Orwell on an Isomorphic Keyboard
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. 272¢) 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:
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
Hexads
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 ! -113.207548 -226.415096 -339.622644 -452.830192 -566.03774 -679.245288 271.698113 158.490565 45.283017 -67.924531 -181.132079 -294.339627 -407.547175 656.603774 543.396226 430.188678 316.98113 203.773582 90.566034 -22.641514 928.301887 815.094339 701.886791 588.679243 475.471695 362.264147 249.056599 1313.207548 1200. 1086.792452 973.584904 860.377356 747.169808 633.96226 1584.905661 1471.698113 1358.490565 1245.283017 1132.075469 1018.867921 905.660373 1969.811322 1856.603774 1743.396226 1630.188678 1516.98113 1403.773582 1290.566034 2241.509435 2128.301887 2015.094339 1901.886791 1788.679243 1675.471695 1562.264147 2513.207548 2400. 2286.792452 2173.584904 2060.377356 1947.169808 1833.96226 2898.113209 2784.905661 2671.698113 2558.490565 2445.283017 2332.075469 2218.867921 3169.811322 3056.603774 2943.396226 2830.188678 2716.98113 2603.773582 2490.566034 3554.716983 3441.509435 3328.301887 3215.094339 3101.886791 2988.679243 2875.471695 3826.415096 3713.207548 3600. 3486.792452 3373.584904 3260.377356 3147.169808 4211.320757 4098.113209 3984.905661 3871.698113 3758.490565 3645.283017 3532.075469