User:Moremajorthanmajor/7L 3s (15/7-equivalent) - Revision history

ArrowHead294 at 16:54, 3 March 2025

2025-03-03T16:54:05Z

← Older revision		Revision as of 16:54, 3 March 2025
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	The generator range reflects two extremes: one where L = s (3\10), and another where s = 0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible edos, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between edIX would be (3+2)\(10+7) = 5\17 – five degrees of [[17ed15/7]]:		The generator range reflects two extremes: one where L = s (3\10), and another where s = 0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible edos, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between edIX would be (3+2)\(10+7) = 5\17 – five degrees of [[17ed15/7]]:

	{{Scale ~~tree\|~~7L 3s <15/7>}}		{{MOS tuning spectrum\|Scale Signature=7L 3s <15/7>}}

	The scale produced by stacks of 5\17 is the [[17ed15/7 neutral scale]]. Between 11/38 and 16/55, with 9/31 in between, is the mohajira/mohaha/mohoho range, where mohaha and mohoho use the MOS as the chromatic scale of a [[Chromatic pairs\|chromatic pair]].		The scale produced by stacks of 5\17 is the [[17ed15/7 neutral scale]]. Between 11/38 and 16/55, with 9/31 in between, is the mohajira/mohaha/mohoho range, where mohaha and mohoho use the MOS as the chromatic scale of a [[Chromatic pairs\|chromatic pair]].

Moremajorthanmajor: /* Intervals */

2024-07-17T04:23:00Z

Intervals

← Older revision		Revision as of 04:23, 17 July 2024
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	2g, then, will fall between 754 cents (4\7) and 792 cents (3\5), the range of [[5L 2s\|diatonic]] subminor sixths.		2g, then, will fall between 754 cents (4\7) and 792 cents (3\5), the range of [[5L 2s\|diatonic]] subminor sixths.

	The "large step" will fall between 188.5 cents (1\7) and ~~132~~ cents (1\10), ranging from a small major second to a [[sinaic]].		The "large step" will fall between 188.5 cents (1\7) and 131.9 cents (1\10), ranging from a small major second to a [[sinaic]].

	The "small step" will fall between 0 cents and ~~132~~ cents, sometimes sounding like a minor second, and sometimes sounding like a quartertone or smaller microtone.		The "small step" will fall between 0 cents and 131.9 cents, sometimes sounding like a minor second, and sometimes sounding like a quartertone or smaller microtone.

	The most frequent interval, then is the major third (and its inversion, the diminished seventh), followed by the superfourth and subminor sixth.		The most frequent interval, then is the major third (and its inversion, the diminished seventh), followed by the superfourth and subminor sixth.

Moremajorthanmajor: /* Intervals */

2023-07-07T23:37:02Z

Intervals

← Older revision		Revision as of 23:37, 7 July 2023
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	==Intervals==		==Intervals==
	The generator (g) will fall between 377 cents (2\7 - two degrees of [[7ed15/7]]) and 396 cents (3\10 - three degrees of [[10ed15/7]]), hence a ~~neutral or~~ major third.		The generator (g) will fall between 377 cents (2\7 - two degrees of [[7ed15/7]]) and 396 cents (3\10 - three degrees of [[10ed15/7]]), hence a major third.

	2g, then, will fall between 754 cents (4\7) and 792 cents (3\5), the range of [[5L 2s\|diatonic]] subminor sixths.		2g, then, will fall between 754 cents (4\7) and 792 cents (3\5), the range of [[5L 2s\|diatonic]] subminor sixths.
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	\|3L+1s		\|3L+1s
	\| -2		\| -2
	\|6		\|6v
	\|minor 6-step		\|minor 6-step
	\|4L+2s		\|4L+2s
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	\|-		\|-
	\|8		\|8
	\|6^		\|6
	\|major 6-step		\|major 6-step
	\|5L+1s		\|5L+1s

Moremajorthanmajor at 00:24, 21 June 2023

2023-06-21T00:24:48Z

← Older revision		Revision as of 00:24, 21 June 2023
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	\|Tuning=7L 3s<15/7>}}		\|Tuning=7L 3s<15/7>}}

	~~'''~~7L 3s<15/7>~~''' refers to the structure of [[MOSScales\|moment of symmetry scales]] built from a 10-tone chain of major thirds:~~		{{MOS intro\|Scale Signature=7L 3s<15/7>}}

	~~L s L L L s L L s L~~

	Graham Breed has a [http://x31eq.com/7plus3.htm page on his website] dedicated to 7+3 scales. He proposes calling the large step "t" for "tone", lowercase because the large step is a narrow neutral tone, and the small step "q" for "quartertone", because the small step is often close to a quartertone. (Note that the small step is not a quartertone in every instance of 7+3, so do not take that "q" literally.) Thus we have:		Graham Breed has a [http://x31eq.com/7plus3.htm page on his website] dedicated to 7+3 scales. He proposes calling the large step "t" for "tone", lowercase because the large step is a narrow neutral tone, and the small step "q" for "quartertone", because the small step is often close to a quartertone. (Note that the small step is not a quartertone in every instance of 7+3, so do not take that "q" literally.) Thus we have:

Moremajorthanmajor at 04:00, 11 June 2023

2023-06-11T04:00:23Z

← Older revision		Revision as of 04:00, 11 June 2023
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	{{Infobox MOS		{{Infobox MOS
	\| ~~Name = Greater dicoid~~		\|Tuning=7L 3s<15/7>}}
	~~\| Periods = 1~~
	~~\| nLargeSteps = 7~~
	~~\| nSmallSteps = 3~~
	~~\| Equalized = 7~~
	~~\| Collapsed = 5~~
	~~\| Pattern = LLLsLLsLLs~~
	~~\| Equave~~=15/7}}

	'''7L 3s''' refers to the structure of [[MOSScales\|moment of symmetry scales]] built from a 10-tone chain of ~~neutral or~~ major thirds ~~(assuming a period of an octave up to 10/[[9edo]])~~:		'''7L 3s<15/7>''' refers to the structure of [[MOSScales\|moment of symmetry scales]] built from a 10-tone chain of major thirds:

	L s L L L s L L s L		L s L L L s L L s L
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	==Intervals==		==Intervals==
	The generator (g) will fall between ~~343~~ cents (2\7 - two degrees of [[~~7edo\|7edo~~]] and ~~400~~ cents (3\9 - three degrees of [[~~10edo\|9edo~~]]), hence a neutral or major third.		The generator (g) will fall between 377 cents (2\7 - two degrees of [[7ed15/7]]) and 396 cents (3\10 - three degrees of [[10ed15/7]]), hence a neutral or major third.

	2g, then, will fall between ~~686~~ cents (4\7) and ~~800~~ cents (2\3), the range of [[5L 2s\|diatonic]] ~~fifths~~.		2g, then, will fall between 754 cents (4\7) and 792 cents (3\5), the range of [[5L 2s\|diatonic]] subminor sixths.

	The "large step" will fall between ~~171~~ cents (1\7) and ~~120~~ cents (1\10), ranging from a ~~submajor~~ second to a [[sinaic]].		The "large step" will fall between 188.5 cents (1\7) and 132 cents (1\10), ranging from a small major second to a [[sinaic]].

	The "small step" will fall between 0 cents and ~~120~~ cents, sometimes sounding like a minor second, and sometimes sounding like a quartertone or smaller microtone.		The "small step" will fall between 0 cents and 132 cents, sometimes sounding like a minor second, and sometimes sounding like a quartertone or smaller microtone.

	The most frequent interval, then is the ~~neutral~~ third (and its inversion, the ~~neutral sixth~~), followed by the ~~perfect fourth~~ and fifth. Thus, 7+3 combines the familiar sound of perfect fifths and fourths with the unfamiliar sounds of neutral intervals. They are compatible with Arabic and Turkish scales, but not with traditional Western ones.		The most frequent interval, then is the major third (and its inversion, the diminished seventh), followed by the superfourth and subminor sixth.

	Note: In TAMNAMS, a k-step interval class in dicoid may be called a "k-step", "k-mosstep", or "k-dicostep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.		Note: In TAMNAMS, a k-step interval class in dicoid may be called a "k-step", "k-mosstep", or "k-dicostep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.
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	\|1L+2s		\|1L+2s
	\|-		\|-
	\| colspan="8" style="text-align:center" \|The chromatic 17-note MOS (either [[7L 10s]], [[10L 7s]], or [[~~17edIX~~]]) also has the following intervals (from some root):		\| colspan="8" style="text-align:center" \|The chromatic 17-note MOS (either [[7L 10s (15/7-equivalent)\|7L 10s]], [[10L 7s (15/7-equivalent)\|10L 7s]], or [[17ed15/7]]) also has the following intervals (from some root):
	\|-		\|-
	\|12		\|12
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	The generator range reflects two extremes: one where L = s (3\10), and another where s = 0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible edos, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between edIX would be (3+2)\(10+7) = 5\17 – five degrees of [[~~17edIX~~]]:		The generator range reflects two extremes: one where L = s (3\10), and another where s = 0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible edos, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between edIX would be (3+2)\(10+7) = 5\17 – five degrees of [[17ed15/7]]:

	{{Scale tree\|7L 3s <15/7>}}		{{Scale tree\|7L 3s <15/7>}}

	The scale produced by stacks of 5\17 is the [[~~17edIX~~ neutral scale]]. Between 11/38 and 16/55, with 9/31 in between, is the mohajira/mohaha/mohoho range, where mohaha and mohoho use the MOS as the chromatic scale of a [[Chromatic pairs\|chromatic pair]].		The scale produced by stacks of 5\17 is the [[17ed15/7 neutral scale]]. Between 11/38 and 16/55, with 9/31 in between, is the mohajira/mohaha/mohoho range, where mohaha and mohoho use the MOS as the chromatic scale of a [[Chromatic pairs\|chromatic pair]].

	Other compatible ~~edIXs~~ include: [[~~37edIX~~]], [[~~27edIX~~]], [[~~44edIX~~]], [[~~41edIX~~]], [[~~24edIX~~]], [[~~31edIX~~]].		Other compatible ed15/7s include: [[37ed15/7]], [[27ed15/7]], [[44ed15/7]], [[41ed15/7]], [[24ed15/7]], [[31ed15/7]].

	You can also build this scale by stacking neutral thirds that are not members of ~~edIXs~~ – for instance, frequency ~~ratios 11:9,~~ 5:4~~, 21:17, 16:13~~ – or the square root of ~~3:2 or~~ 11:7 (a bisected ~~just perfect fifth or~~ undecimal subminor sixth).		You can also build this scale by stacking neutral thirds that are not members of ed15/7s – for instance, the frequency ratio 5:4 – or the square root of 11:7 (a bisected undecimal subminor sixth).

	==Rank-2 temperaments==		==Rank-2 temperaments==

Moremajorthanmajor at 22:28, 31 May 2023

2023-05-31T22:28:55Z

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Fredg999: Fredg999 moved page 7L 3s (15/7-equivalent) to User:Moremajorthanmajor/7L 3s (15/7-equivalent): Page not ready for the main namespace

2023-05-20T05:32:10Z

Fredg999 moved page 7L 3s (15/7-equivalent) to User:Moremajorthanmajor/7L 3s (15/7-equivalent): Page not ready for the main namespace

← Older revision	Revision as of 05:32, 20 May 2023
(No difference)

Moremajorthanmajor: Moremajorthanmajor moved page User:Moremajorthanmajor/Greater dicoid to 7L 3s (15/7-equivalent): In order to fix infobox

2023-05-15T21:58:19Z

Moremajorthanmajor moved page User:Moremajorthanmajor/Greater dicoid to 7L 3s (15/7-equivalent): In order to fix infobox

← Older revision	Revision as of 21:58, 15 May 2023
(No difference)

Moremajorthanmajor: /* Scale tree */

2023-05-15T19:38:19Z

Scale tree

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Moremajorthanmajor at 01:20, 6 April 2023

2023-04-06T01:20:44Z

← Older revision		Revision as of 01:20, 6 April 2023
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	\| Collapsed = 5		\| Collapsed = 5
	\| Pattern = LLLsLLsLLs		\| Pattern = LLLsLLsLLs
	\|Equave=15/7}}		\| Equave=15/7}}

	'''7L 3s''' refers to the structure of [[MOSScales\|moment of symmetry scales]] built from a 10-tone chain of neutral or major thirds (assuming a period of an octave up to 10/[[9edo]]):		'''7L 3s''' refers to the structure of [[MOSScales\|moment of symmetry scales]] built from a 10-tone chain of neutral or major thirds (assuming a period of an octave up to 10/[[9edo]]):