Re: irrational meters

[H. S. Teoh]

On Wed, Jan 18, 2023 at 07:27:47PM -0500, David Zelinsky wrote:
> Silvain Dupertuis  writes:
> 
> > It is better not to confuse a /fraction/ (as an expression) and it's
> > /value/ (as a /number/) ­­— a number cannot have a numerator or a
> > denominator!
> 
> Well, a *rational* number does have a well-defined denominator:
> Because of unique factorization of the integers, there is a unique
> representation of a rational number as n/d where n and d are integers
> with no common factor and d is positive.

True, but time signatures do not have a 1-to-1 correspondence with
rational numbers: 6/8 and 3/4 are distinct as time signatures, even
though as fractions they signify the same rational number.


> Now if we wanted to think about time signatures N/D where N and D are
> elements of, say the integers with the square root of -5 adjoined,
> that's another matter.  Any takers, you composers out there?  :)
[...]

Adjoining square roots of some positive number may still be somewhat
imaginable, e.g., √5/4 means each measure consists of √5 (approximately
2.236...) quarter notes. Hard to perform precisely without computer
help, but still possible in theory.  But how is one to interpret √(-5)/4
??  How do you count up to an imaginary number of beats per bar, even in
theory?

//

Further thoughts about √5/4 as a time signature: due to the peculiarity
of standard musical notation, which only has symbols for note values
that are rational subdivisions of a whole note (and even that, not all
rational subdivisions are directly representable), any combination of
notes in a √5/4 bar will not fit exactly within the bar, √5 being
irrational. (This also applies to any other irrational fraction you may
choose for the top component of the time signature.) So that means the
last quarter note beat will be split across the bar line by some
irrational fraction, with the remaining duration overflowing into the
following bar.

Note that changing the notation may not help anything. Suppose we
introduce new notation for representing irrational note values. Then
either the new note values are commensurate with the (irrational) time
signature, or they're not.  If they are, then we've effectively reduced
the time signature to a traditional, rational signature: if we introduce
a note value of √5/6, for example, then 6 such notes would add up to 1
bar in a √5/4 signature, so we've effectively turned it into 6/4 and
it's no longer an irrational time signature. If the new note values are
not commensurate with the time signature, then we will still have notes
split across barlines even if we use the new note values, so nothing has
really changed.

Now if you have a long series of consecutive quarter notes, they will
span some number of bars, and every bar line will split a quarter note
in some unique, irrational fraction -- due to irrationality, no bar line
will fall exactly at the start/end of a quarter note, so excepting the
start of the first bar, everywhere else there will be notes split across
the barline. And each split note will be split in a unique, irrational
fraction.  If we individually move each barline so that it falls on the
closest start/end of a quarter note, then we end up with a series of
bars with regular (rational) time signatures, but with time signature
changes in an irregular pattern -- this is what I referred to in an
earlier post.  So, "rationalizing" an irrational time signature in this
way, we see the irrational number essentially serves as a source of
irregular bar lengths that never repeats.


T

-- 
The two rules of success: 1. Don't tell everything you know. -- YHL

Re: irrational meters

[Damian leGassick]

I’d just like to say that I really appreciate that Lilypond handles these so 
effortlessly, whatever they’re called.

I do wonder whether ‘irrational’ wasn’t originally perjorative.

Damian

Re: irrational meters

[Karim Haddad]

Thank you Valentin,

In fact i am now using the solution #1 which gives correct time settings. By 
the way i am using this in a "poly-metric" and "poly-tempic" context, and i 
must say it works good. Only possible in Lilypond. Thank you to all developpers 
and expert users for all your work and advice.

I am sorry i have unleashed an off topic disscussion, however, i appreciate all 
your remarks which testify of your passion to music, music theory and 
typesetting.

Take care all of you.

Best
K

On Wed, Jan 18, 2023 at 02:22:58PM +0100, Valentin Petzel wrote:
> Hi Karim,
> 
> 2) does not work as #'(ly:make-moment 16/25) is a symbol rather than 
> #(ly:make-moment 
> 16/25). Also (2) still needs \scaleDurations 4/5, unless you do
> 
> \time 4/5
> \set Timing.measureLength = #(ly:make-moment 4/4)
> 
> The idea behind the part
> 
> https://lilypond.org/doc/v2.24/Documentation/snippets/rhythms#rhythms-changing-time-signatures-inside-a-polymetric-section-using-_005cscaledurations[1]
> 
> in the documention is to change TimeSignature while having a scaled Duration, 
> so you 
> want to have an e.g. 4/4 time sig, but the Staff should be scaled by 4/5, so 
> you want the 
> measure length of a 4/5 timesig, thus you do 4/4 and manualy tell Lilypond 
> that you 
> actually want a length of 4/5.
> 
> If you want to use something like 4/5 this is not of relevance to you. As I 
> said you could 
> change measure length to 4/4 and notate everything as if it were 4/4 though.
> 
> Cheers,
> Valentin
> 
> Am Dienstag, 17. Jänner 2023, 12:16:43 CET schrieb Karim Haddad:
> > Hi,
> > 
> > I am wondering which is the best way to write irrational meters (with tempo
> > modulations)
> > 
> > 1)
> > %
> 
> > \version "2.24.0"
> > \score {
> > {
> > 
> > \clef "G"
> > 
> > \scaleDurations 4/5 {
> > \time 4/5
> > \set Staff.timeSignatureFraction = #'(4 . 5)
> > \mark \markup {\left-column {{\line { \smaller \general-align #Y #DOWN 
> > \note {4} #1 " = 60 "}} \tiny "1"}} c'4
> > c'4
> > c'4
> > c'4
> > 
> > }
> > \once \set Staff.whichBar = "|"
> > }
> > 
> > 
> > \layout {
> > 
> > \context {\Score
> >  %measureBarType=#""
> >   }
> > 
> > }
> > }
> > %
> 
> > 
> > or
> > 
> > 2)
> > 
> > %
> 
> > \version "2.24.0"
> > \score {
> > {
> > \clef "G"
> > 
> > \time 4/5
> > \set Staff.timeSignatureFraction = #'(4 . 5)
> > \set Timing.measureLength = #'(ly:make-moment 16/25)
> > \mark \markup {\left-column {{\line { \smaller \general-align #Y #DOWN 
> > \note {4} #1 " = 60 "}} \tiny "1"}} c'4
> > c'4
> > c'4
> > c'4
> > 
> > \once \set Staff.whichBar = "|"
> > }
> > 
> > \layout {
> > 
> > \context {\Score
> >  measureBarType=#""
> >   }
> > 
> > }
> > }
> > %
> 
> > 
> > 
> > Now the first solution outputs:
> > 
> > Processing `irr1.ly'
> > Parsing...
> > Interpreting music...
> > irr1.ly:13:1: warning: strange time signature found: 4/5
> > 
> > \time 4/5
> > Preprocessing graphical objects...
> > 
> > 
> > Which looks good to me as a warning
> > 



-- 
Karim Haddad

Music Representations Team, IRCAM
Research and development manager.
email   : karim.had...@ircam.fr
webpage : http://karim.haddad.free.fr

Re: irrational meters

[Karim Haddad]

Thank you again Leo,

This comes very handy.

BEst
K


On Wed, Jan 18, 2023 at 11:14:39AM +0100, Leo Correia de Verdier wrote:
> If the warnings bother you you could use a function to suppress them, like:
> 
> irrtime = #(define-music-function (frac) (pair?) 
>  #{ #(ly:expect-warning "strange time signature found") 
> \time #frac #} )
> 
> \score { 
>   \relative c' {
> \irrtime 4/5
> \tuplet 5/4 1 {
>   c4 d e f |
>   g a2 g4 | 
>   f2 g |
>   e4 f e d |
>   c1 | }
> }}
> 
> Or  something more elegantly coded…
> 
> And everyone else: Can we talk about breve? It is nowadays usually one of the 
> longest durations. I think we should change its name!  (or possibly keep on 
> topic)
> 
> Best wishes
> /Leo
> 
> > 17 jan. 2023 kl. 16:13 skrev Karim Haddad :
> > 
> > Thank you a lot Leo for your advice.
> > I'll hence stick with solution #1 which looks preferable.
> > 
> > @all
> > Now about "irrational meter" (or "irrational" rhythms), well this 
> > denomination is from the fifties. I am aware that mathematically this is 
> > not correct since it is a fraction.However, "irregular" is somehow more 
> > vague and doesn't relate to anything in particular. Thanks to Hans' link 
> > that shows that it is a somehow a common terminology in music practice. 
> > 
> > Best to all of you, and thank you for all your comments.
> > 
> > Karim
> > 
> > 
> > 
> > On Tue, Jan 17, 2023 at 01:30:49PM +0100, Leo Correia de Verdier wrote:
> >> Hi Karim!
> >> 
> >> Your first example seems to work to me (I don’t do irrational meters 
> >> everyday, so there might be something I’m missing. I would probably write 
> >> the tuplets explicitly rather than use \scaleDurations). 
> >> \set Staff.timeSignatureFraction is superfluous, the time signature 
> >> already does that.
> >> 
> >> I’m not sure what you’re aiming at with the second example. One source of 
> >> error is that you have quoted ly:make-moment, and it wants its arguments 
> >> as elements of a list, not as a fraction, so: 
> >> #(ly:make-moment 16 25)
> >> , not
> >> #'(ly:make-moment 16/25)
> >> But it is still not the right amount of notes in the bar.
> >> 
> >> HTH
> >> /Leo
> >> 
> >>> 17 jan. 2023 kl. 12:16 skrev Karim Haddad :
> >>> 
> >>> Hi,
> >>> 
> >>> I am wondering which is the best way to write irrational meters (with 
> >>> tempo modulations)
> >>> 
> >>> 1)
> >>> %
> >>> \version "2.24.0"
> >>> \score {
> >>> {
> >>> 
> >>> \clef "G"
> >>> 
> >>> \scaleDurations 4/5 {
> >>> \time 4/5
> >>> \set Staff.timeSignatureFraction = #'(4 . 5)
> >>> \mark \markup {\left-column {{\line { \smaller \general-align #Y #DOWN  
> >>> \note {4} #1 " = 60 "}} \tiny "1"}}
> >>> c'4
> >>> c'4
> >>> c'4
> >>> c'4
> >>> |
> >>> }
> >>> \once \set Staff.whichBar = "|"
> >>> }
> >>> 
> >>> 
> >>> \layout {
> >>> 
> >>> \context {\Score
> >>>%measureBarType=#""
> >>> }
> >>> 
> >>> }
> >>> }
> >>> %
> >>> 
> >>> or
> >>> 
> >>> 2)
> >>> 
> >>> %
> >>> \version "2.24.0"
> >>> \score {
> >>> {
> >>> \clef "G"
> >>> 
> >>> \time 4/5
> >>> \set Staff.timeSignatureFraction = #'(4 . 5)
> >>> \set Timing.measureLength = #'(ly:make-moment 16/25)
> >>> \mark \markup {\left-column {{\line { \smaller \general-align #Y #DOWN  
> >>> \note {4} #1 " = 60 "}} \tiny "1"}}
> >>> c'4
> >>> c'4
> >>> c'4
> >>> c'4
> >>> |
> >>> \once \set Staff.whichBar = "|"
> >>> }
> >>> 
> >>> \layout {
> >>> 
> >>> \context {\Score
> >>>measureBarType=#&

Re: irrational meters

[Valentin Petzel]

Hello Silvain,

this is only true if you define a "rational meter" to be a meter which 
evaluates to a rational number. Note that a Time Signature is NOT a rational 
number, else 3/4 and 6/8 would be equivalent.

And similarly to how a rational argument is not an argument that corresponds 
to a rational number a rational Time Signature can have a different meaning to 
a rational Number.

Of course this does leave the question open of what exactly *is* a rational 
Time Signature. And would it even make sense to use a Time Signature that is 
not rational?

Valentin

Am Dienstag, 17. Jänner 2023, 15:20:29 CET schrieb Silvain Dupertuis:
> I wonder about the term “irrational” meter. Should not we say “irregular” ??
> as in mathematics, an irrational number is a number which cannot be
> represented as a fraction...
> 
> Le 17.01.23 à 13:30, Leo Correia de Verdier a écrit :
> > Hi Karim!
> > 
> > Your first example seems to work to me (I don’t do irrational meters
> > everyday, so there might be something I’m missing. I would probably write
> > the tuplets explicitly rather than use \scaleDurations). \set
> > Staff.timeSignatureFraction is superfluous, the time signature already
> > does that.



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Re: irrational meters

[Flaming Hakama by Elaine]

> -- Forwarded message --
> From: Silvain Dupertuis 
> To: lilypond-user@gnu.org
> Cc:
> Bcc:
> Date: Wed, 18 Jan 2023 19:20:35 +0100
> Subject: Re: irrational meters
>
> To make things clear, a *fraction* is a mathematical expression which is
> a *specific representation* of a number (or of a formal expression),
> comprising a numerator, a denominator, and one kind of division sign (which
> can be written in different ways, as there are different ways to write the
> operator).
>
> A *ratio* of two numbers is a number resulting from the division of those
> two. It can therefore very naturally expressed as a fraction.
>
> So I have no problem considering a musical metric as a fraction!
>
> It is better not to confuse a *fraction* (as an expression) and it's
> *value* (as a *number*) ­­— a number cannot have a numerator or a
> denominator!
>
> But whenever we write a fraction in a mathematical expression, it is the
> *value* which is implied, not the fraction itself.
>
> So we do confuse them very commonly, like we commonly confuse a word and
> it's meaning in common language (and we survive quite well with this
> confusion).
>
> In case we need to avoid these confusions, one can use quotation marks...
> It can be useful or essential when teaching mathematics or when working in
> mathematical logic or in linguistics.
>
> Hope this clarify the matter.
>
> Silvain
>
>
>
> Le 18.01.23 à 18:51, Shane Brandes a écrit :
>
> Because terminology amuses me here. Years ago, I learned that time
> signatures were decidedly not fractions but ratios from a one Richard
> Hoffman. But even before that I learned ratios consisted of antecedents and
> consequents, which also seems to overlap musical structural terminology in
> a weird way making that also fairly useless as a nomenclature.
>
> Shane
>
>
> --
> Silvain Dupertuis
>

Thanks, that was a wonderful discourse.

It made me wonder about the caution to not mix up the fractional
representation with the number it evaluates to.

Made me wonder, what does the value represent?

I guess it is obvious once you think about it, but it represents the number
of whole notes in the bar.

So, 4/4, 2/2, 1/1, and 8/8 all have a value of 1 and represent a whole note
in total duration.

Also makes me wonder:  do we have a word for time signatures that have
duration other than a whole note?

In this sense, evaluating the duration of non-dyadic signatures is just as
transparent as those that are not a whole note in duration.

For example, understanding the length of 3/4 is straightforward, and
evaluating the length of 6/8 and 4/6 are about the same, since you have to
reduce the fraction to 3/4 or 2/3.

However, from a philosophical perspective, I have a difficult time thinking
of the time signature itself as a fraction.  I feel like it is rather the
combination of a multiplier and a fraction.

The bottom number tells you what note gets the beat, which we represent as
fractions of a whole note, with an implied numerator of 1.  Then the top
number tells you how many beats are in the bar.

Combining a multiplier with a fraction of course yields another fraction.

But the meaning of the resulting fraction is not as obvious, or I guess is
not typically directly musically relevant.  So musically, I don't think we
tend to think of time signatures as fractions.

In fact, even the fractional part of this, which is baked into the concept
of which note type gets the beat, I would argue, is not typically
experienced as a fraction.  In fact, it seems like what time signatures are
doing is more integer-ization of a fraction:  it says that this thing that
was previously defined as a fraction, that thing should now be considered 1
unit beat.  (Ignoring compound time conventions).

So, I guess I come to the conclusion that the only reason we think of the
time signature as a fraction is because we define our note values as
fractions of a whole note.


Elaine Alt
415 . 341 .4954   "*Confusion is
highly underrated*"
ela...@flaminghakama.com
Producer ~ Composer ~ Instrumentalist ~ Educator
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

Re: irrational meters

[David Zelinsky]

Silvain Dupertuis  writes:

> It is better not to confuse a /fraction/ (as an expression) and it's
> /value/ (as a /number/) ­­— a number cannot have a numerator or a
> denominator!

Well, a *rational* number does have a well-defined denominator: Because
of unique factorization of the integers, there is a unique
representation of a rational number as n/d where n and d are integers
with no common factor and d is positive.  Now if we wanted to think
about time signatures N/D where N and D are elements of, say the
integers with the square root of -5 adjoined, that's another matter.
Any takers, you composers out there?  :)

-David

Re: irrational meters

[Silvain Dupertuis]

To make things clear, a /fraction/ is a mathematical expression which is a /specific 
representation/ of a number (or of a formal expression), comprising a numerator, a 
denominator, and one kind of division sign (which can be written in different ways, as 
there are different ways to write the operator).


A /ratio/ of two numbers is a number resulting from the division of those two. It can 
therefore very naturally expressed as a fraction.


So I have no problem considering a musical metric as a fraction!

It is better not to confuse a /fraction/ (as an expression) and it's /value/ (as a 
/number/) ­­— a number cannot have a numerator or a denominator!


But whenever we write a fraction in a mathematical expression, it is the /value/ which is 
implied, not the fraction itself.


So we do confuse them very commonly, like we commonly confuse a word and it's meaning in 
common language (and we survive quite well with this confusion).


In case we need to avoid these confusions, one can use quotation marks... It can be useful 
or essential when teaching mathematics or when working in mathematical logic or in 
linguistics.


Hope this clarify the matter.

Silvain




Le 18.01.23 à 18:51, Shane Brandes a écrit :
Because terminology amuses me here. Years ago, I learned that time signatures were 
decidedly not fractions but ratios from a one Richard Hoffman. But even before that I 
learned ratios consisted of antecedents and consequents, which also seems to overlap 
musical structural terminology in a weird way making that also fairly useless as a 
nomenclature.


Shane



--
Silvain Dupertuis
Route de Lausanne 335
1293 Bellevue (Switzerland)
tél. +41-(0)22-774.20.67
portable +41-(0)79-604.87.52
web: silvain-dupertuis.org 

Re: irrational meters

[Shane Brandes]

Because terminology amuses me here. Years ago, I learned that time
signatures were decidedly not fractions but ratios from a one Richard
Hoffman. But even before that I learned ratios consisted of antecedents and
consequents, which also seems to overlap musical structural terminology in
a weird way making that also fairly useless as a nomenclature.

Shane

On Wed, Jan 18, 2023 at 9:38 AM David Wright 
wrote:

> On Wed 18 Jan 2023 at 08:22:19 (+), Mark Knoop wrote:
> > At 16:46 on 17 Jan 2023, "H. S. Teoh" via LilyPond user discussion wrote:
> > > On Tue, Jan 17, 2023 at 07:08:41PM -0500, David Zelinsky wrote:
> > >> Kieren MacMillan  writes:
> > >>>
> >  I wonder about the term “irrational” meter. Should not we say
> >  “irregular” ??  as in mathematics, an irrational number is a number
> >  which cannot be represented as a fraction...
> > >>>
> > >>> As both a published composer *and* a published number theorist, I
> > >>> wholeheartedly concur with your intuition — I’ve been pushing for
> > >>> decades against “irrational” as a descriptor for time signatures
> > >>> [except where it actually applies, of course, as in π/4].
> > >>>
> > >>> “Irregular” is better… but ultimately I prefer “non-dyadic” to
> > >>> describe any time signature where the bottom number (a.k.a.
> > >>> “denominator”, a label I also avoid) is not an integer power of 2.
> > > [...]
> > >> As another professional number theorist and musician (though not a
> > >> composer), I also find this use of "irrational" to mean "non-dyadic"
> > >> very grating.  But I once said as much on the Music Engraving Tips
> > >> facebook group, and got summarily shot down as ignorant and elitist.
> > >> The argument, such as it was, held that this is about *music*, not
> > >> *mathematics*, so there's no reason to adopt mathematicians' quirky
> > >> terminology.  This left me rather speechless, so I gave up.  However,
> > >> if I ever have reason to discuss this type of meter, will always call
> > >> it "non-dyadic".
> > > [...]
> >
> > > This is off-topic, but it would be interesting if somebody composed a
> > > piece with an actually irrational meter, like π/4 or 3/π.  Only thing
> > > is, it would be impossible for human performers to play correctly,
> since
> > > there isn't any way to count the beats correctly (counting beats
> implies
> > > a rational fraction, since by definition it's impossible to count up to
> > > an irrational ratio by counting finite parts).
> >
> > Perhaps one should define "correctly" before assuming impossibility. By
> > any definition of correctly which makes sense in this context (i.e.
> > precise rhythmic execution), it is arguably equally impossible to play
> > music in a *dyadic* meter correctly.
>
> I understood TSH's "correctly" to mean "precisely", and I would say
> that by convention, one is not expected to play music in a dyadic
> meter with precision. For example, most people are familiar with the
> Viennese Waltz and its anticipated second beat, or the ebb and flow of
> most solo piano music, and so on.
>
> OTOH specifying a (mathematically) irrational meter implies a
> precision that I would agree is virtually impossible to perform
> without artificial aids like computer synthesis.
>
> Cheers,
> David.
>

Re: irrational meters

[David Wright]

On Wed 18 Jan 2023 at 08:22:19 (+), Mark Knoop wrote:
> At 16:46 on 17 Jan 2023, "H. S. Teoh" via LilyPond user discussion wrote:
> > On Tue, Jan 17, 2023 at 07:08:41PM -0500, David Zelinsky wrote:
> >> Kieren MacMillan  writes:
> >>>
>  I wonder about the term “irrational” meter. Should not we say
>  “irregular” ??  as in mathematics, an irrational number is a number
>  which cannot be represented as a fraction...
> >>>
> >>> As both a published composer *and* a published number theorist, I
> >>> wholeheartedly concur with your intuition — I’ve been pushing for
> >>> decades against “irrational” as a descriptor for time signatures
> >>> [except where it actually applies, of course, as in π/4].
> >>>
> >>> “Irregular” is better… but ultimately I prefer “non-dyadic” to
> >>> describe any time signature where the bottom number (a.k.a.
> >>> “denominator”, a label I also avoid) is not an integer power of 2.
> > [...]
> >> As another professional number theorist and musician (though not a
> >> composer), I also find this use of "irrational" to mean "non-dyadic"
> >> very grating.  But I once said as much on the Music Engraving Tips
> >> facebook group, and got summarily shot down as ignorant and elitist.
> >> The argument, such as it was, held that this is about *music*, not
> >> *mathematics*, so there's no reason to adopt mathematicians' quirky
> >> terminology.  This left me rather speechless, so I gave up.  However,
> >> if I ever have reason to discuss this type of meter, will always call
> >> it "non-dyadic".
> > [...]
> 
> > This is off-topic, but it would be interesting if somebody composed a
> > piece with an actually irrational meter, like π/4 or 3/π.  Only thing
> > is, it would be impossible for human performers to play correctly, since
> > there isn't any way to count the beats correctly (counting beats implies
> > a rational fraction, since by definition it's impossible to count up to
> > an irrational ratio by counting finite parts).
> 
> Perhaps one should define "correctly" before assuming impossibility. By
> any definition of correctly which makes sense in this context (i.e.
> precise rhythmic execution), it is arguably equally impossible to play
> music in a *dyadic* meter correctly.

I understood TSH's "correctly" to mean "precisely", and I would say
that by convention, one is not expected to play music in a dyadic
meter with precision. For example, most people are familiar with the
Viennese Waltz and its anticipated second beat, or the ebb and flow of
most solo piano music, and so on.

OTOH specifying a (mathematically) irrational meter implies a
precision that I would agree is virtually impossible to perform
without artificial aids like computer synthesis.

Cheers,
David.

Re: irrational meters

[Hans Åberg]

> On 18 Jan 2023, at 01:46, H. S. Teoh via LilyPond user discussion 
>  wrote:
> 
> … it would be interesting if somebody composed a
> piece with an actually irrational meter, like π/4 or 3/π.  

I gave an example [1] where the numerator is an irrational number, 8+2√5.

If one wants to typeset them in LilyPond, one can apply continued fraction 
convergents to a suitable degree of accuracy.

> Only thing
> is, it would be impossible for human performers to play correctly, since
> there isn't any way to count the beats correctly (counting beats implies
> a rational fraction, since by definition it's impossible to count up to
> an irrational ratio by counting finite parts).

The example [1] is based on a popular Macedonian meter 12=3+2+2+3+2 [2], which 
in performance has heavy metric time bends [3].

A musical motivation writing such a meter might be to make performers to avoid 
trying to play an exact 3+2+2+3+2.


1. https://lists.gnu.org/archive/html/lilypond-user/2014-06/msg00237.htm
2. https://en.wikipedia.org/wiki/Leventikos
3. https://www.youtube.com/watch?v=vYR_pvRWO_g

Re: irrational meters

[David Kastrup]

Valentin Petzel  writes:

> Hi Karim,
>
> 2) does not work as #'(ly:make-moment 16/25) is a symbol rather than

It isn't a symbol but a list consisting of the elements ly:make-moment
(a symbol) and the rational number 16/25 .

-- 
David Kastrup

Re: irrational meters

[Valentin Petzel]

Hi Karim,

2) does not work as #'(ly:make-moment 16/25) is a symbol rather than 
#(ly:make-moment 
16/25). Also (2) still needs \scaleDurations 4/5, unless you do

\time 4/5
\set Timing.measureLength = #(ly:make-moment 4/4)

The idea behind the part

https://lilypond.org/doc/v2.24/Documentation/snippets/rhythms#rhythms-changing-time-signatures-inside-a-polymetric-section-using-_005cscaledurations[1]

in the documention is to change TimeSignature while having a scaled Duration, 
so you 
want to have an e.g. 4/4 time sig, but the Staff should be scaled by 4/5, so 
you want the 
measure length of a 4/5 timesig, thus you do 4/4 and manualy tell Lilypond that 
you 
actually want a length of 4/5.

If you want to use something like 4/5 this is not of relevance to you. As I 
said you could 
change measure length to 4/4 and notate everything as if it were 4/4 though.

Cheers,
Valentin

Am Dienstag, 17. Jänner 2023, 12:16:43 CET schrieb Karim Haddad:
> Hi,
> 
> I am wondering which is the best way to write irrational meters (with tempo
> modulations)
> 
> 1)
> %

> \version "2.24.0"
> \score {
> {
> 
> \clef "G"
> 
> \scaleDurations 4/5 {
> \time 4/5
> \set Staff.timeSignatureFraction = #'(4 . 5)
> \mark \markup {\left-column {{\line { \smaller \general-align #Y #DOWN 
> \note {4} #1 " = 60 "}} \tiny "1"}} c'4
> c'4
> c'4
> c'4
> 
> }
> \once \set Staff.whichBar = "|"
> }
> 
> 
> \layout {
> 
> \context {\Score
>  %measureBarType=#""
>   }
> 
> }
> }
> %

> 
> or
> 
> 2)
> 
> %

> \version "2.24.0"
> \score {
> {
> \clef "G"
> 
> \time 4/5
> \set Staff.timeSignatureFraction = #'(4 . 5)
> \set Timing.measureLength = #'(ly:make-moment 16/25)
> \mark \markup {\left-column {{\line { \smaller \general-align #Y #DOWN 
> \note {4} #1 " = 60 "}} \tiny "1"}} c'4
> c'4
> c'4
> c'4
> 
> \once \set Staff.whichBar = "|"
> }
> 
> \layout {
> 
> \context {\Score
>  measureBarType=#""
> }
> 
> }
> }
> %

> 
> 
> Now the first solution outputs:
> 
> Processing `irr1.ly'
> Parsing...
> Interpreting music...
> irr1.ly:13:1: warning: strange time signature found: 4/5
> 
> \time 4/5
> Preprocessing graphical objects...
> 
> 
> Which looks good to me as a warning
> 

signature.asc
Description: This is a digitally signed message part.

Re: irrational meters

[Aaron Hill]

On 2023-01-18 1:23 am, Paul Hodges wrote:
As for alternatives, I suppose dyadic will do; but irregular is 
certainly wrong - there is no reason for an irrational tempo to be 
irregular, in fact, anything that can be expressed as a time signature 
is being given a regular definition.


Church hymnary already uses the term "irregular meter" to describe hymns 
that have no consistent metrical structure.  ("Peculiar meter" is also 
used.)  Though to be clear, there one is talking about the poetry and 
verse as opposed to musical structures such as measures.  However, as 
there is a practical connection between texts and tunes, it might be 
best to avoid confusion with overloaded terms that span the topics.



-- Aaron Hill

Re: irrational meters

[Leo Correia de Verdier]

If the warnings bother you you could use a function to suppress them, like:

irrtime = #(define-music-function (frac) (pair?) 
 #{ #(ly:expect-warning "strange time signature found") 
\time #frac #} )

\score { 
  \relative c' {
\irrtime 4/5
\tuplet 5/4 1 {
  c4 d e f |
  g a2 g4 | 
  f2 g |
  e4 f e d |
  c1 | }
}}

Or  something more elegantly coded…

And everyone else: Can we talk about breve? It is nowadays usually one of the 
longest durations. I think we should change its name!  (or possibly keep on 
topic)

Best wishes
/Leo

> 17 jan. 2023 kl. 16:13 skrev Karim Haddad :
> 
> Thank you a lot Leo for your advice.
> I'll hence stick with solution #1 which looks preferable.
> 
> @all
> Now about "irrational meter" (or "irrational" rhythms), well this 
> denomination is from the fifties. I am aware that mathematically this is not 
> correct since it is a fraction.However, "irregular" is somehow more vague and 
> doesn't relate to anything in particular. Thanks to Hans' link that shows 
> that it is a somehow a common terminology in music practice. 
> 
> Best to all of you, and thank you for all your comments.
> 
> Karim
> 
> 
> 
> On Tue, Jan 17, 2023 at 01:30:49PM +0100, Leo Correia de Verdier wrote:
>> Hi Karim!
>> 
>> Your first example seems to work to me (I don’t do irrational meters 
>> everyday, so there might be something I’m missing. I would probably write 
>> the tuplets explicitly rather than use \scaleDurations). 
>> \set Staff.timeSignatureFraction is superfluous, the time signature already 
>> does that.
>> 
>> I’m not sure what you’re aiming at with the second example. One source of 
>> error is that you have quoted ly:make-moment, and it wants its arguments as 
>> elements of a list, not as a fraction, so: 
>> #(ly:make-moment 16 25)
>> , not
>> #'(ly:make-moment 16/25)
>> But it is still not the right amount of notes in the bar.
>> 
>> HTH
>> /Leo
>> 
>>> 17 jan. 2023 kl. 12:16 skrev Karim Haddad :
>>> 
>>> Hi,
>>> 
>>> I am wondering which is the best way to write irrational meters (with tempo 
>>> modulations)
>>> 
>>> 1)
>>> %
>>> \version "2.24.0"
>>> \score {
>>> {
>>> 
>>> \clef "G"
>>> 
>>> \scaleDurations 4/5 {
>>> \time 4/5
>>> \set Staff.timeSignatureFraction = #'(4 . 5)
>>> \mark \markup {\left-column {{\line { \smaller \general-align #Y #DOWN  
>>> \note {4} #1 " = 60 "}} \tiny "1"}}
>>> c'4
>>> c'4
>>> c'4
>>> c'4
>>> |
>>> }
>>> \once \set Staff.whichBar = "|"
>>> }
>>> 
>>> 
>>> \layout {
>>> 
>>> \context {\Score
>>>%measureBarType=#""
>>> }
>>> 
>>> }
>>> }
>>> %
>>> 
>>> or
>>> 
>>> 2)
>>> 
>>> %
>>> \version "2.24.0"
>>> \score {
>>> {
>>> \clef "G"
>>> 
>>> \time 4/5
>>> \set Staff.timeSignatureFraction = #'(4 . 5)
>>> \set Timing.measureLength = #'(ly:make-moment 16/25)
>>> \mark \markup {\left-column {{\line { \smaller \general-align #Y #DOWN  
>>> \note {4} #1 " = 60 "}} \tiny "1"}}
>>> c'4
>>> c'4
>>> c'4
>>> c'4
>>> |
>>> \once \set Staff.whichBar = "|"
>>> }
>>> 
>>> \layout {
>>> 
>>> \context {\Score
>>>measureBarType=#""
>>>   }
>>> 
>>> }
>>> }
>>> %
>>> 
>>> 
>>> Now the first solution outputs:
>>> 
>>> Processing `irr1.ly'
>>> Parsing...
>>> Interpreting music...
>>> irr1.ly:13:1: warning: strange time signature found: 4/5
>>> 
>>> \time 4/5
>>> Preprocessing graphical objects...
>>> 
>>> 
>>> Which looks good to me as a warning
>>> 
>>> However, the second solution gives:
>>> 
>>> Processing `irr2.ly'
>>> Parsing...
>>> Interpreting music...
>>> warning: type check for `measureLength' failed; value `(ly:make-moment 
>>> 16/25)' must be of type `moment'
>>> irr2.ly:12:1: warning: strange time signature found: 4/5
>>> 
>>> \time 4/5
>>> irr2.ly:20:1: warning: barcheck failed at: 1/5
>>> 
>>> |
>>> Preprocessing graphical objects...
>>> 
>>> 
>>> And if we comment measureBarType=#"" we will have a strange bar at the end.
>>> 
>>> 
>>> Best Regards
>>> 
>>> 
>>> -- 
>>> Karim Haddad
>>> 
>>> Music Representations Team, IRCAM
>>> Research and development manager.
>>> 
>>> 
>> 
> 
> -- 
> Karim Haddad
> 
> Music Representations Team, IRCAM
> Research and development manager.
> 

Re: irrational meters

[Paul Hodges]

From:   Mark Knoop  
 To:   H. S. Teoh  
 Cc:
 Sent:   18/01/2023 8:22 
 Subject:   Re: irrational meters 

Perhaps one should define "correctly" before assuming impossibility. By 
any definition of correctly which makes sense in this context (i.e. 
precise rhythmic execution), it is arguably equally impossible to play 
music in a *dyadic* meter correctly. 
 
 
Agreed.  In any case the impossibility assumes that a numeric tempo has been 
assigned using a rational note-value as base.  Also, it's only really an issue 
if the numerator of the signature is irrational, not the denominator.


As for alternatives, I suppose dyadic will do; but irregular is certainly wrong 
- there is no reason for an irrational tempo to be irregular, in fact, anything 
that can be expressed as a time signature is being given a regular definition.


Finally, if we're appealing to ancient meanings and etymology, consider the use 
of irrational in Greek and Latin prosody to mean the use of quantities which 
are not correctly part of the metre - I think that would transfer nicely to the 
musical use.


Anyway, I'm more exercised by people who talk about their weight when they mean 
their mass!


Paul

Re: irrational meters

[Mark Knoop]

At 16:46 on 17 Jan 2023, "H. S. Teoh" via LilyPond user discussion wrote:
> On Tue, Jan 17, 2023 at 07:08:41PM -0500, David Zelinsky wrote:
>> Kieren MacMillan  writes:
>>
>>> Hi Silvain,
>>>
 I wonder about the term “irrational” meter. Should not we say
 “irregular” ??  as in mathematics, an irrational number is a number
 which cannot be represented as a fraction...
>>>
>>> As both a published composer *and* a published number theorist, I
>>> wholeheartedly concur with your intuition — I’ve been pushing for
>>> decades against “irrational” as a descriptor for time signatures
>>> [except where it actually applies, of course, as in π/4].
>>>
>>> “Irregular” is better… but ultimately I prefer “non-dyadic” to
>>> describe any time signature where the bottom number (a.k.a.
>>> “denominator”, a label I also avoid) is not an integer power of 2.
> [...]
>> As another professional number theorist and musician (though not a
>> composer), I also find this use of "irrational" to mean "non-dyadic"
>> very grating.  But I once said as much on the Music Engraving Tips
>> facebook group, and got summarily shot down as ignorant and elitist.
>> The argument, such as it was, held that this is about *music*, not
>> *mathematics*, so there's no reason to adopt mathematicians' quirky
>> terminology.  This left me rather speechless, so I gave up.  However,
>> if I ever have reason to discuss this type of meter, will always call
>> it "non-dyadic".
> [...]

> This is off-topic, but it would be interesting if somebody composed a
> piece with an actually irrational meter, like π/4 or 3/π.  Only thing
> is, it would be impossible for human performers to play correctly, since
> there isn't any way to count the beats correctly (counting beats implies
> a rational fraction, since by definition it's impossible to count up to
> an irrational ratio by counting finite parts).

Perhaps one should define "correctly" before assuming impossibility. By
any definition of correctly which makes sense in this context (i.e.
precise rhythmic execution), it is arguably equally impossible to play
music in a *dyadic* meter correctly.

--
Mark Knoop

Re: irrational meters

[David Nalesnik]

On Tue, Jan 17, 2023 at 6:47 PM H. S. Teoh via LilyPond user discussion <
lilypond-user@gnu.org> wrote:

> On Tue, Jan 17, 2023 at 07:08:41PM -0500, David Zelinsky wrote:
> > Kieren MacMillan  writes:
> >
> > > Hi Silvain,
> > >
> > >> I wonder about the term “irrational” meter. Should not we say
> > >> “irregular” ??  as in mathematics, an irrational number is a number
> > >> which cannot be represented as a fraction...
> > >
> > > As both a published composer *and* a published number theorist, I
> > > wholeheartedly concur with your intuition — I’ve been pushing for
> > > decades against “irrational” as a descriptor for time signatures
> > > [except where it actually applies, of course, as in π/4].
> > >
> > > “Irregular” is better… but ultimately I prefer “non-dyadic” to
> > > describe any time signature where the bottom number (a.k.a.
> > > “denominator”, a label I also avoid) is not an integer power of 2.
> [...]
> > As another professional number theorist and musician (though not a
> > composer), I also find this use of "irrational" to mean "non-dyadic"
> > very grating.  But I once said as much on the Music Engraving Tips
> > facebook group, and got summarily shot down as ignorant and elitist.
> > The argument, such as it was, held that this is about *music*, not
> > *mathematics*, so there's no reason to adopt mathematicians' quirky
> > terminology.  This left me rather speechless, so I gave up.  However,
> > if I ever have reason to discuss this type of meter, will always call
> > it "non-dyadic".
> [...]
>
> This is off-topic, but it would be interesting if somebody composed a
> piece with an actually irrational meter, like π/4 or 3/π.  Only thing
> is, it would be impossible for human performers to play correctly, since
> there isn't any way to count the beats correctly (counting beats implies
> a rational fraction, since by definition it's impossible to count up to
> an irrational ratio by counting finite parts).


Speaking of non-human performers, you’ll find examples in the player piano
studies of Conlon Nancarrow.

Best,
David

Re: irrational meters

[David Zelinsky]

Jean Abou Samra  writes:

> Le 18/01/2023 à 01:29, David Zelinsky a écrit :
>> No, it's really not quirky.  A "rational" number is a ratio of two
>> integers.  An irrational number is one that cannot be so expressed.  The
>> word "ratio" comes from Latin for calculation.  The common english usage
>> of "rational" meaning sensible presumably stems from the ancient Greeks
>> view that only rational numbers make sense.  But the mathematical
>> definition is really more fundamental.  More rational, one might say :)
>
>
> Oh, I was being sarcastic against the fallacious “argument”.
> I know what a rational number is; I've been a math student,
> you know :)


Sorry I missed the sarcasm :)  But in fact it's not an unreasoble
question.  If one thinks the mathematical usage originally came from the
common english usage, then it does seem pretty arbitrary.  I myself had
to think for a second when first presented this argument, to realize
that's not the etymology of the mathematical term.

-David

Re: irrational meters

[Saul Tobin]

Doesn't "Night Fantasies" by Elliott Carter use an extremely obscure
structural polyrhythm? Not an actual irrational meter but similar idea.

On Tue, Jan 17, 2023 at 4:47 PM H. S. Teoh via LilyPond user discussion <
lilypond-user@gnu.org> wrote:

> On Tue, Jan 17, 2023 at 07:08:41PM -0500, David Zelinsky wrote:
> > Kieren MacMillan  writes:
> >
> > > Hi Silvain,
> > >
> > >> I wonder about the term “irrational” meter. Should not we say
> > >> “irregular” ??  as in mathematics, an irrational number is a number
> > >> which cannot be represented as a fraction...
> > >
> > > As both a published composer *and* a published number theorist, I
> > > wholeheartedly concur with your intuition — I’ve been pushing for
> > > decades against “irrational” as a descriptor for time signatures
> > > [except where it actually applies, of course, as in π/4].
> > >
> > > “Irregular” is better… but ultimately I prefer “non-dyadic” to
> > > describe any time signature where the bottom number (a.k.a.
> > > “denominator”, a label I also avoid) is not an integer power of 2.
> [...]
> > As another professional number theorist and musician (though not a
> > composer), I also find this use of "irrational" to mean "non-dyadic"
> > very grating.  But I once said as much on the Music Engraving Tips
> > facebook group, and got summarily shot down as ignorant and elitist.
> > The argument, such as it was, held that this is about *music*, not
> > *mathematics*, so there's no reason to adopt mathematicians' quirky
> > terminology.  This left me rather speechless, so I gave up.  However,
> > if I ever have reason to discuss this type of meter, will always call
> > it "non-dyadic".
> [...]
>
> This is off-topic, but it would be interesting if somebody composed a
> piece with an actually irrational meter, like π/4 or 3/π.  Only thing
> is, it would be impossible for human performers to play correctly, since
> there isn't any way to count the beats correctly (counting beats implies
> a rational fraction, since by definition it's impossible to count up to
> an irrational ratio by counting finite parts).
>
> But perhaps a more practicable approach is to use an irrational fraction
> as an endless source of diverse beat divisions that has no long-term
> patterns (because another property of an irrational number is that its
> base-n expansion does not produce a repeating sequence).  For example,
> one could take the digits of π (in whatever base one fancies) and use
> that as the number of beats to divide each bar into. In base 10, the
> first bar would be 3/4, the second bar 1/4, the third 4/4, then 1/4,
> then 5/4, etc..  Or, if one wishes, use pairs of digits for time
> signatures: 3/1, 4/1, 5/9, ... etc.. It doesn't have to be base 10, of
> course. Base 12 would yield 3/1, 8/4, 8/0, and so on (not sure how to
> interpret 8/0, but I'm sure someone could come up with something).
>
>
> T
>
> --
> "The whole problem with the world is that fools and fanatics are always so
> certain of themselves, but wiser people so full of doubts." -- Bertrand
> Russell. "How come he didn't put 'I think' at the end of it?" -- Anonymous
>
>

Re: irrational meters

[H. S. Teoh]

On Tue, Jan 17, 2023 at 07:08:41PM -0500, David Zelinsky wrote:
> Kieren MacMillan  writes:
> 
> > Hi Silvain,
> >
> >> I wonder about the term “irrational” meter. Should not we say
> >> “irregular” ??  as in mathematics, an irrational number is a number
> >> which cannot be represented as a fraction...
> >
> > As both a published composer *and* a published number theorist, I
> > wholeheartedly concur with your intuition — I’ve been pushing for
> > decades against “irrational” as a descriptor for time signatures
> > [except where it actually applies, of course, as in π/4].
> >
> > “Irregular” is better… but ultimately I prefer “non-dyadic” to
> > describe any time signature where the bottom number (a.k.a.
> > “denominator”, a label I also avoid) is not an integer power of 2.
[...]
> As another professional number theorist and musician (though not a
> composer), I also find this use of "irrational" to mean "non-dyadic"
> very grating.  But I once said as much on the Music Engraving Tips
> facebook group, and got summarily shot down as ignorant and elitist.
> The argument, such as it was, held that this is about *music*, not
> *mathematics*, so there's no reason to adopt mathematicians' quirky
> terminology.  This left me rather speechless, so I gave up.  However,
> if I ever have reason to discuss this type of meter, will always call
> it "non-dyadic".
[...]

This is off-topic, but it would be interesting if somebody composed a
piece with an actually irrational meter, like π/4 or 3/π.  Only thing
is, it would be impossible for human performers to play correctly, since
there isn't any way to count the beats correctly (counting beats implies
a rational fraction, since by definition it's impossible to count up to
an irrational ratio by counting finite parts).

But perhaps a more practicable approach is to use an irrational fraction
as an endless source of diverse beat divisions that has no long-term
patterns (because another property of an irrational number is that its
base-n expansion does not produce a repeating sequence).  For example,
one could take the digits of π (in whatever base one fancies) and use
that as the number of beats to divide each bar into. In base 10, the
first bar would be 3/4, the second bar 1/4, the third 4/4, then 1/4,
then 5/4, etc..  Or, if one wishes, use pairs of digits for time
signatures: 3/1, 4/1, 5/9, ... etc.. It doesn't have to be base 10, of
course. Base 12 would yield 3/1, 8/4, 8/0, and so on (not sure how to
interpret 8/0, but I'm sure someone could come up with something).


T

-- 
"The whole problem with the world is that fools and fanatics are always so 
certain of themselves, but wiser people so full of doubts." -- Bertrand 
Russell. "How come he didn't put 'I think' at the end of it?" -- Anonymous

Re: irrational meters

[Jean Abou Samra]

Le 18/01/2023 à 01:29, David Zelinsky a écrit :

No, it's really not quirky.  A "rational" number is a ratio of two
integers.  An irrational number is one that cannot be so expressed.  The
word "ratio" comes from Latin for calculation.  The common english usage
of "rational" meaning sensible presumably stems from the ancient Greeks
view that only rational numbers make sense.  But the mathematical
definition is really more fundamental.  More rational, one might say :)



Oh, I was being sarcastic against the fallacious “argument”.
I know what a rational number is; I've been a math student,
you know :)



OpenPGP_signature
Description: OpenPGP digital signature

Re: irrational meters

[David Zelinsky]

Jean Abou Samra  writes:

> Le 18/01/2023 à 01:08, David Zelinsky a écrit :
>> As another professional number theorist and musician (though not a
>> composer), I also find this use of "irrational" to mean "non-dyadic"
>> very grating.  But I once said as much on the Music Engraving Tips
>> facebook group, and got summarily shot down as ignorant and elitist.
>> The argument, such as it was, held that this is about *music*, not
>> *mathematics*, so there's no reason to adopt mathematicians' quirky
>> terminology.  This left me rather speechless, so I gave up.  However, if
>> I ever have reason to discuss this type of meter, will always call it
>> "non-dyadic".
>
>
>
> An interesting argument, given that “irrational” *is* “quirky” mathematic
> terminology in the first place ...
>
> Cheers,
> Jean

No, it's really not quirky.  A "rational" number is a ratio of two
integers.  An irrational number is one that cannot be so expressed.  The
word "ratio" comes from Latin for calculation.  The common english usage
of "rational" meaning sensible presumably stems from the ancient Greeks
view that only rational numbers make sense.  But the mathematical
definition is really more fundamental.  More rational, one might say :)

-David

Re: irrational meters

[Jean Abou Samra]

Le 18/01/2023 à 01:08, David Zelinsky a écrit :

As another professional number theorist and musician (though not a
composer), I also find this use of "irrational" to mean "non-dyadic"
very grating.  But I once said as much on the Music Engraving Tips
facebook group, and got summarily shot down as ignorant and elitist.
The argument, such as it was, held that this is about *music*, not
*mathematics*, so there's no reason to adopt mathematicians' quirky
terminology.  This left me rather speechless, so I gave up.  However, if
I ever have reason to discuss this type of meter, will always call it
"non-dyadic".




An interesting argument, given that “irrational” *is* “quirky” mathematic
terminology in the first place ...

Cheers,
Jean



OpenPGP_signature
Description: OpenPGP digital signature

Re: irrational meters

[David Zelinsky]

Kieren MacMillan  writes:

> Hi Silvain,
>
>> I wonder about the term “irrational” meter. Should not we say “irregular” ??
>> as in mathematics, an irrational number is a number which cannot be 
>> represented as a fraction...
>
> As both a published composer *and* a published number theorist, I
> wholeheartedly concur with your intuition — I’ve been pushing for
> decades against “irrational” as a descriptor for time signatures
> [except where it actually applies, of course, as in π/4].
>
> “Irregular” is better… but ultimately I prefer “non-dyadic” to
> describe any time signature where the bottom number
> (a.k.a. “denominator”, a label I also avoid) is not an integer power
> of 2.
>
> Cheers,
> Kieren.

As another professional number theorist and musician (though not a
composer), I also find this use of "irrational" to mean "non-dyadic"
very grating.  But I once said as much on the Music Engraving Tips
facebook group, and got summarily shot down as ignorant and elitist.
The argument, such as it was, held that this is about *music*, not
*mathematics*, so there's no reason to adopt mathematicians' quirky
terminology.  This left me rather speechless, so I gave up.  However, if
I ever have reason to discuss this type of meter, will always call it
"non-dyadic".

-David

Re: irrational meters

[Hans Åberg]

I gave an example [1] where the numerator is an irrational number, 8+2√5. It is 
implementable in LilyPond using continued fractions.

1. https://lists.gnu.org/archive/html/lilypond-user/2014-06/msg00237.html


> On 17 Jan 2023, at 18:40, Silvain Dupertuis  
> wrote:
> 
> Thanks for the reference.
> This wikipedia article in English does not have it's counterpart in my 
> language (French), but a corresponding but different French article which 
> does not mention this notion.
> So this term “irrational” is indeed used that way in music (at least in 
> English) ­­— but I still think it would be better to use the terme «non 
> dyadic», also mentioned in the article, so as to harmonize teminology between 
> music and maths
> Silvain
> 
> Le 17.01.23 à 15:52, Hans Åberg a écrit :
>> 
>>> On 17 Jan 2023, at 15:20, Silvain Dupertuis  
>>> wrote:
>>> 
>>> I wonder about the term “irrational” meter. Should not we say “irregular” ??
>>> as in mathematics, an irrational number is a number which cannot be 
>>> represented as a fraction...
>>> 
>> The denominator is not a power of two. See:
>> 
>> https://en.wikipedia.org/wiki/Time_signature#Irrational_meters
>> 
>> 
>> 
> 
> -- 
> Silvain Dupertuis
> Route de Lausanne 335
> 1293 Bellevue (Switzerland)
> tél. +41-(0)22-774.20.67
> portable +41-(0)79-604.87.52
> web: silvain-dupertuis.org

Re: irrational meters

[David Poon]

My $0.02 on terminology: if you think of the maths definition of
"irrational" as
"cannot be represented as a ratio of two integers",

we can translate this definition into music as
"cannot be represented as a ratio of an integer and a non-dotted,
non-tuplet note value".

I.e., treat the categorisation of integer->rational->irrational from maths
as "whole measure"->"basic" notes->"any duration" in music

-David

On Tue, 17 Jan 2023 at 09:41, Silvain Dupertuis <
silvain-dupert...@bluewin.ch> wrote:

> Thanks for the reference.
>
> This wikipedia article in English does not have it's counterpart in my
> language (French), but a corresponding but different French article which
> does not mention this notion.
>
> So this term “irrational” is indeed used that way in music (at least in
> English) ­­— but I still think it would be better to use the terme «non
> dyadic», also mentioned in the article, so as to harmonize teminology
> between music and maths
>
> Silvain
>
> Le 17.01.23 à 15:52, Hans Åberg a écrit :
>
> On 17 Jan 2023, at 15:20, Silvain Dupertuis  
>  wrote:
>
> I wonder about the term “irrational” meter. Should not we say “irregular” ??
> as in mathematics, an irrational number is a number which cannot be 
> represented as a fraction...
>
> The denominator is not a power of two. See:
> https://en.wikipedia.org/wiki/Time_signature#Irrational_meters
>
>
> --
> Silvain Dupertuis
> Route de Lausanne 335
> 1293 Bellevue (Switzerland)
> tél. +41-(0)22-774.20.67
> portable +41-(0)79-604.87.52
> web: silvain-dupertuis.org 
>

Re: irrational meters

[Silvain Dupertuis]

Thanks for the reference.

This wikipedia article in English does not have it's counterpart in my language (French), 
but a corresponding but different French article which does not mention this notion.


So this term “irrational” is indeed used that way in music (at least in English) ­­— but I 
still think it would be better to use the terme «non dyadic», also mentioned in the 
article, so as to harmonize teminology between music and maths


Silvain


Le 17.01.23 à 15:52, Hans Åberg a écrit :

On 17 Jan 2023, at 15:20, Silvain Dupertuis  
wrote:

I wonder about the term “irrational” meter. Should not we say “irregular” ??
as in mathematics, an irrational number is a number which cannot be represented 
as a fraction...

The denominator is not a power of two. See:

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




--
Silvain Dupertuis
Route de Lausanne 335
1293 Bellevue (Switzerland)
tél. +41-(0)22-774.20.67
portable +41-(0)79-604.87.52
web: silvain-dupertuis.org 

Re: irrational meters

[Karim Haddad]

Thank you a lot Leo for your advice.
I'll hence stick with solution #1 which looks preferable.

@all
Now about "irrational meter" (or "irrational" rhythms), well this denomination 
is from the fifties. I am aware that mathematically this is not correct since 
it is a fraction.However, "irregular" is somehow more vague and doesn't relate 
to anything in particular. Thanks to Hans' link that shows that it is a somehow 
a common terminology in music practice. 

Best to all of you, and thank you for all your comments.

Karim



On Tue, Jan 17, 2023 at 01:30:49PM +0100, Leo Correia de Verdier wrote:
> Hi Karim!
> 
> Your first example seems to work to me (I don’t do irrational meters 
> everyday, so there might be something I’m missing. I would probably write the 
> tuplets explicitly rather than use \scaleDurations). 
> \set Staff.timeSignatureFraction is superfluous, the time signature already 
> does that.
> 
> I’m not sure what you’re aiming at with the second example. One source of 
> error is that you have quoted ly:make-moment, and it wants its arguments as 
> elements of a list, not as a fraction, so: 
> #(ly:make-moment 16 25)
> , not
> #'(ly:make-moment 16/25)
> But it is still not the right amount of notes in the bar.
> 
> HTH
> /Leo
> 
> > 17 jan. 2023 kl. 12:16 skrev Karim Haddad :
> > 
> > Hi,
> > 
> > I am wondering which is the best way to write irrational meters (with tempo 
> > modulations)
> > 
> > 1)
> > %
> > \version "2.24.0"
> > \score {
> > {
> > 
> > \clef "G"
> > 
> > \scaleDurations 4/5 {
> > \time 4/5
> > \set Staff.timeSignatureFraction = #'(4 . 5)
> > \mark \markup {\left-column {{\line { \smaller \general-align #Y #DOWN  
> > \note {4} #1 " = 60 "}} \tiny "1"}}
> > c'4
> > c'4
> > c'4
> > c'4
> > |
> > }
> > \once \set Staff.whichBar = "|"
> > }
> > 
> > 
> > \layout {
> > 
> > \context {\Score
> > %measureBarType=#""
> >  }
> > 
> > }
> > }
> > %
> > 
> > or
> > 
> > 2)
> > 
> > %
> > \version "2.24.0"
> > \score {
> > {
> > \clef "G"
> > 
> > \time 4/5
> > \set Staff.timeSignatureFraction = #'(4 . 5)
> > \set Timing.measureLength = #'(ly:make-moment 16/25)
> > \mark \markup {\left-column {{\line { \smaller \general-align #Y #DOWN  
> > \note {4} #1 " = 60 "}} \tiny "1"}}
> > c'4
> > c'4
> > c'4
> > c'4
> > |
> > \once \set Staff.whichBar = "|"
> > }
> > 
> > \layout {
> > 
> > \context {\Score
> > measureBarType=#""
> >   }
> > 
> > }
> > }
> > %
> > 
> > 
> > Now the first solution outputs:
> > 
> > Processing `irr1.ly'
> > Parsing...
> > Interpreting music...
> > irr1.ly:13:1: warning: strange time signature found: 4/5
> > 
> > \time 4/5
> > Preprocessing graphical objects...
> > 
> > 
> > Which looks good to me as a warning
> > 
> > However, the second solution gives:
> > 
> > Processing `irr2.ly'
> > Parsing...
> > Interpreting music...
> > warning: type check for `measureLength' failed; value `(ly:make-moment 
> > 16/25)' must be of type `moment'
> > irr2.ly:12:1: warning: strange time signature found: 4/5
> > 
> > \time 4/5
> > irr2.ly:20:1: warning: barcheck failed at: 1/5
> > 
> > |
> > Preprocessing graphical objects...
> > 
> > 
> > And if we comment measureBarType=#"" we will have a strange bar at the end.
> > 
> > 
> > Best Regards
> > 
> > 
> > -- 
> > Karim Haddad
> > 
> > Music Representations Team, IRCAM
> > Research and development manager.
> > 
> > 
> 

-- 
Karim Haddad

Music Representations Team, IRCAM
Research and development manager.

Re: irrational meters

[Hans Åberg]

> On 17 Jan 2023, at 15:20, Silvain Dupertuis  
> wrote:
> 
> I wonder about the term “irrational” meter. Should not we say “irregular” ??
> as in mathematics, an irrational number is a number which cannot be 
> represented as a fraction...

The denominator is not a power of two. See:

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

Re: irrational meters

[Kieren MacMillan]

Hi Silvain,

> I wonder about the term “irrational” meter. Should not we say “irregular” ??
> as in mathematics, an irrational number is a number which cannot be 
> represented as a fraction...

As both a published composer *and* a published number theorist, I 
wholeheartedly concur with your intuition — I’ve been pushing for decades 
against “irrational” as a descriptor for time signatures [except where it 
actually applies, of course, as in π/4].

“Irregular” is better… but ultimately I prefer “non-dyadic” to describe any 
time signature where the bottom number (a.k.a. “denominator”, a label I also 
avoid) is not an integer power of 2.

Cheers,
Kieren.

Re: irrational meters

[J Martin Rushton]

I would have thought so.  I assumed this post was about weird modern
music.  Irregular grabs my attention though, I occasionally try to set
plainchant.Martin
On Tue, 2023-01-17 at 15:20 +0100, Silvain Dupertuis wrote:
> I wonder about the term “irrational”
>   meter. Should not we say “irregular” ??
> 
> 
> as in mathematics, an irrational number
>   is a number which cannot be represented as a fraction...
> 
> 
> 
> Le 17.01.23 à 13:30, Leo Correia de
>   Verdier a écrit :
> 
> 
> 
> >   Hi Karim!
> > Your first example seems to work to me (I don’t do irrational
> > meters everyday, so there might be something I’m missing. I would
> > probably write the tuplets explicitly rather than use
> > \scaleDurations). \set Staff.timeSignatureFraction is superfluous,
> > the time signature already does that.
> > 
> 
> 
> 
> -- 
> 
>   Silvain Dupertuis
> 
>   Route de Lausanne 335
> 
>   1293 Bellevue (Switzerland)
> 
>   tél. +41-(0)22-774.20.67
> 
>   portable +41-(0)79-604.87.52
> 
>   web: silvain-dupertuis.org
>   
> 
-- 
J Martin Rushton MBCS

Re: irrational meters

[Silvain Dupertuis]

I wonder about the term “irrational” meter. Should not we say “irregular” ??
as in mathematics, an irrational number is a number which cannot be represented as a 
fraction...


Le 17.01.23 à 13:30, Leo Correia de Verdier a écrit :

Hi Karim!

Your first example seems to work to me (I don’t do irrational meters everyday, 
so there might be something I’m missing. I would probably write the tuplets 
explicitly rather than use \scaleDurations).
\set Staff.timeSignatureFraction is superfluous, the time signature already 
does that.


--
Silvain Dupertuis
Route de Lausanne 335
1293 Bellevue (Switzerland)
tél. +41-(0)22-774.20.67
portable +41-(0)79-604.87.52
web: silvain-dupertuis.org <https://perso.silvain-dupertuis.org>

Re: irrational meters

[Leo Correia de Verdier]

Hi Karim!

Your first example seems to work to me (I don’t do irrational meters everyday, 
so there might be something I’m missing. I would probably write the tuplets 
explicitly rather than use \scaleDurations). 
\set Staff.timeSignatureFraction is superfluous, the time signature already 
does that.

I’m not sure what you’re aiming at with the second example. One source of error 
is that you have quoted ly:make-moment, and it wants its arguments as elements 
of a list, not as a fraction, so: 
#(ly:make-moment 16 25)
, not
#'(ly:make-moment 16/25)
But it is still not the right amount of notes in the bar.

HTH
/Leo

> 17 jan. 2023 kl. 12:16 skrev Karim Haddad :
> 
> Hi,
> 
> I am wondering which is the best way to write irrational meters (with tempo 
> modulations)
> 
> 1)
> %
> \version "2.24.0"
> \score {
> {
> 
> \clef "G"
> 
> \scaleDurations 4/5 {
> \time 4/5
> \set Staff.timeSignatureFraction = #'(4 . 5)
> \mark \markup {\left-column {{\line { \smaller \general-align #Y #DOWN  \note 
> {4} #1 " = 60 "}} \tiny "1"}}
> c'4
> c'4
> c'4
> c'4
> |
> }
> \once \set Staff.whichBar = "|"
> }
> 
> 
> \layout {
> 
> \context {\Score
> %measureBarType=#""
>  }
> 
> }
> }
> %
> 
> or
> 
> 2)
> 
> %
> \version "2.24.0"
> \score {
> {
> \clef "G"
> 
> \time 4/5
> \set Staff.timeSignatureFraction = #'(4 . 5)
> \set Timing.measureLength = #'(ly:make-moment 16/25)
> \mark \markup {\left-column {{\line { \smaller \general-align #Y #DOWN  \note 
> {4} #1 " = 60 "}} \tiny "1"}}
> c'4
> c'4
> c'4
> c'4
> |
> \once \set Staff.whichBar = "|"
> }
> 
> \layout {
> 
> \context {\Score
> measureBarType=#""
> }
> 
> }
> }
> %
> 
> 
> Now the first solution outputs:
> 
> Processing `irr1.ly'
> Parsing...
> Interpreting music...
> irr1.ly:13:1: warning: strange time signature found: 4/5
> 
> \time 4/5
> Preprocessing graphical objects...
> 
> 
> Which looks good to me as a warning
> 
> However, the second solution gives:
> 
> Processing `irr2.ly'
> Parsing...
> Interpreting music...
> warning: type check for `measureLength' failed; value `(ly:make-moment 
> 16/25)' must be of type `moment'
> irr2.ly:12:1: warning: strange time signature found: 4/5
> 
> \time 4/5
> irr2.ly:20:1: warning: barcheck failed at: 1/5
> 
> |
> Preprocessing graphical objects...
> 
> 
> And if we comment measureBarType=#"" we will have a strange bar at the end.
> 
> 
> Best Regards
> 
> 
> -- 
> Karim Haddad
> 
> Music Representations Team, IRCAM
> Research and development manager.
> 
> 

irrational meters

[Karim Haddad]

Hi,

I am wondering which is the best way to write irrational meters (with tempo 
modulations)

1)
%
\version "2.24.0"
\score {
{

\clef "G"

\scaleDurations 4/5 {
\time 4/5
\set Staff.timeSignatureFraction = #'(4 . 5)
\mark \markup {\left-column {{\line { \smaller \general-align #Y #DOWN  \note 
{4} #1 " = 60 "}} \tiny "1"}}
c'4
c'4
c'4
c'4
|
}
\once \set Staff.whichBar = "|"
}


\layout {

\context {\Score
 %measureBarType=#""
  }

}
}
%

or

2)

%
\version "2.24.0"
\score {
{
\clef "G"

\time 4/5
\set Staff.timeSignatureFraction = #'(4 . 5)
\set Timing.measureLength = #'(ly:make-moment 16/25)
\mark \markup {\left-column {{\line { \smaller \general-align #Y #DOWN  \note 
{4} #1 " = 60 "}} \tiny "1"}}
c'4
c'4
c'4
c'4
|
\once \set Staff.whichBar = "|"
}

\layout {

\context {\Score
 measureBarType=#""
  }

}
}
%


Now the first solution outputs:

Processing `irr1.ly'
Parsing...
Interpreting music...
irr1.ly:13:1: warning: strange time signature found: 4/5

\time 4/5
Preprocessing graphical objects...


Which looks good to me as a warning

However, the second solution gives:

Processing `irr2.ly'
Parsing...
Interpreting music...
warning: type check for `measureLength' failed; value `(ly:make-moment 16/25)' 
must be of type `moment'
irr2.ly:12:1: warning: strange time signature found: 4/5

\time 4/5
irr2.ly:20:1: warning: barcheck failed at: 1/5

|
Preprocessing graphical objects...


And if we comment measureBarType=#"" we will have a strange bar at the end.


Best Regards


-- 
Karim Haddad

Music Representations Team, IRCAM
Research and development manager.