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Isomorphic keyboard layouts can be useful for playing and composing in Orwell and other regular temperaments. As pitch space in rank-2 temperaments is 2-dimensional, the structure can be directly mapped to a 2-dimensional array of keys.

Axis-49


The Axis-49 has 98 velocity-sensitive buttons arranged in a honeycomb pattern. One key mapping for Orwell Temperament on the Axis-49 maps the Orwell generator (approx. 272ยข) to one move of "down and to the right" and the octave period to one move of "up and to the right" and three moves of "down and to the right". This gives the Orwell[13] MOS scale the following shape on the Axis-49 keyboard:

orwell13_axis49.png
We can see from the diagram that just over four octaves are available on the Axis-49 keyboard (more on the Axis-64 or on other larger isomorphic keyboards). Note that the numbers above indicate multiples of the orwell generator (NOT ascending pitch order), ignoring octaves. Each duplicate number to the right is one octave higher than its counterpart to the left. The starting place is arbitrary; if we select another hex to be 0, we can build another orwell[13] scale. Note also that the choice to focus here on the 13-tone MOS is also somewhat arbitrary, as clearly more tones are available on the keyboard, represented by the hexes outlined in gray with no number.

To help with visualizing what an Orwell[13] "chromatic scale" looks like, note that the pitches in ascending order go: 0 9 5 1 10 6 2 11 7 3 12 8 4 0. The large step of Orwell[13] maps to one move upward (as well as -4 generators, eg. 8 to 4). The small step of Orwell[13] maps to two moves downward and one move "down and to the right" (as well as +9 generators, eg. 1 to 10). Thus, this (or any) 2-dimensional regular arrangement of the Orwell[13] scale makes it easy to distinguish between the two different step sizes, as they are represented by different "moves" on the keyboard.

Dyadic Pentads and Hexads of Orwell[13] on the Axis-49


The page Chords of Orwell offers one system for identifying and naming dyadic chords available in Orwell Temperament. The following diagrams show how some of those chords would map to an Axis-49 (or similar keyboard, eg. Opal Chameleon) tuned as above. These diagrams only look at the pentads and hexads available in Orwell[13]. The "chords of orwell" page also lists triads and tetrads, as well as chords which require a generator chain larger than that of Orwell[13]. The "types" come from the "chords of orwell" page and say something about which commas must be tempered out (if any) for this chord to be possible.

At the time of writing, the essentially-tempered dyadic chords of Orwell Temperament have been little explored; perhaps these diagrams will give isomorphic keyboardists some encouragement to explore them.

Pentads


orwell13_pentad01.pngorwell13_pentad02.pngorwell13_pentad03.png
orwell13_pentad04.pngorwell13_pentad05.pngorwell13_pentad06.png
orwell13_pentad07.pngorwell13_pentad08.pngorwell13_pentad09.png
orwell13_pentad10.pngorwell13_pentad11.pngorwell13_pentad12.png
orwell13_pentad13.pngorwell13_pentad14.pngorwell13_pentad15.png
orwell13_pentad16.pngorwell13_pentad17.pngorwell13_pentad18.png
orwell13_pentad19.pngorwell13_pentad20.pngorwell13_pentad21.png
orwell13_pentad22.pngorwell13_pentad23.pngorwell13_pentad24.png
orwell13_pentad25.pngorwell13_pentad26.pngorwell13_pentad27.png
orwell13_pentad28.pngorwell13_pentad29.pngorwell13_pentad30.png
orwell13_pentad31.pngorwell13_pentad32.pngorwell13_pentad33.png
orwell13_pentad34.pngorwell13_pentad35.png

Hexads


orwell13_hexad01.pngorwell13_hexad02.pngorwell13_hexad03.png

orwell13_hexad04.pngorwell13_hexad05.pngorwell13_hexad06.png

Scala File


The following Scala file is specifically for the Axis-49, which, in "selfless mode," can send a separate midi note on each of its 98 keys from note numbers 1 to 98. The tuning file will only work if it is set to start on midi note 1 ("C# -2" in "MIDI Standard", "C# -1" in "ISO 16:1975", and "C# 0" in "Cakewalk standard" -- see here for details on the variety of MIDI note-naming schemes). You can tell it's working if the same shape consistently produces the same pattern of intervals, i.e. if it is regularly mapped. It is left to the reader to choose a suitable base frequency for their purposes.

= = =
! orwell53edo_-113x272_axis49.scl
A regular mapping of Orwell Temperament (53edo version) for the Axis-49 isomorphic keyboard.
97
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