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Message: 8626 Date: Tue, 02 Dec 2003 18:28:32 Subject: Re: Enumerating pitch class sets algebraically From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote: > --- In tuning-math@xxxxxxxxxxx.xxxx "Dante Rosati" <dante@i...> wrote: > > > All I meant was in set theory [0,3,7] is just another trichord with > no > > priveleged status. > > And 12 is just another equal division of the octave with no > priivledge status, and equal divisions are without a priveledged > status either. Take that, Forteans!
Message: 8631 Date: Tue, 02 Dec 2003 07:06:46 Subject: Re: Enumerating pitch class sets algebraically From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Dante Rosati" <dante@i...> wrote: > > Thanks. I found a url by googling for this, which gives the complete > > 351 (or 352, for the null chord is listed as number zero.) > > > > Table of Pitch Class Sets (Set Classes) * 20This% > > 20Table > > Interesting. I didn't know Forte's methodology could be challenged. After > reading the explanation on this page, I'm still not convinced it can be. I'm in complete agreement with the author of the page. > I > don't think introducing that kind of redundancy into the prime form list is > going to do anything but create confusion. Noone said that different > inversional and transpositional forms of prime sets sound the same, thats > not the point. The point is reducibility. "Tonal" theory is a limiting case > of set theory, just like Newtonian physics is a limiting case of relativity. > > Dante Hi Dante. I must be totally ignorant of how this 'limiting' happens, but what you are saying seems impossible. If Forte's methodology eliminates the distinction between mirror inverses, how can any limiting case of it possible restore that distinction?
Message: 8634 Date: Tue, 02 Dec 2003 11:23:54 Subject: Re: Enumerating pitch class sets algebraically From: Carl Lumma >PC set theory is a science. What does PC stand for? -C.
Message: 8635 Date: Tue, 02 Dec 2003 08:36:23 Subject: Re: Enumerating pitch class sets algebraically From: Paul Erlich Since the distinction does exist in tonal theory, the analogy to Newtonian and relativistic gravitation, or calling tonal theory a 'limiting case' or 'special case' of Fortean set theory, seems totally wrong. In what sense is it right? --- In tuning-math@xxxxxxxxxxx.xxxx "Dante Rosati" <dante@i...> wrote: > Hi Paul- > > The distinction is not "restored", it simply doesn't exist from the > set-theoretic perspective. Now, you may then say that this perspective is > therefore useless to "explain" tonal music, which may very well be. But any > music (tonal or not) can very well be >described< from a set- theoretic > perspective. Functional harmony, as a cultural construct, will not > necessarily "show up" in this type of description. I find this kind of set > stuff more useful for precompositional material than analysis (see Carter's > "Harmony" book). > > Dante > > > -----Original Message----- > > From: Paul Erlich [mailto:perlich@a...] > > Sent: Tuesday, December 02, 2003 2:07 AM > > To: tuning-math@xxxxxxxxxxx.xxx > > Subject: [tuning-math] Re: Enumerating pitch class sets algebraically > > > > > > --- In tuning-math@xxxxxxxxxxx.xxxx "Dante Rosati" <dante@i...> wrote: > > > > Thanks. I found a url by googling for this, which gives the > > complete > > > > 351 (or 352, for the null chord is listed as number zero.) > > > > > > > > Table of Pitch Class Sets (Set Classes) * > > 20This% > > > > 20Table > > > > > > Interesting. I didn't know Forte's methodology could be challenged. > > After > > > reading the explanation on this page, I'm still not convinced it > > can be. > > > > I'm in complete agreement with the author of the page. > > > > > I > > > don't think introducing that kind of redundancy into the prime form > > list is > > > going to do anything but create confusion. Noone said that different > > > inversional and transpositional forms of prime sets sound the same, > > thats > > > not the point. The point is reducibility. "Tonal" theory is a > > limiting case > > > of set theory, just like Newtonian physics is a limiting case of > > relativity. > > > > > > Dante > > > > Hi Dante. I must be totally ignorant of how this 'limiting' happens, > > but what you are saying seems impossible. If Forte's methodology > > eliminates the distinction between mirror inverses, how can any > > limiting case of it possible restore that distinction? > > > > > > > > To unsubscribe from this group, send an email to: > > tuning-math-unsubscribe@xxxxxxxxxxx.xxx > > > > > > > > Your use of Yahoo! Groups is subject to Yahoo! Terms of Service * > > > >
Message: 8636 Date: Tue, 02 Dec 2003 19:27:08 Subject: Re: Enumerating pitch class sets algebraically From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote: > >PC set theory is a science. hrmm . . . > What does PC stand for? > > -C. pitch-class.
Message: 8637 Date: Tue, 02 Dec 2003 11:35:25 Subject: Re: Enumerating pitch class sets algebraically From: Carl Lumma >> >PC set theory is a science. > >hrmm . . . For the record, I didn't write that bit. >> What does PC stand for? >> >> -C. > >pitch-class. Thanks! -Carl
Message: 8646 Date: Wed, 03 Dec 2003 12:35:03 Subject: Re: Enumerating pitch class sets algebraically From: Carl Lumma [Dante] >> > I repeat- if someone writes a piece using this equivilence, >> > and someone else likes how it sounds, then it is relevant to >> > the music in question. >> >> [Carl] >> Actually, listener enjoyment by itself isn't justification for >> anything. > > [Dante] >I'm going to go shoot myself now. People enjoy all sorts of things. For an algorithmic comp. method to be justified it should at least produce results that are distinct from other methods. That means listeners should be able to identify it. Now PC Set Theory may meet this condition, although it probably demands some training. I certainly have nothing against PC Set Theory or training (fugues certainly take some training to fully appreciate). In fact, I'd like to learn more about PC Set Theory... () Does it generalize the serial technique, or is it different? () Was it started/coined by Babbitt? () Does it claim to be / is it a prescriptive (ie algo comp) process, a descriptive process, or both? () What's the best piece for a beginner to start with, and what should he listen for? -Carl
Message: 8647 Date: Wed, 03 Dec 2003 22:13:05 Subject: Re: Enumerating pitch class sets algebraically From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Dante Rosati" <dante@i...> wrote: > I dont get it- who said 12 is anything but the system that is most >used? Of > course you can generalize these methods to any edo you want. But you're still restricted to equal divisions!
Message: 8648 Date: Wed, 03 Dec 2003 22:14:31 Subject: Re: Enumerating pitch class sets algebraically From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Dante Rosati" <dante@i...> wrote: > > > Eh? I think you've got it backwards. Tonal music relates to how your > > ears hear, whereas using 12 notes to the octave without reference to > > he fact that 12 provides good approximations seems like an arbitrary > > cultural construct. > > All music is cultural construct. Its just a matter of what you're familiar > with and what floats your boat. I recommend reading this paper: http://homepage.mac.com/cariani/CarianiWebsite/CarianiNP99.pdf - Ok * *harmony*, to a certain degree, is innate. > If composer A writes a piece this way and listener B digs it, > then thats all the "justification" necessary (if you're into > justifications). Agreed. Music speaks louder than words, theory, etc . . .
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