This is an Opt In Archive . We would like to hear from you if you want your posts included. For the contact address see About this archive. All posts are copyright (c).
Contents Hide Contents S 65000 5050 5100 5150 5200 5250 5300 5350 5400 5450 5500 5550 5600 5650 5700 5750 5800 5850 5900 5950
5250 - 5275 -
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"
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"
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"
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
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
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
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"
5000 5050 5100 5150 5200 5250 5300 5350 5400 5450 5500 5550 5600 5650 5700 5750 5800 5850 5900 5950
5250 - 5275 -