... This torb24 scale isn't epimorphic, of course, but it has a related property of abelian group structure nonetheless. It shows in the following way: if we...
... Not easier, but perhaps more elegant--a Fokker block. An example Fokker block with C2 x C12 structure, obtained from commas 648/625 and 2048/2025, is 1,...
... the ... and ... steps, ... Could you explain epimorphic again? I looked it up in Tonalsoft, but don't quite get it. Is h=<12 19 28). How does h(qn)=n? Paul...
same as superparticular. the top number is one higher than the lower.as in 3/2, 7/6 49,48 etc. If you construct a lambdoma with any series where one uses...
... Heya Kraig, You're thinking of epimoric http://tonalsoft.com/enc/epimore.htm Gene's got something else called "epimorphic". Paul E. possibly understands...
... "h" is whatever it needs to be to make the epimorphic condition true; you can find it by sticking the scale in Scala and using the show data command. Let's...
Hi Gene, How does one effect the reduction to SNF? Yahya ... From: "Gene Ward Smith" <gwsmith@...> Subject: Smith normal form I've talked quite a bit about the...
... I'd recommend using a program (eg Maple, Mathematicia, etc.) which has such a reduction function already available. If you want to write your own, I am...
This whole torsion business started out with the question of what you get by tempering a Fokker block, and Paul's hypothesis, so it is interesting to note that...
Here are 7-limit r2 temperaments which have a MOS less than 40 in size, and greater than or equal to their 7-limit Graham complexity in size. I've also...
... but ... true; ... data ... corresponds ... scale ... but ... abelian ... being ... I take it S=24, G=2 and Z=12? one free part, like the integers Z, and a...
... Sorry, wrong h. I forgot to edit the above so that h = <7 11 16| after deciding to use a seven note scale example. If we use the right h, h(3/2) = <7 11...
Here is a curiosity for anyone who finds Blackjack too boringly regular. This is detempered to 1/4 kleismic marvel, so that some of the chords become more...
By "memag", I mean the 19-note Fokker blocks uaing 81/80 and 3125/3072 as commas. One of these, "memag.scl", is already known to the Scala archives as...
... Yes, I thought it was those commas. Interesting. Another question: What is the value of epimorphic scales? What special properties do they have?...
... Epimorphic scales, and the very closely related property of constant stucture scales, give the scale a systematic, orderly structure. If a fifth consists...
This is a permutation epimorphic 7-limit scale, both Hahn and TM reduced, for <18 29 42 50|. Since this val does not order the 7-limit diamond in increasing...
The symmetrical lattice norm on 5-limit note classes is given by ... This produces the familiar lattice where triads are equilateral triangles, and the 5-limit...
If s is a set of notes, then diamond(s) is the set of notes which are octave reductions of ratios of elements of s--the diamond of s. By a 5-limit diamond...
... A few observations: If we use four generators for the diamond, the only way to get a tetrad is from {1,3,5,7}--so we get the 7-limit tonality diamond. The ...
... wrote: If we add two such integers, we get many ... This doesn't make it completely unique, I should add. If we don't assume we need to start from...
The complete list of marvel-tempered 5-limit diamonds of 19 notes or less and containing 7 otonal tetrads or more consists of three scales, generated from...
... wrote: Here is a list of all marvel diamonds with six generators and of 21 notes or less and 8 otonal tetrads or more. They all have exactly this many, and...
... The list has duplicates--for instance the first two are the same (and the same as rostaim, the marvelized Dante Rosati scale) and the second two are...
Hello, Excuse me if my post results to be off-topic, but I could find no help with this anywhere else. I am trying to build an electronic musical instrument...
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