Chair scale

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 scales 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.

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.

Scales

The Chair of Mr. Bob

The chair of Mr. Bob is the prototypical chair scale, created by DotuXil.

! ChairOfMrBob.scl
!
Once upon a time, there was a scale crafter named Mr Bob. He walked for a long, long time traversing the lands of tuning space, but no scale he found could support his tired self. Frustrated, he took to making his own, and so the throne was created.
10
!
21/20
35/32
6/5
21/16
7/5
3/2
8/5
105/64
7/4
2/1

The Chair of Tristan Bay

! ChairOfTristanBay.scl
!
Chair scale shared by Tristan Bay
10
!
35/32
7/6
5/4
4/3
35/24
3/2
5/3
7/4
15/8
2/1