Off-topic: does anybody know about these accidentals?

[Jean Abou Samra]

Hi folks,

A friend of mine asked the following question, which I find pretty mysterious.

In the Unicode musical symbols block, the available microtonal accidentals are 
these:

- 𝄬 U+1D12C MUSICAL SYMBOL FLAT UP and 𝄭 U+1D12D MUSICAL SYMBOL FLAT DOWN
- 𝄮 U+1D12E MUSICAL SYMBOL NATURAL UP and 𝄯 U+1D12F MUSICAL SYMBOL NATURAL DOWN
- 𝄰 U+1D130 MUSICAL SYMBOL SHARP UP and 𝄱 U+1D131 MUSICAL SHARP DOWN
- 𝄲 U+1D132 MUSICAL SYMBOL QUARTER TONE SHARP and 𝄳 U+1D133 MUSICAL SYMBOL
  QUARTER TONE FLAT

In case you have fonts where these are as ridiculously small as on my
system, attached is a chart made with

\markuplist \override #'((padding . 2) (baseline-skip . 5))
\table #`(,CENTER ,RIGHT ,CENTER ,RIGHT) {
  \fontsize #10 𝄬 "flat up" \fontsize #10 𝄭 "flat down"
  \fontsize #10 𝄮 "natural up" \fontsize #10 𝄯 "natural down"
  \fontsize #10 𝄰 "sharp up" \fontsize #10 𝄱 "sharp down"
  \fontsize #15 𝄲 "quarter tone sharp" \fontsize #15 𝄳 "quarter tone flat"
}

The glyphs with arrows are AFAIK standard, and available in LilyPond
as accidentals.{flat,natural,sharp}.arrow{down,up}. But what about
the "quarter tone {sharp,flat}", which look like a sharp/flat with
an added digit 4?

I've never seen these. LilyPond's Emmentaler font doesn't have them
https://lilypond.org/doc/v2.25/Documentation/notation/accidental-glyphs .

The SMuFL standard has a *very* extensive set of accidentals, see
https://w3c.github.io/smufl/latest/tables/standard-accidentals-12-edo.html
and the following sections; yet I couldn't find them there either.

There is a Unicode proposal not yet accepted
https://unicode.org/L2/L2023/23276-quarter-tone-accidentals.pdf
to encode the more standard accidentals which are the default
in LilyPond (try { ceh' cih' } ): a sharp with only one
vertical branch, and a mirrored flat. The proposal quotes
https://tug.org/TUGboat/tb38-2/tb119hufflen-music.pdf :

"The glyphs defined by Unicode at present are 𝄲(U+1D132) and
𝄳(U+1D133): we have *never* seen them in *any* score."

The original proposal to encode these in Unicode was
https://unicode.org/L2/L1998/98045.pdf
and gives zero details.

Does anybody have a clue where the heck these glyphs come from?
Which composers might have used them?

Cheers,
Jean

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