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Say, a quarter note, how is it most commonly represented? "1/4"?, "quarter"? What if it's a dotted-note?
It would be useful to have a simplified numeric representation for note values, e.g. the exponent that determines its relative duration, -3 for a large note, 2 for a quarter, etc. 1/4, 1/256 is numeric, but it's a rational and needs two figures. Dotted-notes can only be represented as fractions.
Are there non-conventional representation systems based on that premise of minimal numeric form? (I don't mean the numbered or the integer notation, that do not contribute much to note value representation in this sense).

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    To throw another wrench into this question... answers should also consider triplets, duplets, sextuplets, and other -tuplets in general. – Caleb Hines Nov 24 '15 at 2:40
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Perhaps I've misunderstood the question, but how about using lilypond notation? A whole note is denoted with a "1", half note "2", quarter "4" etc. For dotted notes add a ".".

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    Lilypond is pretty standard. +1 Here's the relevant bit, along with another piece of shorthand the OP may find useful - you can leave off the number to say the note is the same as the previous one. – Josiah Nov 24 '15 at 1:46
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well, midi is the only standard that turns note durations to integers. you take a particular resolution in ticks per quarter note.

so let's say your whole note is 768 (=256*3)

it's divisible down to the 256th note and can be a triplet.

Or you can use higher resolutions for more precision, maybe multiply by 3 a few more times.

keep in mind that held notes' durations can get intricate. you can slur together any number of 16th notes.

if you really need small integers, you might try flipping the note denominator to the top to use, then triplet or dot or slur those. that'll pretty much do what standard notation does.

but as far as standards, midi is about it. well, maybe you could check into musicxml. i don't know much about it.

  • MusicXML is designed for MIDI compatibility, so it handles duration in much the same way. The terminology is a little different, but you specify a number of "divisions" per quarter note and note durations are given in multiples of those divisions. – hopper Nov 24 '15 at 15:04
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In abcnotation note length is specified relative to a unit note. So if unit note is quarter, an eighth is A/2, a half a2, dotted quarter A3/2. Since it was originally developed for transcribing folk music, various short hands are allowed. More details at http://abcnotation.com/wiki/abc:standard:v2.1#note_lengths.

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