Collection of scales: Difference between revisions

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Created page with "This page serves as a collection of less notable scales. == JI lattices == thumb|218x218px|The lattice for the Chair of Mr. Bob === Kee'ra (Chair of Mr. Bob) === This scale consists of the intervals 21/20, 35/32, 6/5, 21/16, 7/5, 3/2, 8/5, 105/64, and 7/4 within the octave 2/1. When it is loaded in Scale Workshop, the lattice resembles a chair. The name "Chair of Mr. Bob" was given by dotuXil. The name "Kee'ra" was given by Vector Gr..."
 
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This page serves as a collection of less notable [[Scale|scales.]]
This page serves as a collection of less notable [[Scale|scales]], other than MOSes, which are covered at [[MOS]].


== JI lattices ==
[[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]]


=== Kee'ra (Chair of Mr. Bob) ===
== Kee'ra ==
This scale consists of the intervals 21/20, 35/32, 6/5, 21/16, 7/5, 3/2, 8/5, 105/64, and 7/4 within the octave 2/1. When it is loaded in Scale Workshop, the lattice resembles a chair. The name "Chair of Mr. Bob" was given by [[dotuXil]]. The name "Kee'ra" was given by [[Vector Graphics]] to serve as a single-word name consistent with the most common scale names.
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}} (41edo tuning - the JI scale distinguishes 15/14 and 16/15-sized steps). Its intervals give it a "minor" sound in the default mode, with some characteristics of Phrygian; it supports the 6/5-3/2-7/4 tetrad on the root, with the interval 35/24 (roughly 16/11) between the third and seventh.


=== Duodene ===
== 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.


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


=== Mellow chromatic ===
=== Just intonation ===
The mellow chromatic scale is the MOS pattern 7L 5s. It is the soft child of the MOS [[diatonic]] scale, and is the chromatic scale of [[meantone]]. It lacks a symmetric [[mode]], having an even number of steps per period.
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}} (46edo tuning).


=== Pychromatic ===
=== Kleismic temperament ===
The pychromatic scale is the MOS pattern 5L 7s. It is the hard child of the MOS [[diatonic]] scale and is the [[Scale size|chromatic]] scale of [[superpyth]] and of [[Pythagorean tuning|Pythagorean]] tuning. It lacks a symmetric [[mode]], having an even number of steps per period.
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}} (34edo tuning). 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]: {{Interval ruler|37|0, 80, 160, 220, 310, 390, 500, 560, 640, 700, 810, 890, 980, 1040, 1130, 1200}} (37edo tuning).
 
=== 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}} (27edo tuning).
 
=== 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}} (40edo tuning).
 
=== 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}} (17edo tuning).

Latest revision as of 03:07, 15 May 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 (41edo tuning - the JI scale distinguishes 15/14 and 16/15-sized steps). Its intervals give it a "minor" sound in the default mode, with some characteristics of Phrygian; it supports the 6/5-3/2-7/4 tetrad on the root, with the interval 35/24 (roughly 16/11) between the third and seventh.

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 (46edo tuning).

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 (34edo tuning). 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 (37edo tuning).

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 (27edo tuning).

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 (40edo tuning).

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 (17edo tuning).

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