: What do uncommon time signatures consist of? Take a X/4, it means "the measure will contain X notes, the value of which are 1/4" I understand this concept for X/Y signatures, with Y being a power of 2. But what does that

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The denominator doesn't have to be a power of 2. From Wikipedia:

The lower numeral indicates the note value that represents one beat (the beat unit).
The upper numeral indicates how many such beats there are grouped together in a bar.


For instance, 2/4 means two quarter-note (crotchet) beats per bar and 3/8 means three eighth-note (quaver) beats per bar.

So 3/9 means 3 ninth-note beats per bar.

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Take a simpler example: what would a time signature of 2/3 mean?

If you divide a whole note into three equal parts, in conventional notation you would write that as a triplet of half-notes (= UK minims). But suppose you want the music contain some normal-length half-notes followed by just two notes at the speed of a triplet, and them continue normal-length notes.

You could mark one bar to be played at a faster tempo (MM mark) and then revert to the original tempo, but the performer would then have to "do the math" to figure out what was intended. If the tempo marks were MM 76 and 114 it's not obvious to most people that the ratio is exactly 3:2.

You could write a series of triplets with notes tied from one to the next, but that would be unreadable except for a short passage of music.

The new notation of a 2/3 time signature was invented as a neater way to write this. It's easier to "read" the exact relation between time signatures like 2/3 and 2/4 than between MM marks of say 76 and 114.

Some composers have used a different notation, where the denominator remains a power of two (showing the length of the beats) but the numerator is itself a fraction - for example (5/3)/4 would be a bar length of a quarter-note plus two-thirds of a triplet of 8th-notes. Of course you could write that more conventionally as 3+2+2/8 or 7/8, but hey, avant garde music needs to look cool, and 7/8 is way too old school for that.

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While the typical notes are based on divisions of 2 (i.e. whole, half, quarter, 8th, 16th, ect) using tuples you can have almost any ratio of notes you can utilize to split up a measure.

Here is a layout of notes evenly splitting up a measure of 4/4 from whole notes to what you could call 9ths:

As you can see all take up a whole measure of 4/4 and divided them equally and you could theoretically give any one of the notes below the beat which is what the denominator is for.

In practice however, this is not really very useful as not only notating something like 3/9 difficult due it's tuple nature, but in reality you would be much more inclined to view it as 3/8 because the only difference you would feel is a slightly faster tempo which is much easier to notate then part of a sequence of tuples across a measure.

The version of Finale I have won't even let me mock up a measure of 3/9 for you for that reason, but it can be achieved and I'll eventually show it on manuscript.