The 11-limit version of the breed temperament takes the same generators, a 49/40 neutral third and 10/7, and tempers them according to the {243/242, 441/440}...
... moments ... just ... step ... two ... another size ... keep ... of the ... small ... old ... B1. ... column ... C1 and ... pseudocode ... Very nice,...
... Thanks! Here http://web.syr.edu/~rsholmes/music/xen/scale_nonlinear.html you tell us: "One thing I initially found bothersome about Erlich's scales is ...
... get ... What I would like to do, if possible, is take two commas in 7-limit space, which I believe act as planes, find their intersection, which I believe...
... Your problem is that there isn't a unique solution. Finding the line you should know -- it comes down to finding the 2-D temperament. For finding the...
... line ... Could you give an example? ... commas ... three ... pair, ... Thanks. How do you fill out a square matrix with only two 7-limit temperaments in...
... Here's another interesting quote from the same page: "Note carefully he is saying 22-equal gives consonant harmony but out of tune scales -- the important...
... 12, 19, 26, 31, 43 and 55-equal are all meantones. So if you temper out 81:80, you need some other information to determine which two equal temperaments...
... I call on another black box function--Hermite reduction--in the case of finding vals, which in this instance means period and generator. However, these...
... The problem with the comma finding is that the initial commas had torsion, and TM reduction couldn't remove it. I suspect LLL wouldn't either, so it must...
... I'm not sure what example you are talking about; I was speaking in general. However, neither LLL nor TM reduction will remove torsion; it is, however,...
... Using this method with miracle, I get the following commas: (0, 3, 4, -5), (15, 0, 2, -7), (10, -1, 0, -3), (25, -7, -6, 0) which are all genuine commas....
... What I do is feed it to my favorite black boxes: first hermite reduction to get the basic answer, and then LLL to clean up the result in preparation to TM...
http://www-cse.ucsd.edu/users/daniele/papers/HNFalg.html www.scg.uwaterloo.ca/~glabahn/Papers/arne2.pdf Probably implementing one of these is more work than...
... The ... 1 ... temperament. ... This is very interesting. I've been playing with this in Excel. What troubles me though, is the fact that I obtain different...
... Why do you think you get different temperaments? The easiest way to determine if you get the same temperament is to take the wedge product, which Excel...
... What ... temperaments, ... I'll have to figure out a way to do wedgies in Excel. What I have done: Using 49/49 and 15/14 as chromatic unison vectors and...
Here is what I think to be an interesting marvel-tempered scale I'll call "stellar". It is formed by first taking the stellated hexany, aka the 2x2x2 chord...
... Presumably you mean 126/125&1029/1024. These give <<9 5 -3 -13 -30 -21||, which is the valentine temperament. You don't really get things such as "17" or...
... 126/125&1029/1028 ... don't ... Hmm when I take the adjoint I do get <17 26 39 48| and <15 24 35 42| as vals in the first two columns (!?) ... 2 ... ...
... I've got this: def hermite(m): result = [list(row) for row in m] for i in range(len(m)-1): for j in range(i, len(m)): if result[j][i] != 0: result[i],...
These are seven limit temperaments from a single comma, thus rank 3, and the ones considered here are planar in the strict sense--the octave is not divided...
Many of Ervs papers includes an actual formula which is quite simple. if you look at page 3 of http://anaphoria.com/meantone-mavila.PDF one starts with the log...
A simple yet effective way to get scales with a lot of some particular structure in them is to take the structure, dilate it by an integer factor N, and take...
Of the dilation scales, if we exclude chains of generators such as DE/MOS, the simplest examples will be planar--that is, the note classes can be arranged in a...
These are isosceles triangles in the breed plane, with b(n) = 2n^2+2n+1 notes, b(n-1) otonal tetrads, b(n-2) utonal tetrads, for a total of 4n^2-8n+6 tetrads,...
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