Collection of scales: Difference between revisions

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[[File:Mr bob.png|thumb|218x218px|The lattice for the Chair of Mr. Bob]]
[[File:Mr bob.png|thumb|218x218px|The lattice for the Chair of Mr. Bob]]
{| class="wikitable"
 
|+
== Kee'ra ==
!Name
The '''kee'ra''' scale, or the Chair of Mr. Bob as named by dotuXil, is the prototype of a family of "chair scales", so named for the lattice's resemblance to a chair. Its intervals are [21/20 35/32 6/5 21/16 7/5 3/2 8/5 105/64 7/4 2/1]; {{Interval ruler|41|0, 85, 150, 315, 460, 580, 700, 820, 850, 970, 1200}}.
!Intervals
 
!Comments
== Roklotian ==
!Good edos
The Roklotian scale is constructed in just intonation or an equal temperament from the DKW signature of the 5-limit; 9/8-16/15-25/24-16/15-9/8-16/15-25/24-16/15-9/8 (which contains the 5-odd-limit, 9/8, and 16/9) - steps of 25/24 are added into each 9/8, bounding a middle interval of 648/625. This has differing behavior depending on the temperament.
|-
 
|Kee'ra, Chair of Mr. Bob
Studying scales like Roklotian is useful because it illustrates how temperaments affect the structure of just intonation.
|21/20 35/32 6/5 21/16 7/5 3/2 8/5 105/64 7/4 2/1
 
|When it is loaded in Scale Workshop, the lattice resembles a chair.
=== Just intonation ===
|31
In just intonation (and temperaments that do not equate or temper out any of the relevant intervals, such as 46edo), it is a ternary scale: msmLmLmsmLmLmsm, with s = 648/625, m = 25/24, and L = 16/15; {{Interval ruler|46|0, 80, 130, 200, 310, 390, 500, 580, 630, 700, 810, 890, 1000, 1070, 1130, 1200}}.
|-
 
|Duodene
=== Kleismic temperament ===
|16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 2/1
The most common form of the Roklotian scale is the kleismic form, which is supported by edos such as 34edo and divides the 9/8 into three equal parts. It is binary but MV3, with the step signature sssLsLsssLsLsss: {{Interval ruler|34|0, 80, 130, 200, 310, 390, 500, 580, 630, 700, 810, 890, 1000, 1070, 1130, 1200}}. It is a MODMOS of 4L 11s, a notable kleismic MOS.
|5-limit detempering of 12edo formed by all ratios with powers -1, 0, 1, and 2 of the third harmonic and powers -1, 0, and 1 of the fifth.
 
|12, 34, 41, 53
=== Porcupine temperament ===
|}
Roklotian also reduces to a binary scale in porcupine, which equates the 648/625 and 16/15 steps. This is actually a MOS - it is porcupine[15]: {{Interval ruler|37|0, 80, 160, 220, 310, 390, 500, 560, 640, 700, 810, 890, 980, 1040, 1130, 1200}}.
 
=== Augmented temperament ===
Augmented temperament equates the 16/15 and 25/24 steps. The result is the scale LsLLLLLsLLLLLsL, which is a MODMOS of augmented[15] - {{Interval ruler|27|0, 80, 140, 220, 310, 390, 500, 560, 640, 700, 810, 890, 980, 1060, 1130, 1200}}.
 
=== Diminished temperament ===
Diminished temperament tempers out the 648/625 entirely, resulting in ssLsLssLsLss, a MODMOS of diminished[12] - {{Interval ruler|40|0, 90, 180, 300, 390, 510, 600, 690, 810, 900, 1020, 1110, 1200}}.
 
=== Dicot temperament ===
Dicot temperament tempers out 25/24, notably equating 648/625 to 9/8. Since the majority of the scale's steps are 25/24, the scale's cardinality is reduced drastically, and the result is LssLssL, a MODMOS of dicot[7] - {{Interval ruler|17|0, 200, 350, 500, 700, 850, 1000, 1200}}.

Revision as of 03:29, 19 April 2026

This page serves as a collection of less notable scales, other than MOSes, which are covered at MOS.

The lattice for the Chair of Mr. Bob

Kee'ra

The kee'ra scale, or the Chair of Mr. Bob as named by dotuXil, is the prototype of a family of "chair scales", so named for the lattice's resemblance to a chair. Its intervals are [21/20 35/32 6/5 21/16 7/5 3/2 8/5 105/64 7/4 2/1]; ├──┴─┴─────┴────┴───┴───┴───┴┴───┴───────┤ 3 2 6 5 4 4 4 1 4 8.

Roklotian

The Roklotian scale is constructed in just intonation or an equal temperament from the DKW signature of the 5-limit; 9/8-16/15-25/24-16/15-9/8-16/15-25/24-16/15-9/8 (which contains the 5-odd-limit, 9/8, and 16/9) - steps of 25/24 are added into each 9/8, bounding a middle interval of 648/625. This has differing behavior depending on the temperament.

Studying scales like Roklotian is useful because it illustrates how temperaments affect the structure of just intonation.

Just intonation

In just intonation (and temperaments that do not equate or temper out any of the relevant intervals, such as 46edo), it is a ternary scale: msmLmLmsmLmLmsm, with s = 648/625, m = 25/24, and L = 16/15; ├──┴─┴──┴───┴──┴───┴──┴─┴──┴───┴──┴───┴──┴─┴──┤ 3 2 3 4 3 4 3 2 3 4 3 4 3 2 3.

Kleismic temperament

The most common form of the Roklotian scale is the kleismic form, which is supported by edos such as 34edo and divides the 9/8 into three equal parts. It is binary but MV3, with the step signature sssLsLsssLsLsss: ├─┴─┴─┴──┴─┴──┴─┴─┴─┴──┴─┴──┴─┴─┴─┤ 2 2 2 3 2 3 2 2 2 3 2 3 2 2 2. It is a MODMOS of 4L 11s, a notable kleismic MOS.

Porcupine temperament

Roklotian also reduces to a binary scale in porcupine, which equates the 648/625 and 16/15 steps. This is actually a MOS - it is porcupine[15]: ├─┴──┴─┴──┴─┴──┴─┴──┴─┴──┴─┴──┴─┴──┴─┤ 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2.

Augmented temperament

Augmented temperament equates the 16/15 and 25/24 steps. The result is the scale LsLLLLLsLLLLLsL, which is a MODMOS of augmented[15] - ├─┴┴─┴─┴─┴─┴─┴┴─┴─┴─┴─┴─┴┴─┤ 2 1 2 2 2 2 2 1 2 2 2 2 2 1 2.

Diminished temperament

Diminished temperament tempers out the 648/625 entirely, resulting in ssLsLssLsLss, a MODMOS of diminished[12] - ├──┴──┴───┴──┴───┴──┴──┴───┴──┴───┴──┴──┤ 3 3 4 3 4 3 3 4 3 4 3 3.

Dicot temperament

Dicot temperament tempers out 25/24, notably equating 648/625 to 9/8. Since the majority of the scale's steps are 25/24, the scale's cardinality is reduced drastically, and the result is LssLssL, a MODMOS of dicot[7] - ├──┴─┴─┴──┴─┴─┴──┤ 3 2 2 3 2 2 3.

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