## "Irrational" time signatures?

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W3R3W00F
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"Irrational" time signatures? 2011-09-14 00:23:13

Hi guys. :) I have an unusual question.

I'm studying time signatures: Particularly, "Irrational" time signatures. Irrational time signatures are time signatures that don't have a denominator to a power of 2 (E.g., 3/10, 5/6, 4/3). Here's a line of text copied from the Wikipedia page.

"Notationally, rather than using Cowell's elaborate series of notehead shapes, the same convention has been invoked as when normal tuplets are written; for example, one beat in 4/5 is written as a normal quarter note, four quarter notes complete the bar, but the whole bar lasts only 4/5 of a reference whole note, and a beat 1/5 of one (or 4/5 of a normal quarter note). This is notated in exactly the same way that one would write if one were writing the first four quarter notes of five quintuplet quarter notes."

With that in mind, I tried to create 4/5 time as well as I could using FL Studio 10... however, I have no idea if I even read the Wikipedia article correctly and if the end result matches up with what the article said. :P

In the picture, I've selected only the first 4 light green colored quintuplet quarter notes, since 4 quintuplet quarter notes complete 1 bar in 4/5. The last light purple colored quintuplet quarter note is just a reference to show you that I've equally divided a 4/4 bar into 5 quintuplet quarter notes, but only used the first 4.

Seriously, I have no clue if I'm doing this right. I'm just curious and exploring what's musically possible. That's why I'm wondering if any of you know if I'm doing this correctly.

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ProudAardvark
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Response to "Irrational" time signatures? 2011-09-14 01:01:16

Irrational time signatures are usually compound time signatures, i.e. 7/8 is really 2+3+2/8 or some other arrangement. Its a really common idea in eastern European folk music for example to have repeating patterns like this. I like it a lot and use it a lot in my own work.

Some suggested listening:
Prokofiev, Piano Sonata No. 7 Third Movement
Bartok, Contrasts

Happy composing!

BigRed
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Response to "Irrational" time signatures? 2011-09-14 01:23:53

I was expecting actual irrational numbers and square roots in the time signatures.

W3R3W00F
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Response to "Irrational" time signatures? 2011-09-14 01:50:10

At 9/14/11 01:01 AM, ProudAardvark wrote: Irrational time signatures are usually compound time signatures, i.e. 7/8 is really 2+3+2/8 or some other arrangement. Its a really common idea in eastern European folk music for example to have repeating patterns like this. I like it a lot and use it a lot in my own work.

Some suggested listening:
Prokofiev, Piano Sonata No. 7 Third Movement
Bartok, Contrasts

Happy composing!

Hm... I think that 2+3+2 would be an 'additive' time signature. That's what Wikipedia calls it, anyway. I need to start experimenting with those, they seem like they'd be handy...

Either way, thanks for the reply! :)

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WizMystery
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Response to "Irrational" time signatures? 2011-09-14 07:33:47

At 9/14/11 01:01 AM, ProudAardvark wrote: Irrational time signatures are usually compound time signatures, i.e. 7/8 is really 2+3+2/8 or some other arrangement. Its a really common idea in eastern European folk music for example to have repeating patterns like this. I like it a lot and use it a lot in my own work.

Some suggested listening:
Prokofiev, Piano Sonata No. 7 Third Movement
Bartok, Contrasts

Happy composing!

This isn't what he's talking about. He means a different bottom number which is different from normal compound time signatures.

It's interesting but few combinations have much use if you can just organize notes into tuplets anyway - unless it was liteally irrational and the numerator or denominator had a decimal point.

Breed
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Response to "Irrational" time signatures? 2011-09-14 07:47:35

The quote is just wrong. The bottom number is irrelevant to the theory behind the signature. It's simply for notation purposes and tempo purposes. 4/5 in theory would just be a nonconventional way to notate 4/4 and would require a strange odd numbered system of notation to be built all around it, basically just coming out to be an illogical and pointless version of what we use already.

If you really want to study time signatures, look into metric modulation, and natural rhythmic accents for meters. From there you can branch out to other rhythmic studies like syncopation and polyrhythms.

Kor-Rune
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Response to "Irrational" time signatures? 2011-09-14 10:29:50

I did this in FL studio two nights ago coincidentally, but of course it wasn't perfect. But sometimes, that's okay, and makes it a little more human.

Theory wise, I'm positive you'd still have 4/4 or whatever time signature you're using, and you'd just be using quintuplets for the song instead of making the time signature some weird 4/5 thing.

Here's a septuplet rhythm I found on wikipedia, quintuplets would be written the same way.

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Envy
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Response to "Irrational" time signatures? 2011-09-14 12:27:01

I use a lot of 4/3

You end up with a swing because its the same as 4/4 but instead of regular sixteenth notes you have sixteenth triplets.

At 3/27/11 10:22 PM, sugarsimon wrote:
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Envy
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Response to "Irrational" time signatures? 2011-09-14 12:33:02

At 9/14/11 10:29 AM, Kor-Rune wrote: I did this in FL studio two nights ago coincidentally, but of course it wasn't perfect. But sometimes, that's okay, and makes it a little more human.

Theory wise, I'm positive you'd still have 4/4 or whatever time signature you're using, and you'd just be using quintuplets for the song instead of making the time signature some weird 4/5 thing.

Here's a septuplet rhythm I found on wikipedia, quintuplets would be written the same way.

I guess thats essentially what I meant.

You still have a "normal" time signature, just the spacing of the beats per measure would be different (like 4/3 giving you triplets)

At 3/27/11 10:22 PM, sugarsimon wrote:
the brilliant songs who create a production for music
Wat

Chris-V2
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Response to "Irrational" time signatures? 2011-09-14 12:42:55

But 4/3 is surely just an irregular way to write a 12/8 rhythm. Since it'd be 8 quaver triplets per bar, you'd just have 2 bars of 4/3 to 1 bar of 12/8.

I'll say it once and I'll say it again, the western notation system is going to be succesively less useful the further we move away from the styles which the system was designed for.

boney-man
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Response to "Irrational" time signatures? 2011-09-14 12:56:02

At 9/14/11 01:23 AM, BigRed wrote: I was expecting actual irrational numbers and square roots in the time signatures.

Yeah, I was expecting a time signature like e/%u03C0 or something

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boney-man
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Response to "Irrational" time signatures? 2011-09-14 12:57:48

At 9/14/11 12:56 PM, boney-man wrote:
At 9/14/11 01:23 AM, BigRed wrote: I was expecting actual irrational numbers and square roots in the time signatures.
Yeah, I was expecting a time signature like e/%u03C0 or something

ew i meant e/pi

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Buoy
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Response to "Irrational" time signatures? 2011-09-14 13:21:02

- Usually, people confuse the denominator and numerator (4/4 with triplets is not 4/3, but some variant of 3/4)
- ANY repeating musical pattern can be expressed as being in a time signature with a 2^n denominator.

W3R3W00F
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Response to "Irrational" time signatures? 2011-09-14 13:47:29

At 9/14/11 10:29 AM, Kor-Rune wrote: I did this in FL studio two nights ago coincidentally, but of course it wasn't perfect. But sometimes, that's okay, and makes it a little more human.

Theory wise, I'm positive you'd still have 4/4 or whatever time signature you're using, and you'd just be using quintuplets for the song instead of making the time signature some weird 4/5 thing.

Here's a septuplet rhythm I found on wikipedia, quintuplets would be written the same way.

I believe you're right, that sounds accurate. If you used 5 quintuplet notes, I think you'd just have a quintuplet rhythm. However, I wonder if, because I only used 4 of the 5 quintuplet notes, that would make it 4/5 time? There must be some way to write "irrational" signatures: John Pickard's 'Eden' used bars of 3/10, and the second movement of Thomas Adès' 'Traced Overhead' used signatures such as 2/6, 9/14, and 5/24 (according to Wikipedia).

An easier alternative to writing 4/5 may be just to use 4/4 at a quicker tempo, I suppose. :I I dunno.

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Thegluestickman
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Response to "Irrational" time signatures? 2011-09-14 17:23:41

Exactly what the people above me have said.

Time signatures are denoted as the numerator being the number of beats in a bar, while the denominator is what note gets 1 beat. There isn't a fifth note, but there is a quintuplet. So the quintuplet gets a beat and there is 4 beat sin a bar. That would be your 4/5 time signature.

Since when we put things in tuplet form, we're really squeezing more notes into one beat. One quintuplet = 1 beat. Therefore, the 4/5 time signature is one that only has tuplets which really gives a swing feel. More of a lively quick feel. It's not really a 4/4 signature because it's forcing quintuplets in to the beat. Hope I helped.

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Buoy
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Response to "Irrational" time signatures? 2011-09-14 17:30:40

if you're using JUST quintuples it's effectively 5/something

MillsApparatus
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Response to "Irrational" time signatures? 2011-09-14 18:11:32

The bottom number of the time signature must be 1, 2, 4, 8, 16, 32, 64, 128, etc. It's based on the division of notes, such as whole, half, quarter, eights, etc. and cannot be anything but. The top number can be changed, for instance 5/8 and 7/8 are common in Greek folk music (and shitty Rack songs). Having no time signature is about as abstract as you can get but this is only found in Renaissance and Medieval music where in some cases where there actually is a time signature, it is usually a sacred or royal symbol or for time, a single number 3 (and in this music it is not uncommon to see several whole notes in the span of a few 8ths in modern music, it can be a real bitch to read and is a reason why a degree in historical performance is mandatory in order to play such pieces, especially in public).

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W3R3W00F
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Response to "Irrational" time signatures? 2011-09-14 18:32:54

At 9/14/11 05:23 PM, Thegluestickman wrote: Exactly what the people above me have said.

Time signatures are denoted as the numerator being the number of beats in a bar, while the denominator is what note gets 1 beat. There isn't a fifth note, but there is a quintuplet. So the quintuplet gets a beat and there is 4 beat sin a bar. That would be your 4/5 time signature.

Since when we put things in tuplet form, we're really squeezing more notes into one beat. One quintuplet = 1 beat. Therefore, the 4/5 time signature is one that only has tuplets which really gives a swing feel. More of a lively quick feel. It's not really a 4/4 signature because it's forcing quintuplets in to the beat. Hope I helped.

That sounds right. That's what I picked up from the Wikipedia article. I wonder, then, if 5 quintuplet beats would just be a quintuplet rhythm or 5/5 time? It seems logical, concerning 2/2 lasts as long as 4/4, 8/8, 16/16, 32/32, etc.

Also, while we're on the subject of "irrational" time signatures, there apparently is one song that uses a mathematically irrational time signature. Wikipedia says this: Conlon Nancarrow's "Studies for Player Piano" contains a canon where one part is augmented in the ratio %u221A42:1 (approximately 6.48:1). Interesting.

At 9/14/11 03:57 PM, Space-Whale wrote:
At 9/14/11 01:23 AM, BigRed wrote: I was expecting actual irrational numbers and square roots in the time signatures.
Well, I've done a song in %u221A-1/4.

I lol'd. xD

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Kor-Rune
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Response to "Irrational" time signatures? 2011-09-14 19:30:35

At 9/14/11 06:32 PM, W3R3W00F wrote:
That sounds right. That's what I picked up from the Wikipedia article. I wonder, then, if 5 quintuplet beats would just be a quintuplet rhythm or 5/5 time? It seems logical, concerning 2/2 lasts as long as 4/4, 8/8, 16/16, 32/32, etc.

I'm not sure. I think 2/2 lasts as long as 16/16 because the duration of those two signatures are the same. I think a fives feel would only be the same duration in a regular x/2^y time signature, using notated quintuplets.

But I'm not a theory buff so i dunno :c

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midimachine
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Response to "Irrational" time signatures? 2011-09-14 21:24:36

At 9/14/11 06:32 PM, W3R3W00F wrote: That sounds right. That's what I picked up from the Wikipedia article. I wonder, then, if 5 quintuplet beats would just be a quintuplet rhythm or 5/5 time? It seems logical, concerning 2/2 lasts as long as 4/4, 8/8, 16/16, 32/32, etc.

AFAIK If you're doing quintuplet rhythms then you put 5 notes in the space that 2 take, draw a square bracket over/under them write a 5 above/below the bracket. If you're doing a whole song like that it'd probably be more courteous to just write in 5/8 or 5/16.

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Breed
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Response to "Irrational" time signatures? 2011-09-15 09:06:42

I'd like to add that FL Studio's setting for meters is totally wrong. It has its own signature system thats pretty odd

W3R3W00F
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Response to "Irrational" time signatures? 2011-09-15 17:17:06

You know, I kind of wondered if it was wrong... I just didn't know if anybody else thought so, too.

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Troisnyx
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Response to "Irrational" time signatures? 2011-09-15 18:39:54

I haven't actually come across an error in the time signature thing - ultimately, it's how you write it, and if you snap something to 1/4 beat, you ultimately have (insert number of counts here) / 4. If you snapped it to 1/6 beat, you get a compound time signature with (whatever number of counts). At the end of the day, it's how the piece is written.

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Response to "Irrational" time signatures? 2011-09-15 22:34:19

At 9/15/11 09:06 AM, LogicalDefiance wrote: I'd like to add that FL Studio's setting for meters is totally wrong. It has its own signature system thats pretty odd

Thankfully I'm not the only one that thinks this, and I thought I was going insane...

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dontpanic01
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Response to "Irrational" time signatures? 2011-09-15 23:12:27

At 9/15/11 09:06 AM, LogicalDefiance wrote: I'd like to add that FL Studio's setting for meters is totally wrong. It has its own signature system thats pretty odd

Can you please elaborate on how Fl's meter settings are off,
(I'd like to know how, just so that my music will suck less)

apparently I'm clever enough to declare myself as a dumbass

W3R3W00F
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Response to "Irrational" time signatures? 2011-09-15 23:58:35

At 9/15/11 11:12 PM, dontpanic01 wrote:
At 9/15/11 09:06 AM, LogicalDefiance wrote: I'd like to add that FL Studio's setting for meters is totally wrong. It has its own signature system thats pretty odd
Can you please elaborate on how Fl's meter settings are off,
(I'd like to know how, just so that my music will suck less)

Hope this helps a bit. :)

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W3R3W00F
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Response to "Irrational" time signatures? 2011-09-16 00:14:18

In addition to my previous post, and just to clarify if needed, I'm not implying that 4 beats will complete 1 bar no matter what. If you switched to 5/4 time, there would be a total of 5 beats per bar, and each beat would last the length of a quarter note. Furthermore, switching to 6/8 would mean that there would be 6 beats per bar, and each beat would last the length of an eighth note. OR, if you did 6/4 time, there would be 6 beats per bar, and each beat would last the length of a quarter note.

Just clearing things up a bit, just in case...

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Response to "Irrational" time signatures? 2011-09-16 00:56:57

I have used 'irrational' time signatures often in my music, and have tried switching them up mid-song too. Venetian Snares, Tool and Yip-Yip are huge influences in this field.

If you're using FL Studio and want to avoid the headache of haphazardly piano rolling stuff all nutty, you can press F10 and select 'General' and you can change the Time Signature to what you wish. The main one is 4/4 and you'll see that when you get to the panel. Beats is how many hits are in a bar and Bar is number of beat sections generally available.

For beat, you don't really need to go past 4 for it; 3 or 6 can be used for triplets, and you can do 8 if you want more intricacy in your step sequence patterns, but ill-advised if you put swing on there. Just a friendly hint. You can also use the 'Beats per bar for this pattern' feature in the upper-left-hand corner, perfect to tidy up one-shot effects.

It's fun to mess with time signatures in music, if not for practice, then just for the hell of it.

W3R3W00F
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Response to "Irrational" time signatures? 2011-09-19 23:02:38

At 9/16/11 12:56 AM, Spikrodd wrote: It's fun to mess with time signatures in music, if not for practice, then just for the hell of it.

Totally agree with you on that. It's not just great practice to explore outside of common time: you can create some of the most intriguing works in time signatures like 5/4, 7/4, 11/8, etc.

Anyway, I have one more question.

4/5 time is entirely possible, therefore, there must be a way to write it out. Does anyone think I wrote out 4/5 time correctly in the first picture or not?

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Troisnyx
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Response to "Irrational" time signatures? 2011-09-21 03:15:52

I should think so, yes.