22L 1s - Revision history

ArrowHead294 at 14:20, 5 May 2025

2025-05-05T14:20:18Z

← Older revision		Revision as of 14:20, 5 May 2025
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	== Scale properties ==		== Scale properties ==
	{{TAMNAMS use}}		{{TAMNAMS use}}
	{{MOS ~~data~~
	~~\| modes note~~ = ~~Eliora proposes naming the brightest~~ mode ~~Alpharabian, after the fact that 33/32 is called Al-Farabi quarter-tone, and the rest after Tarot Major Arcana adjectivals based on how many generators down there is.~~		=== Intervals ===
	}}		{{MOS intervals}}

			=== Generator chain ===
			{{MOS genchain}}

			=== Modes ===
			{{MOS mode degrees}}

	== Scale tree ==		== Scale tree ==

ArrowHead294 at 17:01, 3 March 2025

2025-03-03T17:01:56Z

← Older revision		Revision as of 17:01, 3 March 2025
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	}}		}}
	{{MOS intro}}		{{MOS intro}}
	This scale is produced by stacking the interval of [[33/32]] (around ~~53¢~~).		This scale is produced by stacking the interval of [[33/32]] (around 53{{c}}).

	The name '''quartismoid''' is proposed for this pattern since its harmonic entropy minimum corresponds to tempering out the [[quartisma]] ~~- five~~ 33/32s being equated with 7/6. In addition, both [[22edo]] and [[23edo]], extreme ranges of the MOS temper out the quartisma, as well as a large portion of EDOs up to 100-200 which have this scale.		The name '''quartismoid''' is proposed for this pattern since its harmonic entropy minimum corresponds to tempering out the [[quartisma]]—five 33/32s being equated with 7/6. In addition, both [[22edo]] and [[23edo]], extreme ranges of the MOS temper out the quartisma, as well as a large portion of EDOs up to 100-200 which have this scale.

	== Tuning ranges ==		== Tuning ranges ==
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	From 1\22 to 4\91, 13 steps amount to a diatonic fifth.		From 1\22 to 4\91, 13 steps amount to a diatonic fifth.

	If the pure 33/32 is used as a generator, the resulting fifth is 692.54826 ~~cents~~, which puts it in the category around flattone.		If the pure 33/32 is used as a generator, the resulting fifth is 692.54826{{c}}, which puts it in the category around flattone.

	==== 700-cent, just, and superpyth fifths (step ratio 7:2 and harder) ====		==== 700-cent, just, and superpyth fifths (step ratio 7:2 and harder) ====
	In 156edo, the fifth becomes the [[12edo]] 700~~-cent~~ fifth. In 200edo, the fifth comes incredibly close to just, as the number 200 is a semiconvergent denominator to the approximation of log2(3/2).		In 156edo, the fifth becomes the [[12edo]] 700{{c}} fifth. In 200edo, the fifth comes incredibly close to just, as the number 200 is a semiconvergent denominator to the approximation of log2(3/2).

	When the step ratio is greater than 4.472, then 13 generators amount to a superpyth fifth and the tuning approaches [[22edo]].		When the step ratio is greater than 4.472, then 13 generators amount to a superpyth fifth and the tuning approaches [[22edo]].
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	{{MOS tuning spectrum}}		{{MOS tuning spectrum}}

	~~== Scale tree ==~~		== See also ==
	~~{{Scale tree}}~~

	==See also==
	* [[33/32]]		* [[33/32]]
	* [[33/32 equal step tuning]]		* [[33/32 equal step tuning]]

ArrowHead294 at 16:53, 3 March 2025

2025-03-03T16:53:41Z

← Older revision		Revision as of 16:53, 3 March 2025
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	The name '''quartismoid''' is proposed for this pattern since its harmonic entropy minimum corresponds to tempering out the [[quartisma]] - five 33/32s being equated with 7/6. In addition, both [[22edo]] and [[23edo]], extreme ranges of the MOS temper out the quartisma, as well as a large portion of EDOs up to 100-200 which have this scale.		The name '''quartismoid''' is proposed for this pattern since its harmonic entropy minimum corresponds to tempering out the [[quartisma]] - five 33/32s being equated with 7/6. In addition, both [[22edo]] and [[23edo]], extreme ranges of the MOS temper out the quartisma, as well as a large portion of EDOs up to 100-200 which have this scale.

	==Tuning ranges==		== Tuning ranges ==

	=== Mavila fifth and 91edo (Ultrasoft and supersoft) ===		=== Mavila fifth and 91edo (Ultrasoft and supersoft) ===
	Between 4\91 and 1\23, 13 steps amount to a pelog / mavila fifth, which corresponds to the ultrasoft step ratio range. In [[91edo]], the fifth produced by 13 steps of the quartismoid scale is the same as 4 steps of [[7edo]], and thus is the exact boundary between mavila and diatonic.		Between 4\91 and 1\23, 13 steps amount to a pelog / mavila fifth, which corresponds to the ultrasoft step ratio range. In [[91edo]], the fifth produced by 13 steps of the quartismoid scale is the same as 4 steps of [[7edo]], and thus is the exact boundary between mavila and diatonic.
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	6 steps act as a pseudo-6/5, and when they actually act as 6/5 along with 5 steps being equal to 7/6, [[385/384]] is tempered out. If one were to instead tune in favour of 6/5 instead of 7/6, the resulting hardness would be around 1.233. 114edo and 137edo represent this the best.		6 steps act as a pseudo-6/5, and when they actually act as 6/5 along with 5 steps being equal to 7/6, [[385/384]] is tempered out. If one were to instead tune in favour of 6/5 instead of 7/6, the resulting hardness would be around 1.233. 114edo and 137edo represent this the best.

	== ~~Modes~~ ==		== Scale properties ==
	Eliora proposes naming the brightest mode Alpharabian, after the fact that 33/32 is called Al-Farabi quarter-tone, and the rest after Tarot Major Arcana adjectivals based on how many generators down there is.		{{TAMNAMS use}}
	~~{\| class="wikitable"~~		{{MOS data
	\|+		\| modes note = Eliora proposes naming the brightest mode Alpharabian, after the fact that 33/32 is called Al-Farabi quarter-tone, and the rest after Tarot Major Arcana adjectivals based on how many generators down there is.
	~~!Mode~~		}}
	~~!Name~~
	\|-
	~~\|<nowiki>22\|0</nowiki>~~
	~~\|Alpharabian~~
	\|-
	~~\|<nowiki>21\|1</nowiki>~~
	~~\|Magical~~
	\|-
	~~\|<nowiki>20\|2</nowiki>~~
	~~\|High Priestess's~~
	\|-
	~~\|<nowiki>19\|3</nowiki>~~
	~~\|Empress's~~
	\|-
	~~\|...~~
	~~\|...~~
	\|-
	~~\|<nowiki>2\|20</nowiki>~~
	~~\|Judgemental~~
	\|-
	~~\|<nowiki>1\|21</nowiki>~~
	~~\|Worldwide~~
	\|-
	~~\|<nowiki>0\|22</nowiki>~~
	~~\|Foolish~~
	\|}

	== ~~Intervals~~ ==		== Scale tree ==
	{{MOS ~~intervals~~}}		{{MOS tuning spectrum}}

	== Scale tree ==		== Scale tree ==

BudjarnLambeth: == Intervals == {{MOS intervals}}

2024-12-15T08:37:52Z

== Intervals == {{MOS intervals}}

← Older revision		Revision as of 08:37, 15 December 2024
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	\|Foolish		\|Foolish
	\|}		\|}

			== Intervals ==
			{{MOS intervals}}

	== Scale tree ==		== Scale tree ==

Eliora: /* Scale tree */ adopt template

2024-03-03T00:27:07Z

Scale tree: adopt template

@@ Line 64: / Line 64: @@
 == Scale tree ==
-{| class="wikitable center-all"
+{{Scale tree}}
-! colspan="6" |Generator
 ==See also==
 * [[33/32]]
 * [[33/32 equal step tuning]]

Ganaram inukshuk: a space

2024-02-26T20:36:14Z

a space

← Older revision		Revision as of 20:36, 26 February 2024
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	}}		}}
	{{MOS intro}}		{{MOS intro}}

	This scale is produced by stacking the interval of [[33/32]] (around 53¢).		This scale is produced by stacking the interval of [[33/32]] (around 53¢).

Ganaram inukshuk: Mos intro

2024-02-26T20:36:07Z

Mos intro

← Older revision		Revision as of 20:36, 26 February 2024
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	\| Other names = quartismoid		\| Other names = quartismoid
	}}		}}
	~~22L 1s is the scale that is most commonly produced by stacking the interval of [[33/32]].~~		{{MOS intro}}

	A name '''quartismoid''' is proposed for this pattern since its harmonic entropy minimum corresponds to tempering out the [[quartisma]] - five 33/32s being equated with 7/6. In addition, both [[22edo]] and [[23edo]], extreme ranges of the MOS temper out the quartisma, as well as a large portion of EDOs up to 100-200 which have this scale.		This scale is produced by stacking the interval of [[33/32]] (around 53¢).

			The name '''quartismoid''' is proposed for this pattern since its harmonic entropy minimum corresponds to tempering out the [[quartisma]] - five 33/32s being equated with 7/6. In addition, both [[22edo]] and [[23edo]], extreme ranges of the MOS temper out the quartisma, as well as a large portion of EDOs up to 100-200 which have this scale.

	==Tuning ranges==		==Tuning ranges==

Eliora: /* Tuning ranges */ fix the fact

2023-01-10T16:37:19Z

Tuning ranges: fix the fact

← Older revision		Revision as of 16:37, 10 January 2023
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	From 1\22 to 4\91, 13 steps amount to a diatonic fifth.		From 1\22 to 4\91, 13 steps amount to a diatonic fifth.

	If the pure 33/32 is used as a generator, the resulting fifth is 692.54826 cents, which puts it in the category around flattone		If the pure 33/32 is used as a generator, the resulting fifth is 692.54826 cents, which puts it in the category around flattone.

	==== 700-cent, just, and superpyth fifths (step ratio 7:2 and harder) ====		==== 700-cent, just, and superpyth fifths (step ratio 7:2 and harder) ====
	In 156edo, the fifth becomes the [[12edo]] 700-cent fifth. In 200edo, the fifth comes incredibly close to just, as the number 200 is a ~~convergent~~ denominator to the approximation of log2(3/2).		In 156edo, the fifth becomes the [[12edo]] 700-cent fifth. In 200edo, the fifth comes incredibly close to just, as the number 200 is a semiconvergent denominator to the approximation of log2(3/2).

	When the step ratio is greater than 4.472, then 13 generators amount to a superpyth fifth and the tuning approaches [[22edo]].		When the step ratio is greater than 4.472, then 13 generators amount to a superpyth fifth and the tuning approaches [[22edo]].

Eliora: explain that it's not just stacking 33/32 to get 7/6, but it covers the entire range pretty much.

2023-01-10T16:36:24Z

explain that it's not just stacking 33/32 to get 7/6, but it covers the entire range pretty much.

← Older revision		Revision as of 16:36, 10 January 2023
Line 8:		Line 8:
	\| Other names = quartismoid		\| Other names = quartismoid
	}}		}}
	22L 1s is the scale that is most commonly produced by stacking the interval of [[33/32]]. ~~If it had a~~ name~~, it would most probably be~~ '''quartismoid''', since its harmonic entropy minimum corresponds to tempering out the [[quartisma]] - five 33/32s being equated with 7/6.		22L 1s is the scale that is most commonly produced by stacking the interval of [[33/32]].

			A name '''quartismoid''' is proposed for this pattern since its harmonic entropy minimum corresponds to tempering out the [[quartisma]] - five 33/32s being equated with 7/6. In addition, both [[22edo]] and [[23edo]], extreme ranges of the MOS temper out the quartisma, as well as a large portion of EDOs up to 100-200 which have this scale.

	==Tuning ranges==		==Tuning ranges==

Eliora at 00:47, 15 December 2022

2022-12-15T00:47:50Z

← Older revision		Revision as of 00:47, 15 December 2022
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	\| Collapsed = 1		\| Collapsed = 1
	\| Pattern = LLL...22x...LLLs		\| Pattern = LLL...22x...LLLs
			\| Other names = quartismoid
	}}		}}
	22L 1s is the scale that is most commonly produced by stacking the interval of [[33/32]]. If it had a name, it would most probably be '''quartismoid''', since its harmonic entropy minimum corresponds to tempering out the [[quartisma]] - five 33/32s being equated with 7/6.		22L 1s is the scale that is most commonly produced by stacking the interval of [[33/32]]. If it had a name, it would most probably be '''quartismoid''', since its harmonic entropy minimum corresponds to tempering out the [[quartisma]] - five 33/32s being equated with 7/6.