Hi Dan, ... Well, as you can see from what i wrote, if you carry out the division of the pythagorean-comma's ratio, 531441/524288, as far as it will go, you...
I've adapted Gene's Kees integral tuning, as far as I understand it, to Tenney weighting for arbitrary regular temperaments. The result is that it gives the...
Enter your vote today! A new poll has been created for the tuning-math group: Should we move this list to Google Groups? o Obviously. o No way. To vote,...
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Apr 2, 2007 4:33 pm
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This site is relevant Erv Wilson's lattices, polytopes in general, and the recent pix of the E8 sporadic Lie Group widely distributed in the media this past ...
... Thanks, Graham. I was going to try to see if TOP-RMS is what it did (which seemed as if it ought to be the case.) Note that this makes SDT the Kees and...
Since I posted to URL to Tony Smith's pages, I've followed some of the links. Take what he says with a large grain of salt-- the math may be correct, but his...
... Sorry, I shouldn't be oracular. Check this out: http://en.wikipedia.org/wiki/Equidistribution_theorem http://mathworld.wolfram.com/WeylsCriterion.html...
... Right. I think the proof's actually wrong but the result's still correct. I'll fix it sometime. ... We don't know it always works for the STD: only in...
... It says don't reply to this email, but i am, because i'd like to know more about the pros and cons of both choices. -monz http://tonalsoft.com Tonescape...
... It didn't make sense to me, since it seemed you were using measure polytopes = rectangular hypersolids and not cross-polytopes (n-dimensional octahedrons)...
... Octahedrons? I can see replacing hypercubes with hyperspheres would be more valid, but also more difficult. For now you get weighted hypercubes. What I...
... Tenney wouldn't be a problem, but for 7-limit Kees you are integrating over the Kees unit ball. You'd need to decompose that into pieces you could...
... 41 ... are ... Theory" ... exactly ... offered ... out ... expected ... Question: Since E has to be 1 mod p, would my list have any bearing with respect to...
... Alright, speaking of Googel Groups - I have seen there is this group over there: http://groups.google.com/group/microtonality/ Is that one of "us"? Last...
Monz, thanks for the reply, sheds more light on the whole affair, you could be right about Temple. Regardinging the numbering system of the Sumerians, wasn't...
Hi Dan, ... The Sumerians used ordinary base-10 for everyday stuff, the same as we do. For their more intricate math calculations, they used base-60. Their...
The message quoted below comes from the tuning list: http://launch.groups.yahoo.com/group/tuning/message/71261 Since George wrote that response to Gene's...
It looks as though my post quoted below was the kiss of death for this thread. :-) So I'm just summarising here all the notational commas that got a mention,...
... The 3-limit intervals alike the apotome 3^7/2^11 = 2187/2048 are usually approximated by the: http://www.research.att.com/~njas/sequences/A060528 ...
... Since the 3 error in 2460-ET is extremely low (less than 0.78% of 1deg2460, or 0.00378 cents narrow), I'd say that the two are virtually identical. For...
... Hi Andreas, Your delta-prime which is one degree of 16266-EDO or 1541-EDA (apotome) is certainly in the right size range and is brilliant for approximating...
... When division by two cannot be multiply the thing, by three. When even numbers are in play halve it down all the way. is how I'd translate it, but...
... Dear George, http://mathworld.wolfram.com/PythagoreanTriple.html "The first few primes of the form 4x+1 are 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101,...
... Pschoacoustic experiments yield the result that our brains represent neurologically 5-limit internally as correlate of 2^15/3^8 = 32768/6561 = ~4.99436... ...
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