Chair scale: Difference between revisions

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A '''chair scale''' is a JI or rank-4 scale whose lattice resembles a chair. It is used to refer to any lattice which is shaped like a chair, but formally, the lattice takes the form of a 2x2 cube, with an edge extended along the plane of one of its adjacent faces to another 2 notes, for a total of 10 notes in the scale. In this sense, a chair scale is a [[bipentatonic scale]], because the 10 notes form two parallel [[pentatonic scale]]s.

A '''chair scale''' is a JI or rank-4 scale whose lattice resembles a chair. It is used to refer to any lattice which is shaped like a chair, but formally, the lattice takes the form of a 2x2 cube, with an edge extended along the plane of one of its adjacent faces to another 2 notes, for a total of 10 notes in the scale. In this sense, a chair scale is a [[bipentatonic scale]], because the 10 notes form two parallel [[pentatonic scale]]s by virtue of one half of the lattice being a translation of the other half, which is equivalent to all notes in a pentatonic scale being duplicated and shifted in pitch space.

[[File:Mr bob.png|thumb|The lattice for the Chair of Mr. Bob.]]

A formal chair can be identified, up to different modes of the scale, by its lattice subgroup (conventionally 2.3.5.7), the edge which is extended (out of 12), and which plane it is extended along (out of 2). Thus, for a given subgroup or other rank-4 tuning, there are 24 chair scales.

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-A '''chair scale''' is a JI or rank-4 scale whose lattice resembles a chair. It is used to refer to any lattice which is shaped like a chair, but formally, the lattice takes the form of a 2x2 cube, with an edge extended along the plane of one of its adjacent faces to another 2 notes, for a total of 10 notes in the scale. In this sense, a chair scale is a [[bipentatonic scale]], because the 10 notes form two parallel [[pentatonic scale]]s.
+A '''chair scale''' is a JI or rank-4 scale whose lattice resembles a chair. It is used to refer to any lattice which is shaped like a chair, but formally, the lattice takes the form of a 2x2 cube, with an edge extended along the plane of one of its adjacent faces to another 2 notes, for a total of 10 notes in the scale. In this sense, a chair scale is a [[bipentatonic scale]], because the 10 notes form two parallel [[pentatonic scale]]s by virtue of one half of the lattice being a translation of the other half, which is equivalent to all notes in a pentatonic scale being duplicated and shifted in pitch space.
 [[File:Mr bob.png|thumb|The lattice for the Chair of Mr. Bob.]]
 A formal chair can be identified, up to different modes of the scale, by its lattice subgroup (conventionally 2.3.5.7), the edge which is extended (out of 12), and which plane it is extended along (out of 2). Thus, for a given subgroup or other rank-4 tuning, there are 24 chair scales.