User:BudjarnLambeth/Hall of mirrors: Difference between revisions
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..." |
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{{Idiosyncratic terms}} | {{Idiosyncratic terms}} | ||
The '''hall-of-mirrors scale''' is a 21-tone, [[11-limit]], symmetrical [[just intonation]] scale | 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. | ||
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== Subsets == | == Subsets == | ||
=== 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. ([https://scaleworkshop.plainsound.org/scale/sau52aILB Scale Workshop link].) | |||
* 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 | |||
=== Others === | |||
Ifdomav (''symmetric mode'') | Ifdomav (''symmetric mode'') | ||
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== 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}} | ||
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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''' | ||