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Message: 5000 Date: Tue, 11 Jun 2002 19:48:51 Subject: bye From: Carl Lumma I'm singing off of yahoo groups. Tuning-math and harmonic-entropy tomorrow, and tuning when anything I'm involved in has died down. As always, I reserve the right to change my mind at any point. :) I'll keep up the tuning-math list at freelists.org for a time, if anybody's interested in it. If folks want to switch, I'm happy to do the grunt work, or anyone else who'd like to do it is welcome to what I have so far. The list is very configurable, so there's all sorts of things to vote on, though the current config should be at least as good as anything we've had so far. It's possible to subscribe many people in one go, such as everybody on tuning-math here. Maybe Robert Walker knows how to snag archives. Freelists' web interface and archive search seem quite good. As always, feel free to mail me at carl-lumma.org, where the - is to be replaced by an @. In particular, if Gene ever gets interested in harmonic entropy, or if Paul ever runs the validation exercise, if the new notation is released, or the search of planar temperaments turns up any really good 5-10 tone generalized-diatonics... and if any of you create music; I always love to listen, so drop me a note! -Carl
Message: 5001 Date: Tue, 11 Jun 2002 13:48 +0 Subject: Re: Help requested From: graham@xxxxxxxxxx.xx.xx In-Reply-To: <ae4erq+a8rm@xxxxxxx.xxx> kalleaho wrote: > What should I read in the Web and in the Lists to get a good > understanding of the notation and terminology used in tuning-math? As we haven't written up the processes yet, the best place is still the list archives. > I understand what linear temperaments are but the notation used is > not self-evident to me. I also have a basic understanding of > periodicity blocks but hmm... wedges? commatic/chromatic unison > vectors? Wedge products are explained at <http://mathworld.wolfram.com/wedgeproduct.html *>. The importance here is that the wedge product of the commas defining a linear temperament family is the complement of the wedge product of two equal temperaments belonging to the same family. The chromatic unison vector is the one you don't temper out to get a linear temperament. So for 7 note meantone, this is the chromatic semitone 25:24. Graham
Message: 5003 Date: Tue, 11 Jun 2002 19:49:22 Subject: A twelve-note, 11-limit scale From: genewardsmith This results from tempering a variety of Fokker blocks using the planar temperament defined by 126/125~176/175~1. I've used the 120-et for the results; since I already called the 108-et the crazy uncle of the family, I don't know where to place 120. Scale in 120-et [0, 8, 23, 31, 39, 50, 62, 70, 81, 89, 101, 112] Interval and triad count 5: 23, 12 7: 36, 36 9: 42, 58 11: 49, 82 Connectivities: 2 5 5 8 Fokker blocks which temper to this scale 1, 21/20, 8/7, 6/5, 5/4, 168/125, 10/7, 3/2, 8/5, 42/25, 25/14, 48/25 1, 21/20, 8/7, 25/21, 5/4, 4/3, 10/7, 3/2, 8/5, 5/3, 25/14, 40/21 1, 25/24, 144/125, 6/5, 5/4, 4/3, 36/25, 3/2, 8/5, 5/3, 9/5, 48/25 1, 21/20, 8/7, 6/5, 5/4, 4/3, 10/7, 3/2, 8/5, 5/3, 9/5, 40/21 1, 22/21, 63/55, 6/5, 5/4, 4/3, 63/44, 3/2, 8/5, 5/3, 9/5, 21/11
Message: 5005 Date: Tue, 11 Jun 2002 21:22:41 Subject: Re: A twelve-note, 11-limit scale From: genewardsmith --- In tuning-math@y..., "emotionaljourney22" <paul@s...> wrote: > i mention it in my paper, it's a pajara temperament. You mentioned the temperament, or 120-et? I don't see what either has to do with pajara, since 50/49 is 4 120-et steps and 64/63 is 3.
Message: 5007 Date: Wed, 12 Jun 2002 22:39:34 Subject: Two 9-note scales in the temperamentt From: Gene W Smith Commas {49/48, 21/20, 99/98, 121/120} Block [1, 12/11, 7/6, 14/11, 4/3, 3/2, 11/7, 12/7, 11/6] 22-et version [0, 3, 5, 8, 9, 13, 14, 17, 19] 5: 8, 0 7: 19, 11 9: 29, 41 11: 32, 56 31-et version [0, 4, 7, 11, 13, 18, 20, 24, 27] 5: 5, 0 7: 15, 6 9: 22, 17 11: 32, 56 53-et version [0, 7, 12, 19, 22, 31, 34, 41, 46] 5: 5, 0 7: 15, 6 9: 22, 17 11: 32, 56 Commas {128/125, 36/35, 99/98, 121/120} Block [1, 35/33, 33/28, 5/4, 175/132, 264/175, 8/5, 56/33, 66/35] 22-et version [0, 2, 5, 7, 9, 13, 15, 17, 20] 5: 12, 4 7: 22, 17 9: 27, 32 11: 30, 45 31-et version [0, 3, 7, 10, 13, 18, 21, 24, 28] 5: 12, 4 7: 21, 14 9: 25, 26 11: 30, 45 53-et version [0, 5, 12, 17, 22, 31, 36, 41, 48] 5: 12, 4 7: 21, 14 9: 25, 26 11: 30, 45
Message: 5010 Date: Thu, 13 Jun 2002 05:03:16 Subject: Re: A twelve-note, 11-limit scale From: genewardsmith --- In tuning-math@y..., "emotionaljourney22" <paul@s...> wrote: > that depends on your mapping! if you use pajara with a 710-cent > generator, you're in 120-equal! In this case, the mapping was defined by the fact that it had to temper out 126/125 and 176/175.
Message: 5011 Date: Thu, 13 Jun 2002 15:28:26 Subject: A 9-note scale in the planar temperamentt From: Gene W Smith I looked at a number of these, and this was the best I found: Block [1, 11/10, 8/7, 5/4, 11/8, 16/11, 8/5, 7/4, 20/11] 22-et version [0,3,4,7,10,12,15,18,19] 3: 2 0 5: 11 4 7: 19 12 9: 29 39 11: 33 63 11-limit connectivity 7 31-et version [0,4,6,10,14,17,21,25,27] 3: 2 0 5: 11 4 7: 19 12 9: 22 15 11: 32 58 11-limit connectivity 6 46-et version [0,6,9,15,21,25,31,37,40] 3: 2 0 5: 11 4 7: 19 12 9: 19 12 11: 32 58 11-limit connectivity 6
Message: 5015 Date: Fri, 14 Jun 2002 18:47:34 Subject: Re: Finding linear temperaments From: Gene W Smith Of course, people studying the Riemann Zeta function may in effect have used computers to find ets before anyone, without knowing it. On the last page of Titchmarsh, "The Theory of the Riemann Zeta-Function" (Oxford, 1951) he mentions the 140-et without knowing it, and one of the first things to get worked over when computers came along was Zeta(s).
Message: 5016 Date: Sat, 15 Jun 2002 19:32:03 Subject: Re: figurate number expansions as scales From: genewardsmith --- In tuning-math@y..., "D.Stearns" <STEARNS@C...> wrote: > Some interesting expansions and scales can be derived from figurate > numbers. Numbers of the form n/(n-1) where n is figurate show up a lot; you could look at my discussion of "jacks", for instance. The fact that triangle and square demomenators lead to other triangle and square denomenators allows us to create series of scales.
Message: 5018 Date: Sat, 15 Jun 2002 11:30:02 Subject: Re: A common notation for JI and ETs From: dkeenanuqnetau --- In tuning-math@y..., "gdsecor" <gdsecor@y...> wrote: > I would therefore recommend going back to the rational > complementation system and doing the ET's that way as well. Agreed. Provided we _always_ use rational complements, whether this results in matching half-apotomes or not. > Or, if you like, we could do them both ways and then decide. No need. > I would be agreeable to doing all of the ET's (with the rational > complementation scheme) using the symbols that we agreed on in > message #4443. OK. I will respond to your suggestions for the remaining ones of 6 or less steps per apotome when I get more time. Then move on to 7 steps per apotome 42,49,56,63,70,77,84,91,98,105 8 steps per apotome 54,61,68,75,82,89,96,103,110,117 9 steps per apotome 59,66,73,80,87,94,101,108,115,122,129 10 steps per apotome 71,78,85,92,99,106,113,120,127,134,141 etc. I think we can do some with 23 steps per apotome, maybe even 25.
Message: 5021 Date: Mon, 17 Jun 2002 03:12:55 Subject: Seven and eleven limit comma lists From: genewardsmith Here are comma lists for the 7 and 11 limits. Each comma is less than fifty cents, and each has the property that if the comma is p/q>1 in reduced form, then ln(p-q)/ln(q) < .5 in the 7-limit, and < .3 in the 11-limit. I've found this weaking of the superparticularity condition useful in the past, and it occurred to me it would be one way of getting a finite list of temperaments a la Dave--we could simply require it to have a basis of commas passing such a condition. The lists below may be complete; at least, I haven't been able to add to them. Seven limit list, ln(p-q)/ln(q)<1/2, cents < 50 [1029/1000, 250/243, 36/35, 525/512, 128/125, 49/48, 50/49, 3125/3072, 686/675, 64/63, 875/864, 81/80, 3125/3087, 2430/2401, 2048/2025, 245/243, 126/125, 4000/3969, 1728/1715, 1029/1024, 15625/15552, 225/224, 19683/19600, 16875/16807, 10976/10935, 3136/3125, 5120/5103, 6144/6125, 65625/65536, 32805/32768, 703125/702464, 420175/419904, 2401/2400, 4375/4374, 250047/250000, 78125000/78121827] Eleven limit list ln(p-q)/ln(q) < .3, cents < 50 [36/35, 77/75, 128/125, 45/44, 49/48, 50/49, 55/54, 56/55, 64/63, 81/80, 245/242, 99/98, 100/99, 121/120, 245/243, 126/125, 1331/1323, 176/175, 896/891, 1029/1024, 225/224, 243/242, 3136/3125, 385/384, 441/440, 1375/1372, 6250/6237, 540/539, 4000/3993, 5632/5625, 43923/43904, 2401/2400, 3025/3024, 4375/4374, 9801/9800, 151263/151250, 3294225/3294172]
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