27ED4 Nelindic

This plugin is meant for tuning Musescore playback to 27ED4 (27 equal divisions of the tetratave/fourth harmonic). The notes are tuned to the heptatonic scale known as nelindic. The plugin alters the cent value of the notes. It's not meant for conversion per se, it's a tool for effective composition of 27ED4 pieces. Simply click "Retune!" on a selection, The plugin will retune the whole piece if there's no selection.

Background:

This tuning of 27ED4 is based on the idea of using the 3n+1 harmonics, which are preferentially emphasized on a wind instrument that has a conical shape with the mouth end being the wider end (an anti-saxophone). Nelindic temperament works on the 4.7.10.13 subgroup.

Interval table:

The scale itself has the following structure: **LLLLLLs (L=3, s=2) G-F. This means that there are double sharps and flats everywhere but between F and G. The 13-note extension includes all of the sharps except for F#.

Note Cents ~ Ratios
A 0.00 1/1
A# 88.89 21/20
Bbb 177.78 10/9
Bb 266.67 7/6
B 355.56 16/13
B# 444.44 13/10 9/7
Cbb 533.33 27/20 19/14
Cb 622.22 10/7 13/9
C 711.11 3/2
C# 800.00 8/5
Dbb 888.89 5/3
Db 977.78 7/4
D 1066.67 13/7
D# 1155.56 39/20 35/18
Ebb 1244.44 80/39 72/35
Eb 1333.33 28/13
E 1422.22 16/7
E# 1511.11 12/5
Fbb 1600.00 5/2
Fb 1688.89 8/3
F 1777.78 14/5 36/13
F# 1866.67 80/27 38/13
Gb 1955.55 40/13 28/9
G 2044.44 13/4
G# 2133.33 24/7
Abb 2222.22 18/5
Ab 2311.11 80/21
A 2400.00 4/1

Limitations:
Currently, the plugin can only retune to standard A=440Hz. If you wish to make other non-octave tunings, remember that there is a correction value applied to the Abb, Ab, and Gx, as they are considered (by note.pitch) to be either in the octave below or above the regular selection. This is visible in the comments.

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API compatibility
3.x
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27ed4-nelindic.qml 41.16 KB