third, two of which make 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. Accurately extends to primes 11, 13, 17, and 23.		* [[Sidewalk]] ({{e\|21}} & {{e\|46}}): generated by a neominor third, two of which make 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. Accurately extends to primes 11, 13, 17, and 23.

← Older revision		Revision as of 03:32, 7 June 2026
Line 367:		Line 367:
	* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].		* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].
	{{Cat\|JI groups}}		{{Cat\|JI groups}}
	* [[Sidewalk]] ({{e\|21}} & {{e\|46}}): generated by a neominor third, two of which make 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. ~~Noted for accurately extending~~ to primes 11, 13, 17, and 23.		* [[Sidewalk]] ({{e\|21}} & {{e\|46}}): generated by a neominor third, two of which make 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. Accurately extends to primes 11, 13, 17, and 23.

← Older revision		Revision as of 03:32, 7 June 2026
Line 367:		Line 367:
	* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].		* 3edo.7 (6 & 15): Generates 3L3s with generator ~7/4. Supported by [[Augmented (temperament)\|Augmented]] edos such as [[15edo]], [[21edo]], and [[27edo]].
	{{Cat\|JI groups}}		{{Cat\|JI groups}}
	* [[Sidewalk]] ({{e\|21}} & {{e\|25}}): generated by a neominor third, two of which make 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. Noted for accurately extending to primes 11, 13, 17, and 23.		* [[Sidewalk]] ({{e\|21}} & {{e\|46}}): generated by a neominor third, two of which make 7/5; reaches 8/7 after 5 generator steps and 8/5 after 7 generator steps. Noted for accurately extending to primes 11, 13, 17, and 23.