17L 2s - Revision history

Lucius Chiaraviglio: /* Scale tree */ Add note about warts on Liesel, and add Liese with similar note; also add another column to scale tree due to large size of MOS (and consistency with the scale tree for 15L 2s); remove Todo:complete table

2025-05-12T07:52:11Z

Scale tree: Add note about warts on Liesel, and add Liese with similar note; also add another column to scale tree due to large size of MOS (and consistency with the scale tree for 15L 2s); remove Todo:complete table

← Older revision		Revision as of 07:52, 12 May 2025
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	== Scale tree ==		== Scale tree ==
	{{~~Todo~~\|~~complete table~~\|~~inline~~=1\|~~text~~=~~Add temperaments to table — see the corresponding Talk page for a beta version of this.}}~~		{{MOS tuning spectrum
	~~{{MOS tuning spectrum~~}}		\| Depth = 6
			\| 5/4 = [[Pycnic]]
			\| 4/3 = [[Liese]] (as 74d)
			\| 5/3 = [[Liesel]] (as 91ceef)
			\| 13/4 = [[Alphatricot family#Alphatrident\|Alphatricot/Alphatrident]]
			}}

	{{Stub}}		{{Stub}}

Lériendil at 05:21, 3 May 2025

2025-05-03T05:21:35Z

← Older revision		Revision as of 05:21, 3 May 2025
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	{{Infobox MOS}}		{{Infobox MOS}}
	{{MOS intro}} From a regular temperament theory perspective, this scale is notable for corresponding to the mega chromatic scale of the [[Alphatricot family]] temperaments. Three bright generators can be interpreted to stack to [[3/1]], but unfortunately, the generator of 17L 2s itself does not have a very convenient rational representation, since the simple ratio [[23/16]] is off-scale flat, as is (just barely) the compound ratio [[36/25]], while the prime-over-compound ratio [[13/9]] is off-scale sharp. Using very high prime harmonics/subharmonics, we can make the interpretations of [[~]][[62/43]] (bright generator) or ~[[43/31]] (dark generator); the aforementioned Alphatricot family uses the highly compound ~[[59049/40960]] as a generator; and probably the best rational that falls within the scale is ~[[75/52]], three of which differ from 3/1 by the ~~unnoticeable~~ comma of [[140625/140608]], the catasma.		{{MOS intro}} From a regular temperament theory perspective, this scale is notable for corresponding to the mega chromatic scale of the [[Alphatricot family]] temperaments. Three bright generators can be interpreted to stack to [[3/1]], but unfortunately, the generator of 17L 2s itself does not have a very convenient rational representation, since the simple ratio [[23/16]] is off-scale flat, as is (just barely) the compound ratio [[36/25]], while the prime-over-compound ratio [[13/9]] is off-scale sharp. Using very high prime harmonics/subharmonics, we can make the interpretations of [[~]][[62/43]] (bright generator) or ~[[43/31]] (dark generator); the aforementioned Alphatricot family uses the highly compound ~[[59049/40960]] as a generator; and probably the best rational that falls within the scale is ~[[75/52]], three of which differ from 3/1 by the 0.2-cent comma of [[140625/140608]], the catasma.

	A pitfall of the use of compound harmonics and subharmonics in a generator is that they multiply the effect of shifts in mapping of their respective primes with scale hardness — for instance, ~59049/40960 only maps correctly within a narrow step ratio range close to 10:3, while ~36/25 fails to map correctly even for several EDOs close to the soft end of the scale's tuning spectrum (as does the simpler but flatter ~23/16); the even simpler ~13/9 (off-scale sharp) is likewise affected. Using such generators outside of a narrow subset of the EDOs supporting the scale depends upon direct approximation of a compound harmonic and/or subharmonic such as 9 or 25. This is awkward when one also needs to use a component harmonic as specified in the patent vals of the EDOs, thus requiring the use of nonstandard conditional subgroup temperaments such as 2.3♯.3♭.5 and 2.3.5♯.5♭ (or 2.3.9.5 and 2.3.5.25), with provision of a rule specifying when to use the direct approximation as opposed to the patent val mapping.		A pitfall of the use of compound harmonics and subharmonics in a generator is that they multiply the effect of shifts in mapping of their respective primes with scale hardness — for instance, ~59049/40960 only maps correctly within a narrow step ratio range close to 10:3, while ~36/25 fails to map correctly even for several EDOs close to the soft end of the scale's tuning spectrum (as does the simpler but flatter ~23/16); the even simpler ~13/9 (off-scale sharp) is likewise affected. Using such generators outside of a narrow subset of the EDOs supporting the scale depends upon direct approximation of a compound harmonic and/or subharmonic such as 9 or 25. This is awkward when one also needs to use a component harmonic as specified in the patent vals of the EDOs, thus requiring the use of nonstandard conditional subgroup temperaments such as 2.3♯.3♭.5 and 2.3.5♯.5♭ (or 2.3.9.5 and 2.3.5.25), with provision of a rule specifying when to use the direct approximation as opposed to the patent val mapping.

Lériendil: added Lucius's proposed intro with some minor tweaks

2025-05-03T05:20:13Z

added Lucius's proposed intro with some minor tweaks

← Older revision		Revision as of 05:20, 3 May 2025
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	{{Infobox MOS}}		{{Infobox MOS}}
	{{MOS intro}}		{{MOS intro}} From a regular temperament theory perspective, this scale is notable for corresponding to the mega chromatic scale of the [[Alphatricot family]] temperaments. Three bright generators can be interpreted to stack to [[3/1]], but unfortunately, the generator of 17L 2s itself does not have a very convenient rational representation, since the simple ratio [[23/16]] is off-scale flat, as is (just barely) the compound ratio [[36/25]], while the prime-over-compound ratio [[13/9]] is off-scale sharp. Using very high prime harmonics/subharmonics, we can make the interpretations of [[~]][[62/43]] (bright generator) or ~[[43/31]] (dark generator); the aforementioned Alphatricot family uses the highly compound ~[[59049/40960]] as a generator; and probably the best rational that falls within the scale is ~[[75/52]], three of which differ from 3/1 by the unnoticeable comma of [[140625/140608]], the catasma.

			A pitfall of the use of compound harmonics and subharmonics in a generator is that they multiply the effect of shifts in mapping of their respective primes with scale hardness — for instance, ~59049/40960 only maps correctly within a narrow step ratio range close to 10:3, while ~36/25 fails to map correctly even for several EDOs close to the soft end of the scale's tuning spectrum (as does the simpler but flatter ~23/16); the even simpler ~13/9 (off-scale sharp) is likewise affected. Using such generators outside of a narrow subset of the EDOs supporting the scale depends upon direct approximation of a compound harmonic and/or subharmonic such as 9 or 25. This is awkward when one also needs to use a component harmonic as specified in the patent vals of the EDOs, thus requiring the use of nonstandard conditional subgroup temperaments such as 2.3♯.3♭.5 and 2.3.5♯.5♭ (or 2.3.9.5 and 2.3.5.25), with provision of a rule specifying when to use the direct approximation as opposed to the patent val mapping.

	== Scale properties ==		== Scale properties ==

FloraC: Replace deprecated templates

2025-04-28T12:37:09Z

Replace deprecated templates

← Older revision		Revision as of 12:37, 28 April 2025
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	{{Infobox MOS}}		{{Infobox MOS}}
	{{MOS intro}}		{{MOS intro}}

	== Scale properties ==		== Scale properties ==
	{{TAMNAMS use}}		{{TAMNAMS use}}
	{{MOS ~~data~~}}
			=== Intervals ===
			{{MOS intervals}}

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

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

	== Scale tree ==		== Scale tree ==
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	{{MOS tuning spectrum}}		{{MOS tuning spectrum}}

	{{~~stub~~}}
			{{Stub}}

Lucius Chiaraviglio: /* Scale tree */ See the corresponding Talk page for a beta version of adding temperaments to the MOS tuning spectrum table

2025-04-28T06:45:21Z

Scale tree: See the corresponding Talk page for a beta version of adding temperaments to the MOS tuning spectrum table

← Older revision		Revision as of 06:45, 28 April 2025
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	== Scale tree ==		== Scale tree ==
			{{Todo\|complete table\|inline=1\|text=Add temperaments to table — see the corresponding Talk page for a beta version of this.}}
	{{MOS tuning spectrum}}		{{MOS tuning spectrum}}

	{{stub}}		{{stub}}

ArrowHead294 at 16:33, 3 March 2025

2025-03-03T16:33:50Z

← Older revision		Revision as of 16:33, 3 March 2025
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	{{Infobox MOS}}		{{Infobox MOS}}
	{{MOS intro}}		{{MOS intro}}
	== ~~Modes~~ ==		== Scale properties ==
	{{~~MOS modes~~}}		{{TAMNAMS use}}
	~~== Intervals ==~~		{{MOS data}}
	{{MOS ~~intervals~~}}
	== Scale tree ==		== Scale tree ==
	{{~~Scale tree~~}}		{{MOS tuning spectrum}}


	{{stub}}		{{stub}}

BudjarnLambeth: -todo:expand, already stub which is more accurate; add intervals

2024-12-15T00:26:03Z

-todo:expand, already stub which is more accurate; add intervals

← Older revision		Revision as of 00:26, 15 December 2024
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	== Modes ==		== Modes ==
	{{MOS modes}}		{{MOS modes}}
			== Intervals ==
			{{MOS intervals}}
	== Scale tree ==		== Scale tree ==
	{{Scale tree}}{{~~Stub~~}}		{{Scale tree}}
	~~[[category:todo:expand]]~~

			{{stub}}

Ganaram inukshuk: Replaced no-entries scale tree; stub

2024-03-01T07:28:02Z

Replaced no-entries scale tree; stub

Show changes

BudjarnLambeth: {{Infobox MOS}} {{MOS intro}} == Modes == {{MOS modes}} == Tuning spectrum ==

2024-01-30T06:05:58Z

{{Infobox MOS}} {{MOS intro}} == Modes == {{MOS modes}} == Tuning spectrum ==

← Older revision		Revision as of 06:05, 30 January 2024
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			{{Infobox MOS}}
			{{MOS intro}}
			== Modes ==
			{{MOS modes}}
			== Tuning spectrum ==
	{\| class="wikitable"		{\| class="wikitable"
	! colspan="9" \| generator		! colspan="9" \| generator
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	[[Category:Abstract MOS patterns]]		[[Category:Abstract MOS patterns]]
	~~[[category:todo:intro]]~~
	[[category:todo:expand]]		[[category:todo:expand]]

Fredg999: Undo revision 109959 by Fredg999 (talk) Merge not needed, my mistake

2023-04-28T04:50:06Z

Undo revision 109959 by Fredg999 (talk) Merge not needed, my mistake

← Older revision		Revision as of 04:50, 28 April 2023
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	~~{{todo\|merge articles\|inline=1\|comment=[[Super-Arcturus 17L 2s]] → [[17L 2s]]}}~~
	{\| class="wikitable"		{\| class="wikitable"
	! colspan="9" \| generator		! colspan="9" \| generator

← Older revision		Revision as of 04:50, 28 April 2023
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	~~{{todo\|merge articles\|inline=1\|comment=[[Super-Arcturus 17L 2s]] → [[17L 2s]]}}~~
	{\| class="wikitable"		{\| class="wikitable"
	! colspan="9" \| generator		! colspan="9" \| generator