Unusual time signatures?

Question

I was just wondering if you could get time signatures where the bottom number is 3,5,6,7,9,10,11 and so on. I did not know if you could have dotted notes as your base note

Answer 1

Yes. This kind of time signature is called Irrational.

An irrational time signature is one where the denominator isn't a power of two (like the examples you provided).

There has been another similar question here;

• (1/√π)/√⅔ as a time signature?

Where the asker provides a link from Wikipedia that has many compositions in irrational time signatures.

Answer 2

A dotted note IS the base note in compound time signatures such as 6/8, 9/8, 6/4. Occasionally you'll see such time signatures written like this:

Some composers use 'irrational' time signatures to indicate a tempo change.

https://en.wikipedia.org/wiki/Time_signature#Irrational_meters

Answer 3

No, basically. But of course it depends on what you mean by "could you get?"

A time signature has a bottom number (it's not a denominator, because a time signature is not a fraction) which is a power of 2, representing one of the series of binary-divided notes from semibreve ("whole note") downwards. The top number shows how many of these note-values make up a bar (measure). It would be nice if the bottom number showed how big a beat is, but this is not true: if each beat is a dotted crotchet, then the number on the bottom "ought" to be 3/8, but instead 8 is written on the bottom, and the number on the top is the number of beats multiplied by 3. Similarly, if there are 3 beats each divided into 5 quavers, the time signature is 15/8 (e.g. Scriabin op. 11-14). (And of course this is ambiguous: it could be 5 beats of dotted crotchets.)

You asked about numbers like 3, 5, 7 etc., but unfortunately it is not clear what these would mean, because they do not obviously refer to any sensible notes: if my binary arithmetic is to be trusted, 1/3 in binary is 0.010101..., so 3 on the bottom means that each beat is represented by (let's use American here!): 1/4 + 1/16 + 1/64 + ..., and unending series of notes.

Meanwhile, those regarding fame as more important than music can write anything they like, any some people may buy it.

Carl Orff in Carmina Burana (and I guess elsewhere) pioneered a much better system in which you write the note symbol for each beat (including dotted notes) on the bottom, and the number of beats on the top, but this has never really caught on.

Answer 4

http://homes.sice.indiana.edu/donbyrd/CMNExtremes.htm exhaustively reports:

Non-power-of-2 denominator: A time signature of 12/12 appears in the clarinet part of Franz Berwald's Quartet for Piano and Winds (1819!), II (vol. 13, p. 29 of the complete works). (The obvious way to express what seems to be intended would be simply 12/8! Perhaps the 12/12 is a mere mistake.) (contributed by Guerin) Herbert Bruen has used a denominator of 12, e.g., 5/12, I believe for what most people would write as (3+2/3)/8. Thomas Ades has written a measure of 2/6 time, consisting of a half note with a triplet 3 over it, i.e., 2/3 of a half note; he's also written 1/6 in his *Asyla, II. But this kind of thing can also be written with unconventional numerators instead of denominators: Boulez has written what is probably the same thing as (2/3)/4. Time signatures like 8/9 and 8/12 appear, e.g., in Frescobaldi, but apparently just to cancel previous proportions and not to indicate durations of 8/9 or 8/12 of anything, and this usage should not be considered CMN.