Pythagoras and proportions or divisions of frequency intervals
and how they relate to one another.

-Partev

==========================================================


--- PeterArmstrong@aya.yale.edu wrote:

From: PMA 
To:  csound@lists.bath.ac.uk
Subject: [Csnd] Re: Re: Re: Xenakis etc
Date: Tue, 18 Jan 2011 20:56:07 -0500

Why all this talk of traditional music theory being somehow not 
mathematical?
Aren't we simply seeing two styles of arithmetic: an older, 1-based and 
adding
inclusively; and our newer, 0-based and adding exclusively?

And of course we're uncomfortable with the old.  If there's more to it 
than this,
then of course I'm missing what.

Let's just all be glad Harmony I doesn't *add* with those Roman numerals!


Richard Dobson wrote:
> On 19/01/2011 00:53, Robert or Gretchen Foose wrote:
>> "add"..an example of operator overloading..the same as Python (et al.)
>> use "hot"+"dog" = "hotdog". There the '+' is used for joining two
>> strings. In music 'add' is a matter of combining two theoretical
>> structures (thirds) into one larger structure. Quite similar, but NOT
>> identical, to its use in math. I agree that the similarity is close
>> enough to be misleading, and/or confusing..but only if you expect the
>> two areas of knowledge to be the same.
> 
> 
> 
> As a final footnote, I will "add" that I will believe it when:
> 
> the standard pack of playing cards is redesigned so that the suit order 
> is not A,2,3...10,J,Q,K  but A,1,2...9,J,Q,K. Redefining every card game 
> on the planet is but a small price to pay!
> 
> 
> Richard Dobson
> 
> 
> 
> 
> 
> 
> 
> 
> Send bugs reports to the Sourceforge bug tracker
>            https://sourceforge.net/tracker/?group_id=81968&atid=564599
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> csound"
> 
> 


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_____________________________________________________________
Netscape.  Just the Net You Need.


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There is something scientific in frequency intervals, but I think the
implication was that deciding which ones are more and less pleasant is
still subjective.
-Chuckk

On Fri, Jan 21, 2011 at 6:07 AM, Partev Barr Sarkissian
 wrote:
> Pythagoras and proportions or divisions of frequency intervals
> and how they relate to one another.
>
> -Partev
>
> ==========================================================
>
>
> --- PeterArmstrong@aya.yale.edu wrote:
>
> From: PMA 
> To:  csound@lists.bath.ac.uk
> Subject: [Csnd] Re: Re: Re: Xenakis etc
> Date: Tue, 18 Jan 2011 20:56:07 -0500
>
> Why all this talk of traditional music theory being somehow not
> mathematical?
> Aren't we simply seeing two styles of arithmetic: an older, 1-based and
> adding
> inclusively; and our newer, 0-based and adding exclusively?
>
> And of course we're uncomfortable with the old.  If there's more to it
> than this,
> then of course I'm missing what.
>
> Let's just all be glad Harmony I doesn't *add* with those Roman numerals!
>
>
> Richard Dobson wrote:
>> On 19/01/2011 00:53, Robert or Gretchen Foose wrote:
>>> "add"..an example of operator overloading..the same as Python (et al.)
>>> use "hot"+"dog" = "hotdog". There the '+' is used for joining two
>>> strings. In music 'add' is a matter of combining two theoretical
>>> structures (thirds) into one larger structure. Quite similar, but NOT
>>> identical, to its use in math. I agree that the similarity is close
>>> enough to be misleading, and/or confusing..but only if you expect the
>>> two areas of knowledge to be the same.
>>
>>
>>
>> As a final footnote, I will "add" that I will believe it when:
>>
>> the standard pack of playing cards is redesigned so that the suit order
>> is not A,2,3...10,J,Q,K  but A,1,2...9,J,Q,K. Redefining every card game
>> on the planet is but a small price to pay!
>>
>>
>> Richard Dobson
>>
>>
>>
>>
>>
>>
>>
>>
>> Send bugs reports to the Sourceforge bug tracker
>>            https://sourceforge.net/tracker/?group_id=81968&atid=564599
>> Discussions of bugs and features can be posted here
>> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe
>> csound"
>>
>>
>
>
> Send bugs reports to the Sourceforge bug tracker
>            https://sourceforge.net/tracker/?group_id=81968&atid=564599
> Discussions of bugs and features can be posted here
> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe csound"
>
>
>
>
>
> _____________________________________________________________
> Netscape.  Just the Net You Need.
>
>
> Send bugs reports to the Sourceforge bug tracker
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>
>



-- 
http://www.badmuthahubbard.com


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Xenakis has a different perspective than a lot of other western composers because greece is a different culture and language. He has the concept of music first and foremost taking you to a place, putting your imagination into a journey. He's got very ancient influences going on from the folk traditions of greece and the near east. He's also an archatect as well as a composer, so he composes boths with sound and with physical and even virtual space. But its not music meant for entertainment, its mysterous and sometimes terrifying. That's why modern classical composers can see the most success with film scoring, though these days lots of sound tracks use the music from rock or hip hop groups.

On 21/01/2011 05:27, Chuckk Hubbard wrote:
> There is something scientific in frequency intervals, but I think the
> implication was that deciding which ones are more and less pleasant is
> still subjective.
> -Chuckk
>


The general understanding is that consonance and even tuning is 
dependent on the timbre of the notes concerned. There was an experiment 
done asking people to tune two pure sine tones to specified intervals, 
and apparently even experienced musicians couldn't do it reliably; 
because, whatever the interval, it did not sound "dissonant" in any way, 
and everything somehow sounded "in tune". And there is the added 
complication that when listening to a sine tone (with two ears...), the 
slightest head movement can cause an apparent shift in pitch. Play it 
alternating between two loudspeakers and the two notes will sound 
different in tuning, more often than they will sound the same.

Play a tritone  on two recorders, and it will sound mellow, sweet, maybe 
even boring. Play it on two trumpets, and it may cause walls to tumble, 
and be anywhere between thrilling and terrifying. So there is a way in 
which the consonance of two notes can be measured objectively, by 
looking at the proximity or otherwise of common partials.

Richard Dobson



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There is an article by Parncutt worth reading for anyone interested in
this subject. Fascinating stuff.
http://www-gewi.uni-graz.at/staff/parncutt/publications/PaStr94.pdf


On 21 January 2011 10:38, Richard Dobson  wrote:
> On 21/01/2011 05:27, Chuckk Hubbard wrote:
>>
>> There is something scientific in frequency intervals, but I think the
>> implication was that deciding which ones are more and less pleasant is
>> still subjective.
>> -Chuckk
>>
>
>
> The general understanding is that consonance and even tuning is dependent on
> the timbre of the notes concerned. There was an experiment done asking
> people to tune two pure sine tones to specified intervals, and apparently
> even experienced musicians couldn't do it reliably; because, whatever the
> interval, it did not sound "dissonant" in any way, and everything somehow
> sounded "in tune". And there is the added complication that when listening
> to a sine tone (with two ears...), the slightest head movement can cause an
> apparent shift in pitch. Play it alternating between two loudspeakers and
> the two notes will sound different in tuning, more often than they will
> sound the same.
>
> Play a tritone  on two recorders, and it will sound mellow, sweet, maybe
> even boring. Play it on two trumpets, and it may cause walls to tumble, and
> be anywhere between thrilling and terrifying. So there is a way in which the
> consonance of two notes can be measured objectively, by looking at the
> proximity or otherwise of common partials.
>
> Richard Dobson
>
>
>
> Send bugs reports to the Sourceforge bug tracker
>           https://sourceforge.net/tracker/?group_id=81968&atid=564599
> Discussions of bugs and features can be posted here
> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe
> csound"
>
>


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Music theory has both a scientific aspect, and an ideological or
philosophical aspect.

Certainly there are falsifiable hypotheses, as well as controlled
experiments, on the scientific side of music theory. And there is a
real mathematical component to it. It is a scientific discovery --
i.e. a fact that would be unknown without science -- that the major
and minor triads of the 12 tone equally tempered scale have a
mathematical structure called the Riemannian group. It is a scientific
observation that chords progress much more often by going down a
perfect fifth than by going up a perfect fifth. It is a scientific
hypothesis, well supported  by the evidence, that composers' use of
the Riemannian group and the rules of voice leading are at least in
part caused by the empirical fact, also established by experiment,
that people can distinguish polyphonic voices much more easily if
voices move in few, small motions between the first three to five
harmonics of the harmonic series.

It is an ideological or philosophical claim that there is something
"good" or "right" about this. But, as a composer, I certainly do make
that claim. But also, I do not claim that this is the ONLY way to
organize sound in composition.

Regards,
Mike

On Fri, Jan 21, 2011 at 5:38 AM, Richard Dobson
 wrote:
> On 21/01/2011 05:27, Chuckk Hubbard wrote:
>>
>> There is something scientific in frequency intervals, but I think the
>> implication was that deciding which ones are more and less pleasant is
>> still subjective.
>> -Chuckk
>>
>
>
> The general understanding is that consonance and even tuning is dependent on
> the timbre of the notes concerned. There was an experiment done asking
> people to tune two pure sine tones to specified intervals, and apparently
> even experienced musicians couldn't do it reliably; because, whatever the
> interval, it did not sound "dissonant" in any way, and everything somehow
> sounded "in tune". And there is the added complication that when listening
> to a sine tone (with two ears...), the slightest head movement can cause an
> apparent shift in pitch. Play it alternating between two loudspeakers and
> the two notes will sound different in tuning, more often than they will
> sound the same.
>
> Play a tritone  on two recorders, and it will sound mellow, sweet, maybe
> even boring. Play it on two trumpets, and it may cause walls to tumble, and
> be anywhere between thrilling and terrifying. So there is a way in which the
> consonance of two notes can be measured objectively, by looking at the
> proximity or otherwise of common partials.
>
> Richard Dobson
>
>
>
> Send bugs reports to the Sourceforge bug tracker
>           https://sourceforge.net/tracker/?group_id=81968&atid=564599
> Discussions of bugs and features can be posted here
> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe
> csound"
>
>



-- 
Michael Gogins
Irreducible Productions
http://www.michael-gogins.com
Michael dot Gogins at gmail dot com


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Yes exactly. There is naturally a science of music but that doesn't
make music a science.

P

On 21 January 2011 06:27, Chuckk Hubbard  wrote:
> There is something scientific in frequency intervals, but I think the
> implication was that deciding which ones are more and less pleasant is
> still subjective.
> -Chuckk
>
> On Fri, Jan 21, 2011 at 6:07 AM, Partev Barr Sarkissian
>  wrote:
>> Pythagoras and proportions or divisions of frequency intervals
>> and how they relate to one another.
>>
>> -Partev
>>
>> ==========================================================
>>
>>
>> --- PeterArmstrong@aya.yale.edu wrote:
>>
>> From: PMA 
>> To:  csound@lists.bath.ac.uk
>> Subject: [Csnd] Re: Re: Re: Xenakis etc
>> Date: Tue, 18 Jan 2011 20:56:07 -0500
>>
>> Why all this talk of traditional music theory being somehow not
>> mathematical?
>> Aren't we simply seeing two styles of arithmetic: an older, 1-based and
>> adding
>> inclusively; and our newer, 0-based and adding exclusively?
>>
>> And of course we're uncomfortable with the old.  If there's more to it
>> than this,
>> then of course I'm missing what.
>>
>> Let's just all be glad Harmony I doesn't *add* with those Roman numerals!
>>
>>
>> Richard Dobson wrote:
>>> On 19/01/2011 00:53, Robert or Gretchen Foose wrote:
>>>> "add"..an example of operator overloading..the same as Python (et al.)
>>>> use "hot"+"dog" = "hotdog". There the '+' is used for joining two
>>>> strings. In music 'add' is a matter of combining two theoretical
>>>> structures (thirds) into one larger structure. Quite similar, but NOT
>>>> identical, to its use in math. I agree that the similarity is close
>>>> enough to be misleading, and/or confusing..but only if you expect the
>>>> two areas of knowledge to be the same.
>>>
>>>
>>>
>>> As a final footnote, I will "add" that I will believe it when:
>>>
>>> the standard pack of playing cards is redesigned so that the suit order
>>> is not A,2,3...10,J,Q,K  but A,1,2...9,J,Q,K. Redefining every card game
>>> on the planet is but a small price to pay!
>>>
>>>
>>> Richard Dobson
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>> Send bugs reports to the Sourceforge bug tracker
>>>            https://sourceforge.net/tracker/?group_id=81968&atid=564599
>>> Discussions of bugs and features can be posted here
>>> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe
>>> csound"
>>>
>>>
>>
>>
>> Send bugs reports to the Sourceforge bug tracker
>>            https://sourceforge.net/tracker/?group_id=81968&atid=564599
>> Discussions of bugs and features can be posted here
>> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe csound"
>>
>>
>>
>>
>>
>> _____________________________________________________________
>> Netscape.  Just the Net You Need.
>>
>>
>> Send bugs reports to the Sourceforge bug tracker
>>            https://sourceforge.net/tracker/?group_id=81968&atid=564599
>> Discussions of bugs and features can be posted here
>> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe csound"
>>
>>
>
>
>
> --
> http://www.badmuthahubbard.com
>
>
> Send bugs reports to the Sourceforge bug tracker
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> Discussions of bugs and features can be posted here
> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe csound"
>
>


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