Irrational meters and time signatures

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Slavicek
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Post by Slavicek » Tue Apr 25, 2017 2:55 pm

I'm interested in creating time signatures which composers like Henry Cowell used, such as 3/6 instead of 2/4, for instance, or any time signature that uses tuplet as a beat. Are they possible to be written down in Finale (without cheating with Expression Tool and hiding the actual time signature, that is obviously possible) and could the playback actually perform them?

Thank you in advance.


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motet
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Post by motet » Tue Apr 25, 2017 5:08 pm

I'm not familiar with this, so the following may be worthless.

Presumably 3/6 means 6 divisions per whole note, so three quarter notes to the bar? I suspect you're limited to powers of two in the denominator. Since 3/8 is "triplets" of eighth notes that Cowell might write as 3/12, couldn't you write 3/6 as a "compound meter" of 3/4? I think you would have to fake the time signature with an expression, but playback should be fine. 6/6 would involved writing triplets and hiding the triplet markings, I guess.

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N Grossingink
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Post by N Grossingink » Tue Apr 25, 2017 5:28 pm

The new software Dorico will/does include the capability to render irrational time signatures. Whether or not the program is capable at this early stage of development is uncertain to me. I'd suggest you join the Dorico forum and ask there. Getting in touch with like-minded composers can't hurt.

It seems to me that programming this would be relatively easy in Finale. After all, we're just talking about numbers.

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Peter Thomsen
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Post by Peter Thomsen » Tue Apr 25, 2017 5:45 pm

Slavicek,

Where did you find the term “irrational”?
I am not sure the term “irrational” is (mathematically) correct in this particular context (almost all time signatures are rational) - I would rather use the term “not dyadic rational”.

Time signatures with non-power-of-2-denominator such as 6/7 are possible in Finale - with a workaround.

For the denominator display you will have to “cheat”, and use an expression.

For the playback you have to approximate the exact value via a (not displaying) composite time signature.

Could you give us some examples of the time signatures you have in mind - and perhaps some music notation examples?
The better we understand, the better we can help.
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Slavicek
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Post by Slavicek » Wed Apr 26, 2017 7:21 am

Actually, the term irrational comes from Wikipedia, the article on time signatures. The reference they use is an interview with Brian Ferneyhough who himself mentiones irrational meters on his own website.

So yes, the basic idea is to have a number in the lower part of signature that isn't 1, 2, 4, 8, etc. In the case of polymeter (horizontal, not vertical), one may have one bar that is in normal 2/4 time, hence two quarter notes in it, and the bar that follows would be for instance 2/6, in which number 6 indicates the division of the whole note (full bar, sort to speak) into six equal parts, i.e. tuplet of six quarter notes, or two groups of quarter note triplets. In the case of 2/6 specifically, the bar would contain only two quarter note triplets all together.

When the tempo is steady, that means that the first bar with one normal two quarter notes would last longer than the next bar with two quarter note triplets. Let's take tempo in which one quarter note is 60 bpm; one half note lasts one second and the whole 2/4 bar two seconds. If the two-second bar is divided into three equal quarter tone triplets, that means that one triplet lasts 0.666 seconds, and two of them 1.333, which would be the case of 2/6 time.

The image that I found online: http://www.nicholasperryclark.com/uploa ... 3_orig.jpg

So, Peter, for 2/6 bar, you suggest me to make a bar which lasts 1.333 seconds approximately), write the two quarter tone triplets in it (I suppose I should hide the third one, for I'm not sure if I could only have two in the bar), and then use the Expression tool in which I would simply indicate the time signature at will and place is at the beginning of a bar?

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Post by Peter Thomsen » Wed Apr 26, 2017 7:44 am

Slavicek,

The “real” (not displaying) Finale time signature of a 2/6 measure would be
1/8 + 1/32 + 85/4096

It is as close to the exact value you can get.
The error is so small that it probably will not be audible.

And it works - put two triplet quarters in a such 2/6 measure, and playback will be correct.

I hope that this is clear?
If not, ask again.
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Slavicek
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Post by Slavicek » Wed Apr 26, 2017 9:23 pm

I'm afraid you lost me there a bit. How does 1/8 + 1/32 + 85/4096 equal two quarter note triplets? Eight note plus 32th note and 4096 note aren't even a single quarter note, or quarter note triplet for that matter.

Anyway, I created that bar and couldn't place the two quarter tones triplets. But okay, the point is that I calculate approximate time signature and fake the display, however, I'm not quite sure how to place triplets "partly" within a single bar. Generally speaking, if I wanted to write any triplets in Finale *at all*, I use Tuplet tool and it creates three notes within a triplet slur (to be more precise, one note and two rests which need to be filled, of course). So how could I place two of them only? It just won't let me do it. The triplet is division of a certain duration in a number of beats, so if I wanted triplets at all, I need to divide a bar or one part of that bar into three. I even tried making triplet in another "larger" bar and copy pasting just two notes in my bar, but it breaks them apart into some tiny durations such as 64th and so.

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motet
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Post by motet » Wed Apr 26, 2017 10:36 pm

I think Peter was off by a factor of 2.

4096 is the biggest denominator you can have. 2/6 ~= 1365/4096, but Finale won't let you have a numerator bigger than 100. So you have to set it to 1/4 + 1/16 + 85/4096, then enter a quarter-note triplet and then delete the last note. This slightly underfills the measure, but Finale doesn't fill with a rest, since it's too tiny. I've left the goofy time signature and triplet bracket and number for illustration, but you can deal with that.
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motet
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Post by motet » Wed Apr 26, 2017 10:55 pm

Here it is spruced up, with .musx file. Playback should be correct.
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motet
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Post by motet » Wed Apr 26, 2017 11:38 pm

But after all that, wouldn't it be much easier to simply make the 2/6 bar 2/4 underneath and change the playback speed at each time signature change as appropriate? Too bad Finale doesn't have relative playback speed (e.g. "increase the playback speed by 1/3").

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Post by ttw » Thu Apr 27, 2017 1:01 am

How does a sixth note in 3/6 time differ from a quarter note in 3/4 time? Perhaps I'd have to look at the score, but I'd guess I could notate most anything looking like 3/6 time (no, I don't like 3/6 time) in 3/8 or 3/4 or 3/2. While 6/8 isn't the same meter as 3/4, these can be used together (or alternately as in "I want to be in America" from West Side Story). The mathematical equivalence does allow one to notate the two identically and use beaming and slurring to indicate the actual grouping.

In a time signature, the bottom number is effectively a label, not an actual number. (It has properties of both.) The bottom number can be anything, a quarter note, an eighth note, a breve, a quaver, etc. A close approximation of Sqrt(2) is 41/29. A time signature of 29/8 may work just as well. Perhaps someone wanting to use Sqrt(2) and Sqrt(3) at the same time as time signatures could use and eighth note as the base, and just use enough notes to be accurate to 1% or .1% or whatever. This can always be done. Then just write the time signature in terms of eighth notes and use whatever is necessariy as the top line.

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motet
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Post by motet » Thu Apr 27, 2017 5:02 am

Read the thread carefully. Going from 2/4 to 2/6 is like a tempo change where the new quarter equals a quarter note of a triplet in the old bar.

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Post by peerlessnerd » Thu Apr 27, 2017 5:33 am

American composer Paul Creston (1906-1985) would take issue with the term “irrational” relative to meters like 3/6.

In 1961he called his 216 page textbook “Principals of Rhythm” an introduction. He quotes Paul Hindemith, “it seems impossible at the present time to include rhythm as an integral part of a system of teaching the craft of composition.”

Apparently that point of view hasn’t changed significantly, with the possible exception of Dorico.

Creston describes the intricacies of rhythm like no other composer before him, including the mathematical derivation of meters including X/5, X/12, X/20 and a myriad more. His concepts are not “irrational” in the slightest. More than a half century later, they remain generally misunderstood and overlooked.

It is high time Finale supported 3/6, 11/20, and more, without resorting to the treachery of creating an “expression” in place of a true meter signature.
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Peter Thomsen
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Post by Peter Thomsen » Thu Apr 27, 2017 7:35 am

motet wrote:… Too bad Finale doesn't have relative playback speed (e.g. "increase the playback speed by 1/3").
With the Tempo Tool you can create relative tempo changes in Finale - by using the Tempo Tool (in Finale 2014.5 or older versions).

I wonder whether you can use the MIDI Tool instead?

Or are relative tempo changes only possible with the now defunct Tempo Tool?
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oldmkvi
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Post by oldmkvi » Thu Apr 27, 2017 4:26 pm

Just because the Computer will play it doesn't mean that Musicians will be able to.
Some music is more like a Math Problem.
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motet
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Post by motet » Thu Apr 27, 2017 4:39 pm

I've never used the Tempo tool. If you make a relative change with the Tempo tool and then later change the overall tempo at the beginning of the piece, does the right thing happen? That's really what would be useful.

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Peter Thomsen
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Post by Peter Thomsen » Thu Apr 27, 2017 8:46 pm

motet wrote:… If you make a relative change with the Tempo Tool, and then later change the overall tempo at the beginning of the piece, does the right thing happen? …
Yes - provided that no initial tempo has been set.

You can use the Tempo Tool to set a relative value, e. g. 150 %.

PS
Make sure that Human Playback does not interfere with this.
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Slavicek
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Post by Slavicek » Sat Apr 29, 2017 1:03 am

motet - Thank you for the .mus examples, the triplets work now. I entered them by writing them in the "normal" 4/4 bar first and then simply copy pasted them into the "irrational" bar. One was out, two of them remained. It is a workaround, as Peter said, but I guess it's better than nothing. Pity I need to use the Expression tool, but that's life. As long as it's possible, I'm happy.

peerlessnerd - Among other things, yes, Finale should incorporate updated time signature possibilities, just as it should work on quarter note accidentals (even some old versions of Sibelius had it much easier accessible), instead of reaching up for tricks. But I guess extended technique players and contemporary classical composers isn't what makes Finale's majority of customers.

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Post by peerlessnerd » Sat Apr 29, 2017 5:56 am

It took 17 posts (excluding mine) from some of the brightest Finale minds on the planet for you to arrive at a satisfactory fake workaround. I am glad to know it is at least possible.

In the world of Paul Creston your example is a notational and playback non-issue.

It is true what your are attempting places you outside the majority of Finale customers, but after 26 years Finale, somebody is now attempting to do it.

Hindemith and Creston were correct more than 70 years ago that the principles of rhythm are not yet on equal footing with the other elements of composition.

Many consider the six volumes of Bartok- Mikrokosmos to be groundbreaking. I submit only that when the world is ready, the ten volumes of Creston- Rhythmicon are waiting for discovery by the masses, as well as his books Principles of Rhythm, and Rational Notation, the two volumes of Virtuoso Piano Technique, plus the remainder of his compositions.

It took Felix Mendelssohn and 75 years for the world to “discover” the music of J.S. Bach. Perhaps we are nearly ready for the discovery of Paul Creston, who every morning before beginning his day of composing analyzed a Bach chorale as inspiration.
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