User:BudjarnLambeth/Hall of mirrors - Revision history

BudjarnLambeth: /* Enrichment scale */

2025-11-17T04:18:12Z

Enrichment scale

← Older revision		Revision as of 04:18, 17 November 2025
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	=== Enrichment scale ===		=== Enrichment scale ===
	The '''enrichment scale''' is a triple octave ([[8/1]])-[[period]], 20-tone just intonation scale that occurs as a subset of hall-of-mirrors. It was also described by Lambeth in November 2025.		The '''enrichment scale''' is a triple octave ([[8/1]])-[[period]], 20-tone just intonation scale that occurs as a subset of hall-of-mirrors. It was also described by Lambeth in November 2025. ([https://scaleworkshop.plainsound.org/scale/sau52aILB Scale Workshop link].)
	* 6/5		* 6/5
	* 4/3		* 4/3

BudjarnLambeth: /* Enrichment */

2025-11-17T04:13:48Z

Enrichment

← Older revision		Revision as of 04:13, 17 November 2025
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	== Subsets ==		== Subsets ==

	=== Enrichment ===		=== Enrichment scale ===
	The '''enrichment scale''' is a triple octave ([[8/1]])-[[period]], 20-tone just intonation scale that occurs as a subset of hall-of-mirrors. It was also described by Lambeth in November 2025.		The '''enrichment scale''' is a triple octave ([[8/1]])-[[period]], 20-tone just intonation scale that occurs as a subset of hall-of-mirrors. It was also described by Lambeth in November 2025.
	* 6/5		* 6/5

BudjarnLambeth at 04:05, 17 November 2025

2025-11-17T04:05:50Z

@@ Line 34: / Line 34: @@
 == Subsets ==
-=== One-octave period ===
+=== Enrichment ===
 Ifdomav (''symmetric mode'')
@@ Line 86: / Line 109: @@
 * 11/6
 * 2/1
 == Approximations in other tunings ==

BudjarnLambeth: /* Three-octave period */

2025-11-17T04:03:46Z

Three-octave period

← Older revision		Revision as of 04:03, 17 November 2025
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	=== Three-octave period ===		=== Three-octave period ===
	~~Buzzy mirror~~		Enrichment
	* 6/5		* 6/5
	* 4/3		* 4/3

BudjarnLambeth at 03:57, 17 November 2025

2025-11-17T03:57:27Z

← Older revision		Revision as of 03:57, 17 November 2025
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	== Subsets ==		== Subsets ==

			=== One-octave period ===

	Ifdomav (''symmetric mode'')		Ifdomav (''symmetric mode'')
Line 84:		Line 86:
	* 11/6		* 11/6
	* 2/1		* 2/1

			=== Three-octave period ===
			Buzzy mirror
			* 6/5
			* 4/3
			* 3/2
			* 5/3
			* 11/6
			* 2/1
			* 11/5
			* 12/5
			* 8/3
			* 3/1
			* 10/3
			* 11/3
			* 4/1
			* 48/11
			* 44/9
			* 16/3
			* 64/11
			* 33/5
			* 80/11
			* 8/1

	== Approximations in other tunings ==		== Approximations in other tunings ==

	== In EDOs ==		=== In EDOs ===
	[[EDO]]s up to 200 that approximate hall-of-mirrors well are:		[[EDO]]s up to 200 that approximate hall-of-mirrors well are:
	* {{EDOs\|65, 72, 80, 87, 94, 152, 159, 167, 168, 181, 183, 190}}		* {{EDOs\|65, 72, 80, 87, 94, 152, 159, 167, 168, 181, 183, 190}}
Line 93:		Line 118:
	What most of these edos have in common is that they have an interval in the range 12 to 17 [[cents]], and they have a good approximation of the 2.3.5.11 [[JI subgroup]].		What most of these edos have in common is that they have an interval in the range 12 to 17 [[cents]], and they have a good approximation of the 2.3.5.11 [[JI subgroup]].

	== As a ternary scale ==		=== As a ternary scale ===
	Hall of mirrors is almost exactly the 19-tone [[ternary scale]]:		Hall of mirrors is almost exactly the 19-tone [[ternary scale]]:
	* '''L s L s s M L M s L s M L M s s L s L'''		* '''L s L s s M L M s L s M L M s s L s L'''

BudjarnLambeth at 03:08, 17 November 2025

2025-11-17T03:08:24Z

← Older revision		Revision as of 03:08, 17 November 2025
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	{{Idiosyncratic terms}}		{{Idiosyncratic terms}}

	The '''hall-of-mirrors scale''' is a 21-tone, no-5s [[11-limit]], symmetrical [[just intonation]] scale ~~invented~~ by [[Budjarn Lambeth]] in November 2025.		The '''hall-of-mirrors scale''' is a 21-tone, no-5s [[11-limit]], symmetrical [[just intonation]] scale described by [[Budjarn Lambeth]] in November 2025.

	Its primary use is as a 'meta-scale' to take smaller subsets from.		Its primary use is as a 'meta-scale' to take smaller subsets from.

BudjarnLambeth at 03:08, 17 November 2025

2025-11-17T03:08:05Z

← Older revision		Revision as of 03:08, 17 November 2025
Line 3:		Line 3:
	{{Idiosyncratic terms}}		{{Idiosyncratic terms}}

	The '''hall-of-mirrors scale''' is a 21-tone, [[11-limit]], symmetrical [[just intonation]] scale invented by [[Budjarn Lambeth]] in November 2025.		The '''hall-of-mirrors scale''' is a 21-tone, no-5s [[11-limit]], symmetrical [[just intonation]] scale invented by [[Budjarn Lambeth]] in November 2025.

	Its primary use is as a 'meta-scale' to take smaller subsets from.		Its primary use is as a 'meta-scale' to take smaller subsets from.

BudjarnLambeth: Created page with "{{Editable user page|Don't remove anything (unless it's offensive or factually incorrect), but feel free to add any observations about the scales, subsets, music examples, etc., and feel free to improve the formatting or layout as long as you don't remove information.}} {{Idiosyncratic terms}} The '''hall-of-mirrors scale''' is a 21-tone, 11-limit, symmetrical just intonation scale invented by Budjarn Lambeth in November 2025. Its primary use is as a 'met..."

2025-11-17T03:04:45Z

Created page with "{{Editable user page|Don't remove anything (unless it's offensive or factually incorrect), but feel free to add any observations about the scales, subsets, music examples, etc., and feel free to improve the formatting or layout as long as you don't remove information.}} {{Idiosyncratic terms}} The '''hall-of-mirrors scale''' is a 21-tone, 11-limit, symmetrical just intonation scale invented by Budjarn Lambeth in November 2025. Its primary use is as a 'met..."

New page

{{Editable user page|Don't remove anything (unless it's offensive or factually incorrect), but feel free to add any observations about the scales, subsets, music examples, etc., and feel free to improve the formatting or layout as long as you don't remove information.}}

{{Idiosyncratic terms}}

The '''hall-of-mirrors scale''' is a 21-tone, [[11-limit]], symmetrical [[just intonation]] scale invented by [[Budjarn Lambeth]] in November 2025.

Its primary use is as a 'meta-scale' to take smaller subsets from.

It is designed to be used with aperiodic or metallophone [[timbre]]s like the "aperiodic" presets in [[Scale Workshop]].

== Intervals ==
* 12/11
* 11/10
* 6/5
* 121/100
* 40/33
* 11/9
* 5/4
* 4/3
* 15/11
* 11/8
* 16/11
* 22/15
* 3/2
* 8/5
* 18/11
* 33/20
* 200/121
* 5/3
* 20/11
* 11/6
* 2/1

== Subsets ==

Ifdomav (''symmetric mode'')
* 11/10
* 11/8
* 3/2
* 11/6
* 2/1

Ifdomav (''[[pelog]]-like mode'')
* 12/11
* 6/5
* 3/2
* 18/11
* 2/1

Afdomav (''symmetric mode'')
* 12/11
* 4/3
* 16/11
* 20/11
* 2/1

Afdomav (''pelog-like mode'')
* 11/10
* 6/5
* 22/15
* 8/5
* 2/1

Mirrormav (''symmetric mode'')
* 11/10
* 4/3
* 3/2
* 20/11
* 2/1

Mirrormav (''pelog-like mode'')
* 11/10
* 121/100
* 22/15
* 33/20
* 2/1

Over-30 [[equiheptatonic]]
* 11/10
* 6/5
* 4/3
* 3/2
* 5/3
* 11/6
* 2/1

== Approximations in other tunings ==

== In EDOs ==
[[EDO]]s up to 200 that approximate hall-of-mirrors well are:
* {{EDOs|65, 72, 80, 87, 94, 152, 159, 167, 168, 181, 183, 190}}

What most of these edos have in common is that they have an interval in the range 12 to 17 [[cents]], and they have a good approximation of the 2.3.5.11 [[JI subgroup]].

== As a ternary scale ==
Hall of mirrors is almost exactly the 19-tone [[ternary scale]]:
* '''L s L s s M L M s L s M L M s s L s L'''
with the step size ratio '''10:2:1'''.

[[Category:21-tone scales]]
[[Category:Just intonation scales]]
[[Category:11-limit]]