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Message: 3926 - Contents - Hide Contents Date: Thu, 21 Feb 2002 10:40:35 Subject: Re: 4296 From: genewardsmith --- In tuning-math@y..., "Orphon Soul, Inc." <tuning@o...> wrote:> If you run the Brun algorithm with ONLY the fourth or fifth, 4296 shows up > as a 3rd limit temperament. But the fact that it also shows up in so many > 5th limit algorithms with so many different shaped convergence webs, I found > it to be extremely ductile.It is a semiconvergent for *both* log2(3) and log2(5) (reducing 9975/4296 to 3325/1432 in the case of log2(5)). This is a rather amazing property, and it would be interesing to know what else, if anything, shares it.
Message: 3928 - Contents - Hide Contents Date: Thu, 21 Feb 2002 12:17:42 Subject: Re: 4296 From: paulerlich --- In tuning-math@y..., "Orphon Soul, Inc." <tuning@o...> wrote:> On 2/20/02 2:02 AM, "genewardsmith" <genewardsmith@j...> wrote: >>> The first comma is the smallest one on my list of best 5-limit temperaments, >> and gvies us the map [[0, 49, 15], [1,-6,0]]. This divides the 5 into 15 >> parts, and if we tempered 71 or 84 notes by it, we would get a lot of >> essentially just ratios. If Mark has no objection, perhaps the "Jones" would >> be a good name for this temperament; the Jones generator being 665/4296, >> slightly short of satanic. If we take the Jones comma and wedge it with ... >> Err I didn't see this part before. > > (Wrinkling eyebrows, smacking stale aftertaste...) > > I umm... Naming a TEMPERAMENT after me? Jeesh. Which one are you saying? > 665 or 4296?neither. gene is talking about the _linear_ temperament, not _equal_ temperament, whose _generator_ is about 665/4296 of an octave, but not exactly -- its tuning can be optimized in various ways, so that it will be (inaudibly) different from 4296-equal. kind of like the optimal meantone generator is about 29/50 of an octave, but not exactly . . .
Message: 3929 - Contents - Hide Contents Date: Thu, 21 Feb 2002 12:20:49 Subject: Re: 4296 From: paulerlich --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "Orphon Soul, Inc." <tuning@o...> wrote: >>> If you run the Brun algorithm with ONLY the fourth or fifth, 4296 shows up >> as a 3rd limit temperament. But the fact that it also shows up in so many >> 5th limit algorithms with so many different shaped convergence webs, I found >> it to be extremely ductile. >> It is a semiconvergent for *both* log2(3) and log2(5) (reducing 9975/4296 to 3325/1432 in the case of log2(5)).don't forget to try log2(5/3).>This is a rather amazing property, and it would be interesing to know what >else, if anything, shares it.if you're allowed to reduce like this, 12 does, because 28/12 = 7/3.
Message: 3930 - Contents - Hide Contents Date: Thu, 21 Feb 2002 20:57:43 Subject: comments sought From: paulerlich Chapt. One, IV.4. Group Theory * [with cont.] (Wayb.)
Message: 3932 - Contents - Hide Contents Date: Thu, 21 Feb 2002 23:32:44 Subject: monz's et graph (from my lumma.gif) From: paulerlich hey guys, in the first graph here: Definitions of tuning terms: equal temperament... * [with cont.] (Wayb.) there's no label on the linear temperament that goes through 12, 73, 61, 49, and 37. what is it?
Message: 3933 - Contents - Hide Contents Date: Thu, 21 Feb 2002 19:09:54 Subject: Re: 4296 From: genewardsmith --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:> if you're allowed to reduce like this, 12 does, because 28/12 = 7/3.Yes, this occurred to me after I posted. It would be interesting to know if anything is a semiconvergent for 3/2, 5/3, and 5/4, but these should be finite in number, and if you don't get one fairly quickly you will probably not get one at all.
Message: 3934 - Contents - Hide Contents Date: Thu, 21 Feb 2002 17:05:34 Subject: Re: magma From: Carl Lumma>>>> >ay be of interest to some here: >>>> Magma Computational Algebra System Home Page * [with cont.] (Wayb.) >>>>>> are you sure that's the correct link? >> >> Yes. -C. >>well, i just get "The page cannot be displayed"It's been coming through fine here. Maybe something between you and it is just down. Try "refresh" lately?>carl, why won't you answer us on the tuning list? we're asking about >the cd you made for me of various a capella groups. could you discuss >them please on tuning?Gee, I thought I did respond... here it is: 34636. I've switched to digest mode for tuning and single e-mails for this group and harmonic entropy (stayed web for metatuning), so tuning may take a little longer. BTW Gene, those ad blocking services work by filtering all your http traffic through their server. I think it's safe to say this cannot be a good idea, even without resorting to paranoia. -Carl
Message: 3935 - Contents - Hide Contents Date: Thu, 21 Feb 2002 17:52:34 Subject: Re: comments sought From: Carl Lumma () Any article on Mozart introducing his works by their location in the movie "Amadeus" is automatically disqualified. () Mozart's "formula" doesn't look like very much of a formula at all to me. It looks a loose description -- a lot like the standard music theory the author (correctly) criticizes at the beginning of the article. Let's see the "formula" applied from scratch into something that sounds like Mozart; then we'll talk. () "practically every musical composition has mathematical underpinnings" You can use math to describe almost anything. How deep these descriptions are, how much explanatory power they have for why we like music, is another thing... "the chromatic scale is a simple logarithmic equation", for example, explains nothing. () "Thus, the beginning of Beethoven's Fifth symphony, when translated into mathematical language, reads just like the first chapter of a textbook on group theory, almost sentence for sentence!" I'll leave this to Gene and those who know group theory. Doesn't strike me that that much is being said here, other than a discussion (as opposed to a prediction) of the 5th symphony using fancy lingo. () "He wanted to implant the idea of the theme in our brain before we heard it!" Okay, okay. So what? () There seems to be a lot of good advice on practicing the piano on this site, though I'm still working my way through it. -Carl
Message: 3936 - Contents - Hide Contents Date: Thu, 21 Feb 2002 19:37:35 Subject: Re: comments sought From: monz> From: Orphon Soul, Inc. <tuning@xxxxxxxxxx.xxx> > To: Tuning Math <tuning-math@xxxxxxxxxxx.xxx> > Sent: Thursday, February 21, 2002 3:25 PM > Subject: Re: [tuning-math] comments sought > > > ... > I keep going back to Beethoven's first piano sonata, it's almost like a > fractal structure the way things move around and fold into each other. > Almost like origami.hmmm... that's really interesting, marc. i can see a lot of Beethoven's work in that light, now that you mention it.> I can't ever say exactly what it means to the general > public but I can tell be all the fidget factors he had a solid grip on being > able to balance and calm the mind enraged. Only because if he didn't, in > certain states of mind I wouldn't be able to listen to him.that's really interesting.> There's a sense > of nested scales in his variations as well. A melody will move up into > arpeggiating a different chord, one note will be a diatonic step away, one > note will be a chromatic step away etc. Well not etc. I don't recall any > specific 17 or 19 implications in altered intervals as they evolved.hmm ... i don't recall Beethoven using anything that resembles 19, but i'd say that he certainly implied 17 a l o t in his compositions, both melodically (the "flat 9th" or "flat 2nd") and harmonically (frequent "diminished-7th" chords which imply 10:12:14:17). it's amazing to me how Beethoven could capture in his piano pieces what i c l e a r l y hear as improvisations. in good performances of much of his piano music, i can almost see Ludwig himself sitting at the keyboard making it up on the spot.> Other than the fact that there's an Fb on the first page of the first > piano sonata. I thought that was so cool.whoa! -- it's getting scary now, you and i have thought so many similar things. when i first bought an old used copy of the _32 Sonatas, volume 1_ at Settlement Music School back in the 1970s, i opened to the first page and that was my exact response when i saw the Fb: "wow, that's so cool!".> Oh actually, no, in his first few piano sonatas at least, > IIRC he [Beethoven] works with a span of 19 fifths. Heh.it's been a few months now since i worked on it, but i recall that Mozart used a span of 20 "5ths" in the 1st movement of his 40th Symphony. the Symphony is in G-minor, so G=1/1 gives a meantone chain from -8 (Cb) to +11 (B#) "5th" generators. in my MIDI rendition of the beginning of the piece in 55edo Internet Express - Quality, Affordable Dial Up... * [with cont.] (Wayb.) i was careful to tune the sharps and flats differently to reflect Mozart's notation, which had to be done by hand because none of the programs i know of (Manuel's Scala, Graham's Midiconv, John deLaubenfels adaptune) can retune to more than 12 tones per octave. -monz _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at Yahoo! Mail - The best web-based email! * [with cont.] (Wayb.)
Message: 3937 - Contents - Hide Contents Date: Fri, 22 Feb 2002 00:27:30 Subject: Re: monz's et graph (from my lumma.gif) From: Carl Lumma>Definitions of tuning terms: equal temperament... * [with cont.] (Wayb.) > >there's no label on the linear temperament that goes through 12, 73, >61, 49, and 37. what is it?In Herman Miller's version, you can see that 25 is on the other side of 37 from 12. The 64:63 vanishes as a 7-limit comma in 27, 37, 49, and 12, and as a 9-limit comma in 61. I can't seem to get it to vanish in 73. The generator could be 98 cents... 6/73 gives MOS of 61, 49, 37, 25, 13, and 12 according to Scala. As a method for finding generators from a series of equal temperaments, maybe a spreadsheet that graphs each temperament's intervals on a line. Where the lines get close, you have common generators. Any Excel wizards out there think this is a good idea? More to the point, every line on this plane is a linear temperament, right? So what makes low-numbered (less than 100) equal temperaments cluster on some of them? Finally, re the jumping jacks / ideal comma question... what's the question? How are we defining "most powerful" comma? Have we decided? What's the relationship between a comma vanishing and a map? I say the most powerful maps are the ones with the smallest numbers in them. Sum of abs value would work. What do y'all think? -Carl
Message: 3938 - Contents - Hide Contents Date: Fri, 22 Feb 2002 03:45:12 Subject: Re: magma From: genewardsmith --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:> --- In tuning-math@y..., Carl Lumma <carl@l...> wrote:>> BTW Gene, those ad blocking services work by filtering all your >> http traffic through their server. >> are you serious?? someone tell me this isn't so.It's not true of Proxomitron, at least, since that is a program, not a service: Some time ago I began to notice that many of the wonderful new features added to web browsers, far from making pages better, were instead making the web a more and more hostile place! Cramped frames, pop-up windows, music you can't shut off, stroboscopic animations, and and ever increasing deluge of slow loading advertising content were making web viewing something akin to trying to read a novel in the middle of Times Square on New Years Eve! I decided to try and create a general purpose solution - one that could not only stop the aggravations of today, but also any demonic HTML tags lurking in the future. Thus the Proxomitron was born! At it's heart is a powerful text matching engine. Similar to wildcards and regular expressions, but specially designed for HTML, it can re-write web pages on the fly. Think of it like a very powerful "Search and Replace" for the web. Troublesome HTML can be altered or removed and new content can be added - even your own JavaScripts! By simply selecting some of the many included filters, you can say goodbye to common nuisances like animated GIFs, pop-up windows, advertising banners, dynamic HTML and more. Best of all, these rules are not hard-coded. More than simply flexible - You can completely change them, make them more powerful, and of course, add rules of your own! If it can be written in HTML, it can probably be controlled by the Proxomitron. The final power is yours! Not only can the filters stop general aggravations, but web pages you visit often can be completely customized to suit your own taste. Don't like someone else's choice of colors, fonts, or backgrounds? Use your own instead. Delete useless frames or even change their JavaScripts to work the way you want. There's really no limit! --------------------------------------------------------------------------------
Message: 3939 - Contents - Hide Contents Date: Fri, 22 Feb 2002 07:30:20 Subject: Re: comments sought From: monz> From: <manuel.op.de.coul@xxxxxxxxxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Friday, February 22, 2002 5:20 AM > Subject: Re: [tuning-math] Re: comments sought > >>> What do you mean? Midiconv doesn't have any 12-fetishism! >> I don't think Scala does either. >> They don't, but Joe means the MIDI 12-fetishism. If there's > a F# and a Gb in the score, we aren't able to guess which > because they have the same note number in the MIDI-file.thanks for clarifying that, Manuel. yes, the fault is not with the software designers but with MIDI.> Still doing _all_ notes by hand what Joe does is a waste > of time.that's true, Manuel, and i thank you publicly here for providing me with the entire Mozart 40th retuned to a 12-tone subset of 55edo by Scala. when i ever find time to go back to this project, i can continue by starting from your file and simply changing the pitch-bend on the few required notes (at least i hope it's a few!). -monz _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at Yahoo! Mail - The best web-based email! * [with cont.] (Wayb.)
Message: 3940 - Contents - Hide Contents Date: Fri, 22 Feb 2002 00:32:44 Subject: Re: monz's et graph (from my lumma.gif) From: Carl Lumma>The 64:63 vanishes as a 7-limit comma in 27, 37, 49, and 12,That's supposed to be *25*, 37, 49... -Ca.
Message: 3941 - Contents - Hide Contents Date: Fri, 22 Feb 2002 03:46:39 Subject: Re: comments sought From: genewardsmith --- In tuning-math@y..., "paulerlich" <paul@s...> wrote: If you take out the drivel pretending to be math, you are left with an analysis of how Mozart and Beethoven use motives to build themes.
Message: 3942 - Contents - Hide Contents Date: Fri, 22 Feb 2002 17:10:44 Subject: Re: comments sought From: manuel.op.de.coul@xxxxxxxxxxx.xxx Another possibility is to see if there are unused note numbers in the MIDI-file, change the note numbers of the special notes to those free ones, and retune the whole file in one go with Scala using a 128-note scale with the right pitches. Then you don't need to calculate pitch bends, and you can try different tunings too with very little effort. Manuel
Message: 3943 - Contents - Hide Contents Date: Fri, 22 Feb 2002 08:41:37 Subject: Re: proxomitron From: genewardsmith --- In tuning-math@y..., Carl Lumma <carl@l...> wrote:> Ad blocking software still doesn't address many of my concerns.It doesn't address all my concerns either, but it seems clear a Usenet group isn't about to happen.
Message: 3944 - Contents - Hide Contents Date: Fri, 22 Feb 2002 09:08:25 Subject: Re: [tuning] Monzo's lines From: monz> From: genewardsmith <genewardsmith@xxxx.xxx> > To: <tuning@xxxxxxxxxxx.xxx> > Sent: Friday, February 15, 2002 12:12 AM > Subject: [tuning] Monzo's lines > > > Here are more comma for the lines on Joe's graph at: > > Definitions of tuning terms: equal temperament... * [with cont.] (Wayb.) > > .. > The 59-71-12 line goes with 2^29 3^-8 5^-7 = 536870192/512578125. > ... > Finally the Orwell line of 22-75-53-84-31 is associated to the > semicomma, which is 2^29 3^-8 5^-7 = 2109375/2097152.there's a typo here. i'm assuming that the ratio for the semicomma is correct, in which case the prime-factoring is [2 3 5]**[-21 3 7]. Gene, where did you get the name "semicomma"? -monz _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at Yahoo! Mail - The best web-based email! * [with cont.] (Wayb.)
Message: 3945 - Contents - Hide Contents Date: Fri, 22 Feb 2002 00:51:11 Subject: Re: proxomitron From: Carl Lumma>It doesn't address all my concerns either, but it seems clear a Usenet >group isn't about to happen.I've never used the usenet, but it seems like it would be so much better. -Carl
Message: 3946 - Contents - Hide Contents Date: Fri, 22 Feb 2002 09:18:53 Subject: Re: [tuning] Re: Monzo's lines From: monz> From: genewardsmith <genewardsmith@xxxx.xxx> > To: <tuning@xxxxxxxxxxx.xxx> > Sent: Friday, February 15, 2002 9:22 PM > Subject: [tuning] Re: Monzo's lines > > > --- In tuning@y..., "monz" <joemonz@y...> wrote: >>>> here are a few more linear axes that i can see >> on my adaptation of paul's graph of 5-limit ETs: >> >> Definitions of tuning terms: equal temperament... * [with cont.] (Wayb.) > > ... > >> 26-99-73 >> 2^10 3^40 5^23that's a typo: the minus sign is missing from 3^-40. the correct prime-factoring is [2 3 5]**[10 -40 23] . -monz _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at Yahoo! Mail - The best web-based email! * [with cont.] (Wayb.)
Message: 3947 - Contents - Hide Contents Date: Fri, 22 Feb 2002 08:51:50 Subject: Re: monz's et graph (from my lumma.gif) From: genewardsmith --- In tuning-math@y..., Carl Lumma <carl@l...> wrote:> The generator could be 98 cents... 6/73 gives MOS of 61, 49, 37, 25, > 13, and 12 according to Scala.Right--the comma is 262144/253125, and the rms generator 98.317 cents.
Message: 3948 - Contents - Hide Contents Date: Fri, 22 Feb 2002 18:20:08 Subject: Re: [tuning] Monzo's lines From: manuel.op.de.coul@xxxxxxxxxxx.xxx> Gene, where did you get the name "semicomma"?From Fokker, via the Scala interval list. Manuel
Message: 3949 - Contents - Hide Contents Date: Fri, 22 Feb 2002 00:52:53 Subject: Re: monz's et graph (from my lumma.gif) From: Carl Lumma>> >here's no label on the linear temperament that goes through 12, 73, >> 61, 49, and 37. what is it? >>In Herman Miller's version, you can see that 25 is on the other side >of 37 from 12.He also gives the 5-limit comma for this series as [-4 -5]. -Carl
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