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I would like to ask a perhaps somewhat strange question here in the hope that someone can help me or pave the way. It's about a special kind of rhythmic notation that I have come up with and that I would like to implement in LilyPond.

So: I want to notate odd note values like 5/32, 9/32 and the like in LilyPond without using a tie. I have come up with the following concept: For dotted note values, only the dots (of the respective dotted note) that are circled are counted. (By "circled" I mean that a small circle is drawn around the respective dot of a dotted note).

So if we have a double-dotted note, let's say a double-dotted 16th note, in which both dots are circled, we have a note value with a duration of 7/64 (4+2+1). If, on the other hand, only the last of the two dots is circled, we would have a note value with a duration of 5/64 (4+1). Another example: If we have a quadruple dotted 16th note in which all the dots are circled, we have a note value with a duration of 31 256ths notes (16+8+4+2+1). If, on the other hand, only the first, third and fourth dots are circled, we have a note value with a duration of 27 256ths notes (16+8+2+1); and if only the last two of the four dots are circled, the note value has a duration of 19 256thsn notes (16+2+1). I think the concept should be fairly clear?

Perhaps there is someone here who can help me (and who also enjoys such notational escapades)? Or knows how I should proceed in order to achieve the desired result?

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In effect, this extends the binary system already in place for dots, the difference being that two symbols are needed — 1s and 0s, so to speak. In that regard, any two visually distinct symbols will do.

This being the case, the simplest solution (for the visual aspect) would be to use a markup attached to the note. Using the OP example of a double-dotted sixteenth note, the code would be n16^\markup {++}, but in the case where only the second dot is used, the code could be n16^\markup {_+}. The case of 27 256th notes would be n16^\markup {+_++}.

An advantage to placing the "dots" above or below the note is that it clearly distinguishes the system from the standard note-dotting practice.

If the "circled dot" approach is preferred, then a 7/16 note would be n16^\markup {. \circle .}.

One problem is that the markup is aligned to the left of the note, and LilyPond places the next note according to the current note's duration. Markups quickly begin to overlap. A simple solution there is to rotate the markup.

n16^\markup \left-align {\rotate #90 \concat {. \circle . . \circle .}}

Some additions to this not addressed here could be:

  1. center the markup relative to the note (if horizontal)
  2. encapsulate the markup in a scheme function
  3. cause LilyPond to respect the intended duration of the note when calculating note/bar/line spacing and playback.

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