§ I.5 · The CLI Workshop · No. XI

Microtonality
Scaler.

After Blackwood 1985 · Xenakis 1971

Reads MIDI numbers from stdin, retunes them to a specified tuning system — edo, just intonation, cents, meantone — and writes the resulting frequencies in Hz to stdout, four decimals. Rationals are stored exactly via a small BigInt helper, converted to float only at the boundary. A pocket retuning lab for the corpus.

¶ Why a command line

Composers and ethnomusicologists working with non-12-TET systems need to translate melodies between tuning spaces — "what are these MIDI pitches in 31-EDO?", or "scale this melody to 5-limit just intonation?" The command answers both in a single line: node 02-scaler.js --tuning=edo:31 < melody.txt. Output is plain Hz, suitable for a synthesiser, a CSV, or a frequency-domain analysis script.

¶ Invocation

$ node 02-scaler.js --tuning=edo:31 < midi-pitches.txt
$ echo "60 62 64 65 67" | node 02-scaler.js --tuning=ji:1/1,9/8,5/4,4/3,3/2
$ node 02-scaler.js --tuning=meantone:1/4 --ref=440 < chorale.txt
$ echo "60 64 67" | node 02-scaler.js --tuning=cents:0,386.31,701.96

¶ Sample output

261.6256
293.6648
329.6276
349.2282
391.9954

¶ Scope

input        whitespace-delimited MIDI integers (0..127) on stdin / file

tuning       --tuning=edo:N           N equal divisions of the octave
             --tuning=ji:p1/q1,p2/q2  sparse just intonation, anchored to
                                      the nearest 12-edo semitone within
                                      the octave; uncovered degrees fall
                                      back to 12-edo
             --tuning=cents:c1,c2,…   same anchoring, in cents from 1/1
             --tuning=meantone:p/q    twelve fifths tempered by p/q of the
                                      syntonic comma 81/80; wolf falls
                                      between G# and Eb

flags        --ref=Hz       A4 anchor frequency (default 440)

output       Hz, four decimals, one per line. C (MIDI 60) is the 1/1 anchor
             for ji / cents / meantone modes.

¶ References

• Blackwood, Easley. The Structure of Recognizable Diatonic Tunings. Princeton: Princeton University Press, 1986. — the taxonomy of interval ratios that grounds the tuning mini-language.
• Xenakis, Iannis. Formalized Music: Thought and Mathematics in Composition. Bloomington: Indiana University Press, 1971; rev. ed. 1992.

¶ Source

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