# Cluster MOS

A cluster MOS or cluster scale is a very particular kind of MOS-based system (i.e. a system based on stacks of periods and generators) whose generator is quite near a rational fraction of an octave. Therefore some MOS generated by the generator is quasi-equal (which should be reasonably sized for it to be a good cluster MOS, usually between 5 and 10 notes per octave). But not only that; in a cluster temperament, the different versions of each interval, differing by a chroma ("diminished", "minor", "major", "augmented"...) include many nearby interval colors that are individually recognizable, yet conceptually grouped into the same category (or "cluster") because they're so close.

A cluster temperament (named by Keenan Pepper) is a rank-2 regular temperament interpretation of a cluster MOS. This means that in a cluster temperament, many different versions of each interval, differing by a chroma, these colors represent nearby JI intervals specifically (because a temperament is a JI interpretation of MOS generator chains separated by the period).

An example of something that is not a cluster temperament is amity, because although the amity generator is within 4 cents of 2\7, making amity[7] near equal, amity is too complex of a temperament and most of the intervals differing by a chroma do not represent simple JI intervals at all. For example, the list of amity "thirds" includes ...6/5 (339.5) (363.2) 5/4... where the intervals given in cents are not representable as simple JI intervals (243/200 and 100/81 are about as simple as you can get).

Another way to describe this property is that the chroma of the near-equal MOS is a kind of "super-comma", a set of many useful commas that are tempered to become the same, non-vanishing, interval. It should be obvious that "cluster temperament" is a vague, qualitative phrase and not mathematically well-defined.

Rather than simply denoting one of a list of rank-2 temperaments, the phrase "cluster scale" is also associated with a compositional philosophy. It is often said that temperaments such as slendric are melodically "bad" or have "bad MOS structure", because some MOS (in this case slendric[5]) is "too equal" and the next higher MOSes are "too unequal". But this can be thought of as a feature rather than a bug. Rather than forcing them into the MOS framework, one can think of cluster scales as having two hierarchical levels of melodic structure: the "step" (a step of the quasi-equal MOS), and the "chroma", and a chroma is so much smaller than a step that the steps seldom go out of order no matter how many chromas are involved.

## Examples of cluster MOSes

Parasoft smitonic is a cluster MOS.

## Examples of cluster temperaments

### Slendric

Main article: Slendric

Chroma: 49/48 ~ 64/63

 Steps "Diminished" "Minor" "Major" "Augmented" 1 9/8 8/7 7/6 32/27 2 9/7 21/16 4/3 3 3/2 32/21 14/9 4 27/16 12/7 7/4 16/9

Slendric has two quite different extensions that are both also cluster scales:

#### Mothra

Main article: Mothra

Chroma: 33/32 ~ 36/35 ~ 49/48 ~ 55/54 ~ 56/55 ~ 64/63

 Steps "Diminished" "Minor" "Major" "Augmented" 1 12/11 10/9~9/8 8/7 7/6 6/5 11/9 2 5/4 14/11~9/7 21/16 4/3 11/8 7/5 3 10/7 16/11 3/2 32/21 14/9~11/7 8/5 4 18/11 5/3 12/7 7/4 16/9~9/5 11/6

#### Rodan

Main article: Rodan

Chroma: 49/48 ~ 55/54 ~ 56/55 ~ 64/63 ~ 81/80 ~ 99/98

 Steps "Diminished" "Minor" "Major" "Augmented" 1 12/11 10/9 9/8 8/7 7/6 32/27 6/5 11/9 2 5/4 14/11 9/7 21/16 4/3 27/20 11/8 7/5 3 10/7 16/11 40/27 3/2 32/21 14/9 11/7 8/5 4 18/11 5/3 27/16 12/7 7/4 16/9 9/5 11/6

### Modus (of the tetracot family)

Main article: Tetracot and Modus

Chroma: 40/39 ~ 45/44 ~ 55/54 ~ 65/64 ~ 66/65 ~ 81/80 ~ 121/120

 Steps "Diminished" "Minor" "Major" "Augmented" 1 16/15 13/12~12/11 11/10~10/9 9/8 2 13/11~32/27 6/5 11/9~16/13 5/4 3 13/10 4/3 27/20~15/11 11/8~18/13 4 13/9~16/11 22/15~40/27 3/2 20/13 5 8/5 13/8~18/11 5/3 27/16~22/13 6 16/9 9/5~20/11 11/6~24/13 15/8

### Miracle

Main article: Miracle

Chroma: 45/44 ~ 49/48 ~ 50/49 ~ 55/54 ~ 56/55 ~ 64/63

 Steps "Diminished" "Minor" "Major" "Augmented" 1 22/21~21/20 16/15~15/14 12/11 10/9 2 11/10 9/8 8/7 7/6 32/27 3 6/5 11/9 5/4 14/11 4 9/7 21/16 4/3 5 11/8 7/5 10/7 16/11 6 3/2 32/21 14/9 7 11/7 8/5 18/11 5/3 8 27/16 12/7 7/4 16/9 20/11 9 9/5 11/6 15/8 21/11

### Porcupine

Main article: Porcupine

Chroma: 22/21 ~ 25/24 ~ 26/25* ~ 33/32 ~ 36/35 ~ 45/44 ~ 81/80

 Steps "Diminished" "Minor" "Major" "Augmented" 1 21/20~16/15 12/11~11/10~10/9 9/8~8/7 13/11* 2 7/6 6/5~11/9 5/4 9/7~13/10* 3 14/11 4/3 11/8 10/7~13/9* 4 7/5~18/13* 16/11 3/2 11/7 5 14/9~20/13* 8/5 5/3~18/11 12/7 6 22/13* 7/4~16/9 9/5~11/6 40/21~15/8
* 13-limit porcupinefish interpretation

### Valentino

Chroma: 49/48 ~ 51/50 ~ 52/51 ~ 55/54 ~ 56/55 ~ 64/63 ~ 65/64 ~ 77/75 ~ 85/84 ~ 119/117 ~ 128/125 ~ 143/140

 Steps "Diminished" "Minor" "Major" "Augmented" 1 36/35 21/20~25/24 17/16~16/15 13/12 2 14/13 12/11~11/10 10/9 17/15 20/17 3 9/8 8/7 7/6 32/27 4 13/11 6/5 11/9~17/14 5 16/13~21/17 5/4 14/11 13/10 27/20 6 9/7 21/16~17/13 4/3 34/25 7 27/20 11/8~15/11 7/5 17/12 8 24/17 10/7 16/11~22/15 40/27 9 25/17 3/2 26/17~32/21 14/9 10 40/27 20/13 11/7 8/5 13/8~34/21 11 18/11~28/17 5/3 22/13 12 27/16 12/7 7/4 16/9 13 17/10 30/14 9/5 11/6~20/11 13/7 14 24/13 15/8 40/21~48/25 35/18

### 2.3.5.11.13 hitchcock

Unlike amity itself, this 2.3.5.11.13 amity extension is a cluster temperament because the intervals between 6/5 and 5/4 are mapped to 11/9 and 16/13.

 Steps "Diminished" "Minor" "Major" "Augmented" 1 13/12 12/11~11/10 10/9 9/8 2 13/11 6/5 11/9 16/13 5/4 3 13/10 4/3 27/20 11/8 18/13 4 13/9 16/11 40/27 3/2 20/13 5 8/5 13/8 18/11 5/3 22/13 6 16/9 9/5 11/6 24/13