Interval variety/Maximum variety MOS summing - Revision history

ArrowHead294 at 20:55, 25 November 2024

2024-11-25T20:55:53Z

← Older revision		Revision as of 20:55, 25 November 2024
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	Scales with three step sizes are also derivable by summing MOS scales together. All 5-note and 7-note scales derived this way will have max variety 3.		Scales with three step sizes are also derivable by summing MOS scales together. All 5-note and 7-note scales derived this way will have max variety 3.

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2024-11-25T20:55:42Z

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ArrowHead294: ArrowHead294 moved page Maximum variety/MOS summing to Interval variety/Maximum variety MOS summing: Move to subpage of main article Interval variety

2024-11-25T20:50:58Z

ArrowHead294 moved page Maximum variety/MOS summing to Interval variety/Maximum variety MOS summing: Move to subpage of main article Interval variety

← Older revision	Revision as of 20:50, 25 November 2024
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BudjarnLambeth: Todo link intro

2024-10-20T06:32:43Z

Todo link intro

← Older revision		Revision as of 06:32, 20 October 2024
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	[[Category:MOS scale]]		[[Category:MOS scale]]
	[[Category:Tables]]		[[Category:Tables]]
			{{todo\|link\|intro}}

BudjarnLambeth: Moved from MOS scales to MOS scale

2023-04-28T22:11:00Z

Moved from MOS scales to MOS scale

← Older revision		Revision as of 22:11, 28 April 2023
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	As the 6-note and 9-note addition tables prove, the requirement of having the same number of steps of different sizes makes max variety 3 scales with three step sizes rare.		As the 6-note and 9-note addition tables prove, the requirement of having the same number of steps of different sizes makes max variety 3 scales with three step sizes rare.
	[[Category:MOS ~~scales~~]]		[[Category:MOS scale]]
	[[Category:Tables]]		[[Category:Tables]]

BudjarnLambeth: Moved from category "MOS" to "MOS scales"

2023-04-28T09:37:10Z

Moved from category "MOS" to "MOS scales"

← Older revision		Revision as of 09:37, 28 April 2023
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	As the 6-note and 9-note addition tables prove, the requirement of having the same number of steps of different sizes makes max variety 3 scales with three step sizes rare.		As the 6-note and 9-note addition tables prove, the requirement of having the same number of steps of different sizes makes max variety 3 scales with three step sizes rare.
	[[Category:MOS]]		[[Category:MOS scales]]
	[[Category:Tables]]		[[Category:Tables]]

BudjarnLambeth: Categorised this uncategorised page

2023-04-27T00:31:05Z

Categorised this uncategorised page

← Older revision		Revision as of 00:31, 27 April 2023
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	As the 6-note and 9-note addition tables prove, the requirement of having the same number of steps of different sizes makes max variety 3 scales with three step sizes rare.		As the 6-note and 9-note addition tables prove, the requirement of having the same number of steps of different sizes makes max variety 3 scales with three step sizes rare.
			[[Category:MOS]]
			[[Category:Tables]]

Moremajorthanmajor: Created page with "Scales with three step sizes are also derivable by summing MOS scales together. All 5-note and 7-note scales derived this way will have max variety 3. {| class="wikitable" |+..."

2023-03-01T04:25:52Z

Created page with "Scales with three step sizes are also derivable by summing MOS scales together. All 5-note and 7-note scales derived this way will have max variety 3. {| class="wikitable" |+..."

New page

Scales with three step sizes are also derivable by summing MOS scales together. All 5-note and 7-note scales derived this way will have max variety 3.
{| class="wikitable"
|+
!
!2L 3s
!3L 2s
!4L 1s
|-
!1L 4s
|4 2 3 2 2
1L 1m 3s
|4 3 3 2 2
1L 2m 2s
|4 3 3 3 2
1L 3m 1s
|-
!2L 3s
!2L 3s
|4 3 3 3 2
1L 3m 1s
|4 3 4 3 2
2L 2m 1s
|-
!3L 2s
|
!3L 2s
|4 4 3 4 2
3L 1m 1s
|}
{| class="wikitable"
|+
!
!2L 5s
!3L 4s
!4L 3s
!5L 2s
!6L 1s
|-
!1L 6s
|4 2 2 3 2 2 2
1L 1m 5s
|4 2 2 3 2 3 2
1L 2m 4s
|4 3 2 3 2 3 2
1L 3m 3s
|4 3 2 3 3 3 2
1L 4m 2s
|4 3 3 3 3 3 2
1L 5m 1s
|-
!2L 5s
!2L 5s
|4 2 3 3 3 2 2
[[5L 2s MODMOSes|1L 3m 3s]]
|4 3 2 4 3 3 2
2L 3m 2s
|4 3 2 4 3 3 2
2L 3m 2s
|4 3 3 4 3 3 2
2L 4m 1s
|-
!3L 4s
|
!3L 4s
|4 3 2 3 2 3 2
[[5L 2s MODMOSes|1L 3m 3s]]
|4 3 2 4 3 4 2
3L 2m 2s, [[29edo#Nicetone|Nicetone]]
|4 3 3 4 3 4 2
3L 3m 1s
|-
!4L 3s
|
|
!4L 3s
|4 4 2 4 3 4 2
4L 2m 1s
|4 4 3 4 2 4 2
4L 2m 1s, [[Mohajira]]
|-
!5L 2s
|
|
|
!5L 2s
|4 4 3 4 4 4 2
5L 1m 1s
|}
However, if a scale derived this way has any other number of notes, its three step sizes will not always produce max variety 3.
{| class="wikitable"
!
!2L 4s
!3L 3s
!4L 2s
!5L 1s
|-
!1L 5s
|4 2 2 3 2 2
1L 1m 4s
|4 2 3 2 3 2
1L 2m 3s

fails, max variety 4
|4 3 2 3 2 2
1L 2m 3s

fails, max variety 4
|4 3 3 3 3 2
1L 4m 1s
|-
!2L 4s
!2L 4s
|4 2 3 3 3 2
1L 3m 2s

fails, max variety 4
|4 3 2 4 3 2
2L 2m 2s
|4 3 3 4 3 2
2L 3m 1s

fails, max variety 4
|-
!3L 3s
|
!3L 3s
|4 3 3 4 3 2
2L 3m 1s

fails, max variety 4
|4 3 4 3 4 2
3L 2m 1s

fails, max variety 4
|-
!4L 2s
|
|
!4L 2s
|4 4 3 4 4 2
4L 1m 1s
|}
Since Indonesian gamelan music stems from a tradition with 9-note scales converging from [http://www.neuroscience-of-music.se/Gamelan%20pelog%20A.htm max variety ''7''] to equal, sums of 9-note MOS make for great compromise gamelan tunings when they fail to produce max variety 3.
{| class="wikitable"
!
!2L 7s
!3L 6s
!4L 5s
!5L 4s
!6L 3s
!7L 2s
!8L 1s
|-
!1L 8s
|4 2 2 2 3 2 2 2 2
1L 1m 7s
|4 2 2 3 2 2 3 2 2
1L 2m 6s

fails, max variety 4
|4 2 2 3 2 3 2 3 2
1L 3m 5s

fails, max variety 4
|4 3 2 3 2 3 2 3 2
1L 4m 4s
|4 4 2 3 2 2 3 2 2
2L 2m 5s
|4 3 3 2 3 3 3 3 2
1L 6m 2s

fails, max variety 4
|4 3 3 3 3 3 3 3 2
1L 7m 1s
|-
!2L 7s
!2L 7s
|4 2 2 3 3 2 3 2 2
1L 3m 5s

fails, max variety 4
|4 2 2 3 3 3 2 3 2
1L 4m 4s
|4 3 2 2 4 3 2 2 2

2L 2m 5s
|4 3 2 3 3 2 3 3 2
1L 5m 3s

fails, max variety 4
|4 3 3 2 4 3 3 3 2
2L 5m 2s
|4 3 3 4 4 3 3 3 2
1L 6m 2s

fails, max variety 4
|-
!3L 6s
|
!3L 6s
|4 2 2 4 3 2 3 3 2
2L 3m 4s

fails, max variety 4
|4 3 2 4 2 3 3 3 2
2L 5m 2s
|4 3 2 4 3 2 4 3 2
3L 3m 3s
|4 3 3 3 3 3 3 4 2
2L 6m 1s

fails, max variety 4
|4 3 3 4 3 3 4 3 2
1L 5m 3s

fails, max variety 4
|-
!4L 5s
|
|
!4L 5s
|4 3 2 4 2 4 2 4 2
4L 1m 4s
|4 3 2 3 3 2 3 4 2
2L 4m 3s

fails, max variety 4
|4 4 3 3 3 4 3 4 2
3L 5m 1s

fails, max variety 4
|4 3 3 4 3 4 3 4 2
4L 4m 1s
|-
!5L 4s
|
|
|
!5L 4s
|4 4 2 4 3 3 3 4 4 2
5L 2m 2s, [[diasem]]
|4 4 3 3 3 4 3 4 2
4L 4m 1s
|4 4 3 4 3 4 3 4 2
5L 3m 1s

fails, max variety 4
|-
!6L 3s
|
|
|
|
!6L 3s
|4 4 3 4 3 3 4 4 2
5L 3m 1s

fails, max variety 4
|4 4 3 4 4 3 4 4 2
6L 2m 1s

fails, max variety 4
|-
!7L 2s
|
|
|
|
|
!7L 2s
|4 4 4 3 4 4 4 4 2
7L 1m 1s
|}
As the 6-note and 9-note addition tables prove, the requirement of having the same number of steps of different sizes makes max variety 3 scales with three step sizes rare.