Tuning-Math Digests messages 5250 - 5274

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Message: 5250

Date: Wed, 25 Sep 2002 09:25:25

Subject: Re: a reference pitch

From: monz

hi George,


> From: "gdsecor" <gdsecor@xxxxx.xxx>
> To: <tuning-math@xxxxxxxxxxx.xxx>
> Sent: Wednesday, September 25, 2002 7:18 AM
> Subject: [tuning-math] Re: a reference pitch (was: A common notation for
JI and ETs)
>
>
> --- In tuning-math@y..., "monz" <monz@a...> wrote:
> >
> > umm ... well ... it only means that "middle-C" is 256 Hz.
> > this would make the 12edo "A" = ~430.5 Hz.
> >
> > it was just my thinking that since this is not too far
> > off from most of the pitch-standards already in use today,
> > it makes more sense as a basis from a logical point of view.
> > we commonly use "C" as the reference anyway instead of "A",
> > so why not simply equate it with 1 Hz?
> >
> > -monz
> > "all roads lead to n^0"
>
> The two main obstacles are 1) getting wind instruments to
> play in tune


but that's the case regardless of what intonational or
notational paradigm is in use.


> and 2) getting others to accept this.  I have a feeling
> that the second one is the more formidable obstacle.
>
> --George



yeah, well ... unfortunately, that's my feeling too.

but it's encouraging to me that (as i've already said)
several people have written to me or the tuning list
saying that they were adopting my C = 1 Hz standard.

my hope is that the logic of my choice will ultimately
win out.  if it doesn't happen, then i guess it doesn't
really matter all that much after all.



-monz
"all roads lead to n^0"


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Message: 5251

Date: Fri, 27 Sep 2002 01:20:36

Subject: interesting property concerning meantone intervals

From: monz

i've discovered an interesting property about
1/4-comma meantone which i haven't seen mentioned
before.

this concerns specifically a 12-tone chain of
1/4-comma meantone, which may be described as
the "8ve"-invariant set of pitches determined by
generators  5^(_p_/4), where _p_ = -3...+8.

i've found that the entire set of intervals that
can be found in this scale may be described as
the "8ve"-invariant set of intervals determined
by generators 5^(_i_/4), where _i_ = -11...+11.

i was wondering if this could be generalized to
the set of pitches 5^(_p_/4), where _p_ = a...b,
and the set of intervals 5^(_i_/4), where
i = (a-b)...(b-a).

and how about generalization to other forms of
meantone?  to other types of scales in general?
my guess is that it has been written about before,
but my math-challenged brain missed it.

... ?





-monz
"all roads lead to n^0"


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Message: 5252

Date: Fri, 27 Sep 2002 02:42:47

Subject: mathematical model of torsion-block symmetry?

From: monz

is there some way to mathematically model
the symmetry in a torsion-block?

see the graphic and its related text in my
Tuning Dictionary definition of "torsion"
-- i've uploaded it to here:
Yahoo groups: /monz/files/dict/torsion.htm *



-monz
"all roads lead to n^0"


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Message: 5253

Date: Fri, 27 Sep 2002 16:12:03

Subject: Re: interesting property concerning meantone intervals

From: manuel.op.de.coul@xxxxxxxxxxx.xxx

Ok, I'm not going to say that you shouldn't be surprised, 
otherwise Johnny Reinhard will start laughing.

It is true for all meantone or Pythagorean generated scales.
Suppose _g_ is the size of the generator, and _a_ the size of 
the octave. Then you can express each pitch as
x g + y a, where x in your case is in -3..8, and y such that
the pitch is in the range of one octave.
The intervals are two pitches subtracted, and the result
has the same form, say x'g + y'a.
So if the range of x is -3..8 then the range of the differences
of two x's is -3 - 8 .. 8 - -3 = -11 .. 11.

Manuel


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Message: 5259

Date: Tue, 1 Oct 2002 10:32:03

Subject: Re: mathematical model of torsion-block symmetry?

From: monz

hi paul,


> From: "wallyesterpaulrus" <wallyesterpaulrus@xxxxx.xxx>
> To: <tuning-math@xxxxxxxxxxx.xxx>
> Sent: Monday, September 30, 2002 2:47 PM
> Subject: [tuning-math] Re: mathematical model of torsion-block symmetry?
>
>
> --- In tuning-math@y..., "monz" <monz@a...> wrote:
> > is there some way to mathematically model
> > the symmetry in a torsion-block?
> > 
> > see the graphic and its related text in my
> > Tuning Dictionary definition of "torsion"
> > -- i've uploaded it to here:
> > Yahoo groups: /monz/files/dict/torsion.htm *
> > 
> > 
> > 
> > -monz
> > "all roads lead to n^0"
> 
> i see the green and red lines, but . . . which symmetry exactly are 
> you referring to?


do you see "The thin black line which divides the block in half
diagonally is the torsional interval, 6561:6400 = [-8 2] = (81/80)^2
= (648/625) (2048/2025)^(-1).]" on the diagram?



-monz


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Message: 5268

Date: Tue, 1 Oct 2002 23:23:19

Subject: delays in responding to paul (was: mathematical model...)

From: monz

> From: "wallyesterpaulrus" <wallyesterpaulrus@xxxxx.xxx>
> To: <tuning-math@xxxxxxxxxxx.xxx>
> Sent: Tuesday, October 01, 2002 3:46 PM
> Subject: [tuning-math] Re: mathematical model of torsion-block symmetry?
>
>
> p.s. are you reading my posts on the tuning list, monzieur? i was 
> going to post a (fairly serious) critique of your new 12-edo page, 
> but i'm afraid no one, not even you, would read it, since you haven't 
> really replied to, or incorporated into your webpages, my last two 
> lengthy tuning lists posts to you. if i e-mailed this critique to you 
> privately, would you have a better chance of reading it?



i've been reading everything, but have been insanely busy lately.
since the Sonic Arts website went under last Thursday, i spent
the entire weekend putting up a mirror of my website in that
new Yahoo group i created.  i was a very tedious process, because
Yahoo groups only allow uploading of files one at a time.  then
when Monday rolled around, it was back to a busy work week.

please send your critique of the 12edo page, either to me or
to the list.  i'm always interested in your commentary on my
work, and generally include it in the webpages.  web stuff is
simply going at a slower pace now because i'm very busy with work.



-monz


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Message: 5274

Date: Thu, 3 Oct 2002 04:30:18

Subject: Re: Combinatorics and Tuning Systems?

From: monz

back around September 10,

> --- In tuning-math@y..., <Josh@o...> wrote:
> 
> Somehow, even the great serialists failed to much
> exploit combinatoriality between sets of 5 and 7.
> the 5-12/7-12 aggregate is particularly interesting
> in that 7-12 does not actually include any forms of 5-12.
> It's such an obvious candidate for serialist treatment...
> ...ok, I'll drop that.




i wasn't following this thread, and only remembered seeing
the word "combinatorics" in the subject line.  but i just
stumbled across this:


"Some Combinational Resources of Equal-Tempered Systems"
by Carlton Gamer
_Journal of Music Theory_ 11:1, Spring 1967


in which the opening paragraph gives the following abstract:

>> "The purpose of this article is to reveal and discuss
>> certain resources available to the composer who wishes to
>> employ equal-tempered systems containing either more or
>> less than twelve tones per octave, with particular emphasis
>> upon the former, the so-called "microtonal" systems."


i'm going to completely skirt the issue of Gamer's specific
definition of "microtonal": see the Tuning Dictionary and
the list archives for those arguments.


anyway, i wasn't following the thread, but those who were
would find this paper relevant.



-monz
"all roads lead to n^0"


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