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 98000 8050 8100 8150 8200 8250 8300 8350 8400 8450 8500 8550 8600 8650 8700 8750 8800 8850 8900 8950
8750 - 8775 -
Message: 8777 Date: Thu, 11 Dec 2003 09:36:27 Subject: Re: Enumerating pitch class sets algebraically From: monz hi paul, --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote: > --- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> wrote: > > i think the main reason harmonic analysis would be > > characterised as an "art" is precisely *because* of > > the ambiguity available to a composer like Brahms, > > whether his intended tuning is 12edo or a meantone > > (the only two likely possibilities for Brahms IMO). > > > > my point: that *temperament* allows composers to play > > the kinds of games ("punning") that aren't possible > > in JI. > > Irrelevant -- Dante and I were talking about 'conventional' tonal > harmonic analysis, which never distinguishes any 81:80s anyway. OK, my bad. i didn't follow the thread from the beginning and probably should have just stayed out of it. ... in fact, my eyes have glazed over with nearly every post i've seen here over the last week, except for this one. > > and of course JI is the tuning which offers > > the straightforward "scientific" approach to harmonic > > analysis. > > BS. i guess i didn't express myself clearly enough. you and i both already know each other's viewpoints on this. anyway, since i did miss so much here in the last week, it's probably not worth it for me to try to clarify now ... -monz
Message: 8779 Date: Thu, 11 Dec 2003 00:24:42 Subject: Re: Digest Number 862 From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "gooseplex" <cfaah@e...> wrote: > When I said that some > physicists would agree with me and some with you, I was talking > about agreement on the *real* issue at hand which is the > _mathematical _verses _the _musical _definition _of _the > _harmonic _series, which - I'm sorry - does not involve > acoustics! So you think some physicists would agree with you and say what, exactly? I honestly want to understand you better. > > Sheesh, this has become a royal waste of time... > > Aaron
Message: 8780 Date: Thu, 11 Dec 2003 01:58:02 Subject: Re: An 11-limit linear temperament top 100 list From: Paul Erlich Dave, I have a different interpretation of what's going on here than you. Gene has gone about the process of finding 11-limit linear temperaments in several ways. Proceeding directly from a prescribed set of commas was never one that anyone thought would capture _the_ top 100, or top N, according to any badness function (of complexity and error). That's why Gene wrote "An" and not "The" in the title. Proceeding directly from commas is probably something that I've put more weight on than anyone else, but when there is more than one comma being tempered out, *straightness* enters the picture and some combinations of the "best" commas will be worse than some combinations that include a "non-best" comma. Gene has always seemed fully cognizant of this fact. Still, I think Gene should reply for himself! --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote: > --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith > <genewardsmith@j...>" <genewardsmith@j...> wrote: > ... > > The extra commas I suggested were all that was needed in the 7- limit > all had epimericity less than .46. I suggested .5 as a cutoff for > > the 7-limit and .3 for the 11-limit; I boosted this to .35, with a > 50 cent cutoff for size. This gave me the following list of 51 commas, > > in order of badness of the corresponding planar temperament: > > > > [9801/9800, 3025/3024, 3294225/3294172, 151263/151250, 441/440, > 385/384, 225/224, 2401/2400, 56/55, 176/175, 4375/4374, 540/539, > 64/63, 100/99, 250047/250000, 5632/5625, 36/35, 1375/1372, 126/125, > 45/44, 99/98, 43923/43904, 896/891, 81/80, 49/48, 50/49, 121/120, > 117649/117612, 55/54, 41503/41472, 1771561/1771470, 77/75, 4000/3993, > 6250/6237, 8019/8000, 6144/6125, 1029/1024,5120/5103, 3388/3375, > 3136/3125, 32805/32768, 245/242, 243/242, 128/125, 12005/11979, > 245/243, 1728/1715, 19712/19683, 625/616, 1331/1323, 2200/2187] > > > > Wedging these three at a time led to 6135 wedgies. Taking the best > 100 of these by geometric badness gave me my list. > ... > > Hi Gene, > > I was looking for names for linear temperaments I had found using > Graham's online finder, and I noticed this 11-limit one wasn't in your > list: > > Complex aug fourths > generator mapping [[1, ?, ?, ?, ?], [0, -7, -26, -25, 3]] > minimax generators [1200., 585.14] > minimax error 4.1 c > > Does this mean there is another 11-limit comma that should be added to > your list above? > > I called it "complex" in deference to this one in your list: > > > Tritonic > > [5, -11, -12, -3, -29, -33, -22, 3, 31, 33] [[1, 4, -3, -3, 2], [0, > -5, 11, 12, 3]] > > > > generators [1200., 580.274408364] > > bad 6158.168745 rms 5.154394 comp 70.204409
Message: 8781 Date: Thu, 11 Dec 2003 00:26:06 Subject: Re: Digest Number 862 From: Paul Erlich Aaron, hopefully this post will make it up soon, because my posts have not appeared in order. One crucial post I made before this one has not yet appeared, and it seems we are on bad footing as a result. Please be patient until that post appears. --- In tuning-math@xxxxxxxxxxx.xxxx "gooseplex" <cfaah@e...> wrote: > --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" > <perlich@a...> wrote: > > --- In tuning-math@xxxxxxxxxxx.xxxx "gooseplex" > <cfaah@e...> wrote: > > > > > imaginary because you invoked an army of like-minded > > > physicists in order to rebut my point of view, and this seemed > > > rather fantastical and unnecessary to me. > > > > Fantastical and imaginary as in untrue? > > > > > By the way, Paul, it wasn't necessary to go to the trouble. > > > > If it seemed untrue/imaginary/fantastical before, but now > seems true, > > then certainly *something* changed your mind . . . > > > Ah, I see the problem now. > > Paul, you have not told me anything I do not already know. You > started bringing in these legions of physicists to support your > argument from a physicists point of view and I told you that you > were missing my point completely. When I said that some > physicists would agree with me and some with you, I was talking > about agreement on the *real* issue at hand which is the > _mathematical _verses _the _musical _definition _of _the > _harmonic _series, which - I'm sorry - does not involve > acoustics! > > Sheesh, this has become a royal waste of time... > > Aaron
Message: 8782 Date: Fri, 12 Dec 2003 17:32:14 Subject: Re: Question for Manuel, Gene, Kees, or whomever . . . From: Manuel Op de Coul George wrote: >(For example, why are 64/63 and >63/32 being replaced by 45/44 and 88/45?) Because they have a lower van Prooijen harmonic distance value. Also a lower Erlich complexity, which is easier: log2( max( num and den without factors 2 ) ). Manuel
Message: 8786 Date: Fri, 12 Dec 2003 22:37:36 Subject: Re: Question for Manuel, Gene, Kees, or whomever . . . From: Manuel Op de Coul >However useful those criteria may be, I consider 64/63 and 63/32 >simpler because: >1) The prime numbers in the factors are lower; and >2) The range of numbers in the ratios (32 to 64) is lower (than 44 to >88). Still there are more consonant chords in the scale with the original pitches. Manuel
Message: 8789 Date: Fri, 12 Dec 2003 14:55:53 Subject: Re: Question for Manuel, Gene, Kees From: Carl Lumma >After fixing my program, here is what I am getting for Prooijen and >geometric 11-limit reductions: Thanks for the follow-up, Gene. I wonder what you and Manuel are doing differently? -Carl
Message: 8790 Date: Fri, 12 Dec 2003 23:13:35 Subject: Re: An 11-limit linear temperament top 100 list From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote: > I later added 12 more to my list of 100, but still don't find it on my > top 112 list. The reason seems to be that it is above the badness cutoff. > > Here's some information on Complex Augmented Fourths: > > Wedgie: [7, 26, 25, -3, 25, 20, -29, -15, -97, -95] > > Mapping: [[1, 5, 15, 15, 2], [0, -7, -26, -25, 3]] > > MT basis: <540/539, 896/891, 1375/1372> > > ets: 41, 80, 121 > > rms error: 2.583842867 > geometric complexity (natural log style): 124.3706717 > badness: 8006.869167 OK. Thanks. While it isn't anything to write home about, it doesn't seem as bad to me as the above complexity figure makes it. Can someone please explain what geometric complexity is, and how the badness figure is obtained?
Message: 8791 Date: Sat, 13 Dec 2003 00:10:17 Subject: Re: Question for Manuel, Gene, Kees, or whomever . . . From: Manuel Op de Coul George wrote: >Another question is: why 15/14 and 15/8 (when 16/15 would have been >the inversion of 15/8)? Then it wouldn't be epimorphic anymore, nor a constant structure. The alternatives are limited to changes by the unison vectors of the PB. Manuel
Message: 8792 Date: Sat, 13 Dec 2003 00:11:05 Subject: Re: Question for Manuel, Gene, Kees, or whomever . . . From: Manuel Op de Coul Gene, your geometric reduced scale isn't epimorphic. Is that a mistake? Manuel
Message: 8793 Date: Sat, 13 Dec 2003 00:12:52 Subject: Re: Question for Manuel, Gene, Kees From: Manuel Op de Coul Carl wrote: >Thanks for the follow-up, Gene. I wonder what you and Manuel are >doing differently? We used different periodicity blocks to optimise. At least that's what I think. Manuel
Message: 8796 Date: Mon, 15 Dec 2003 17:59:11 Subject: Re: Question for Manuel, Gene, Kees, or whomever . . . From: Manuel Op de Coul George wrote: >If 15/14 were changed to 16/15, the tuning would still be a constant >structure. Sorry, yes. I must have made a typo when I tried it. Those changes are ok indeed, since 225/224 is one of the unison vectors, the others are 3025/3024, 1375/1372 and 4375/4374. I'll change it in the archive too. >Is there now a definition that does not require a >degree in mathematics to comprehend? See Definitions of tuning terms: epimorphic, (c) 2002 by Joe Monzo * Considering all the higher than 11-limit ratios, I can imagine it would take a lot of time to change the diagram. >(I'm presently trying to finish up the rest of the >sagittal graphics for Scala.) Splendid, by the way I now don't use xpm files anymore, but png, but that doesn't matter to you. Manuel
Message: 8799 Date: Mon, 15 Dec 2003 19:11:19 Subject: Re: Question for Manuel, Gene, Kees, or whomever . . . From: Manuel Op de Coul > Can you tell me >where you think there is a problem? I checked and there's a numerical problem in Scala which was silently ignored. Thanks, I'll see if I can fix it. Manuel
8000 8050 8100 8150 8200 8250 8300 8350 8400 8450 8500 8550 8600 8650 8700 8750 8800 8850 8900 8950
8750 - 8775 -