User:BudjarnLambeth/Hall of mirrors
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This article or section contains multiple idiosyncratic terms. Such terms are used by only a few people and are not regularly used within the community. |
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.
It is designed to be used with aperiodic or metallophone timbres 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
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. (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)
- 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
EDOs up to 200 that approximate hall-of-mirrors well are:
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.