Cluster MOS: Difference between revisions

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A cluster ~~temperament (named by [[Keenan_Pepper|Keenan Pepper]])~~ is a very particular kind of ~~rank~~-~~2 temperament~~ whose generator is quite near a rational fraction of an octave. Therefore some MOS of the ~~temperament~~ is quasi-equal (which should be reasonably sized for it to be a good cluster temperament, 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 ~~JI intervals~~ that are individually recognizable, yet conceptually grouped into the same category (or "cluster") because they're so close.

A '''cluster MOS''' or '''cluster scale''' is a very particular kind of [[MOS]]-based system (i.e. a system based on stacks of [[period]]s and [[generator]]s) 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 temperament, 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|Keenan Pepper]]) is a rank-2 [[regular temperament]] interpretation of a cluster MOS. But not only that; in a cluster temperament, many different versions of each interval, differing by a chroma, these colors ''represent nearby JI intervals'' specifically (because a temmperament is a JI interpretation of MOS generator chains separated by the period).

An example of something that is '''not''' a cluster temperament is [[Amity|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).

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-A cluster temperament (named by [[Keenan_Pepper|Keenan Pepper]]) is a very particular kind of rank-2 temperament whose generator is quite near a rational fraction of an octave. Therefore some MOS of the temperament is quasi-equal (which should be reasonably sized for it to be a good cluster temperament, 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 JI intervals that are individually recognizable, yet conceptually grouped into the same category (or "cluster") because they're so close.
+A  '''cluster MOS''' or '''cluster scale''' is a very particular kind of [[MOS]]-based system (i.e. a system based on stacks of [[period]]s and [[generator]]s) 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 temperament, 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|Keenan Pepper]]) is a rank-2 [[regular temperament]] interpretation of a cluster MOS. But not only that; in a cluster temperament, many different versions of each interval, differing by a chroma, these colors ''represent nearby JI intervals'' specifically (because a temmperament is a JI interpretation of MOS generator chains separated by the period).
 An example of something that is '''not''' a cluster temperament is [[Amity|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).