Take the 924 hexachords (12C6). The sum of their interval vectors is (10C4 * 12) for 1,2,3,4,5 intervals and (10C4 * 6) for tritones. (The proof is in a...
... Here's the full grid for the 924 hexachords, where each cell is divided by 12 (6 for tritones): 0 0 0 0 0 0 5 4 4 0 5 80 50 55 48 81 50 120 100 90 112 54...
The pseudoinverse of a matrix is explained here: http://en.wikipedia.org/wiki/Pseudoinverse If M is a (real) matrix, M' its transpose, then the pseudoinverse...
... Identical to the precision you gave! 1898.4580145736695 1201.2421562716497 Those figures are full precision, and so may be inaccurate in the last digits....
Can you upload or email a copy of this in a word document to retain its formatting? I couldnt make out over half of the text as it seems the formating was ...
Quick question: Is there anything in the definition of a periodicity block that requires all intervals within the block to be larger than the block's unison...
Hi all Reference to my previous mails and considering definition of "schisma" by Philolaus <http://tonalsoft.com/enc/s/schisma.aspx> as (Pythagorean...
Hi all For any EDO , showing an interval (X) near to Pythagorean comma : If we have a fifth as 700+((X)/12) , so it is a good approximation for pythagoean...
Hi This is also true for EDOs with commas greater than pythagoean like 94 , 200 , 335 , 429 , 576-EDO. Shaahin Mohajeri Tombak Player & Researcher , Microtonal...
(Sent to both Tuning and Tuning-math; please ignore it in whichever group it doesn't belong -- I can't figure it out.) Can anyone point me to any work done on...
Maybe you missed the link from my page to here: http://www.kees.cc/tuning/s357.html That's a list of unison vectors and resulting ETs on that lattice. (I admit...
Hi all Refering to : http://launch.groups.yahoo.com/group/tuning/message/68142 <http://launch.groups.yahoo.com/group/tuning/message/68142> using scala , you...
... 5/3 and 7/3 define a group with two generators, hence the situation is analogous to the 3-limit. Periodicity blocks are one-dimensional, and can be found...
Hi all I have noticed that, in music theory, multivectors and wedge products are sometimes used (for instance see http://tonalsoft.com/enc/encyclopedia.aspx)....
... It doesn't work for me. I may have used it before -- at least something similar. ... I use Python for lots of things and I've copied code to Ocaml, C, and...
... I haven't heard of it, but thanks for telling us about it. ... I use it for pure math stuff rather than music, but a freeware program I like and which can...
... I don't think there is much, if anything, new here. Systematic ways of defining division by zero go back to the introduction of zero by Brahmagupta, and...
I've added another search at http://x31eq.com/temper/ so if you want to find temperaments by RMS Tenney-weighted prime limit errors and complexities, you can...
Hello all, I've just updated my webpage on valve trumpet intonation, http://tonalsoft.com/monzo/trumpet/trumpet-intonation.htm greatly expanding the old table...
... AARRRRRRRGGGGGHHH !!!!!!!!! So no matter how much trouble a poster goes thru to format a table correctly, Yahoo is determined to sabotage it. Sucks. -monz ...
... Looks fine in my e-mail client. But, though I didn't read your page, I generally don't like this sort of thing because it tends to imply the trumpet's...
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