Editing Retuning to a regular temperament

LilyPond holds all the information for meantone temperaments or near-Pythagorean intonations. The default tuning is for 12 note equal temperament. This snippet changes that, and can be placed in an include file to work with pre-existing files. Key signatures are not supported.

The MIDI output works as well as any case of microtuning. Chords need to be split into separate voices. The example is a single line of rising pitches.

The tuning is specified as the number of steps to the octave for an equal temperament. Everything follows the nearest fifth to just in that equal temperament.

<lilypond version="2.24.0" full>
%% http://lsr.di.unimi.it/LSR/Item?id=752

% If you want pitchnames other than English, change the include.
% For tunings other than 31 note equal temperament, change the "31".
\include "english.ly"
tuning = #31


% Resets LilyPond's "default scale" containing the pitch of each
% unaltered note (the C major scale).
#(define (retune-nominals ET)
   (ly:set-default-scale
    (ly:make-scale (list->vector 
		    (map (lambda (fifths octaves)
			   (* 6
			      (+ (* fifths (best-fifth ET)) octaves)))
			 '(0 2 4 -1 1 3 5) '(0 -1 -2 1 0 -1 -2))))))

% Finds the best size of fifth in the equal temperement with
% the given number of fifths to the octave.
% Note: the effective equal temperament may end up larger.
% For example, ask for 12 and "quartertones" will give you 24.
#(define (best-fifth ET)
   (/ (inexact->exact (round (* ET 0.5849625007))) ET))

% Takes the association of pitch names and returns a
% new copy where each alteration has the correct value
% relative to fifths in the given equal temperament.
#(define (retuned-pitchnames pitchnames ET)
   (map (lambda (pitchname)
	  (let ((pitch (cdr pitchname)))
	    (cons (car pitchname)
		  (ly:make-pitch
		   (ly:pitch-octave pitch)
		   (ly:pitch-notename pitch)
		   (scale-alteration (ly:pitch-alteration pitch) ET)))))
	pitchnames))

% Takes a list mapping alterations to glyphs
% and re-tunes the alterations according to the size of fifth
% in the given equal temperament.
#(define (retune-glyphs glyphs ET)
   (map (lambda (glyph) (cons (scale-alteration (car glyph) ET) (cdr glyph)))
	glyphs))

% Converts an alteration from the initial alteration size
% (that would give 12-equal) to the given equal temperament.
#(define (scale-alteration alteration ET)
   (* 12 alteration (- (* 7 (best-fifth ET)) 4)))

% Set the innards
newglyphs =
#(begin
   (retune-nominals tuning)
   (ly:parser-set-note-names (retuned-pitchnames pitchnames tuning))
   (retune-glyphs standard-alteration-glyph-name-alist tuning))


\score {
  \new Staff \relative c' {
    \set Staff.extraNatural = ##f
    cff4 ctqf cf cqf
    c4 cqs cs df
    dqf4 d dqs ds
    dtqs4 dx e f
    g4 a bf b
    c1
    \transpose c d \relative c' {
      cff4 ctqf cf cqf
      c4 cqs cs df
      dqf4 d dqs ds
      dtqs4 dx e f
      g4 a bf b
      c1
    }
  }
  % Apply the new glyphs.
  \layout {
    \context {
      \Score
      \override Accidental.alteration-glyph-name-alist = \newglyphs
      \override KeySignature.alteration-glyph-name-alist = \newglyphs
      \override AccidentalCautionary.alteration-glyph-name-alist = \newglyphs
      \override TrillPitchAccidental.alteration-glyph-name-alist = \newglyphs
      \override AmbitusAccidental.alteration-glyph-name-alist = \newglyphs
    }
  }
  \midi {}
}

\paper { tagline = ##f }
</lilypond>

[[Category:Pitches]]
[[Category:Midi]]