... three ... But the names chords and scales (such as 'hexany') are defined such as to be invariant under transposition. ... Nothing is missing when you're...
... the ... distinguishing 'hexanies' ... transposed ... Indeed. No need for antihexanies (It was only because in the cubeoctohedron, the missing hexany items...
(I checked Wikipedia...Hendecagons have 11 sides, so Hendecachords have 11 notes) Some fun facts about 11-note chords in 22-tET: 32,066 chords after reducing...
... ball ... it ... corners ... they ... for ... counterexample? ... TOP ... no ... Where? Here: http://66.98.148.43/~xenharmo/kees.htm or in actual posts?...
... Great. Yahoo is again deleting my posts again and not telling me. The stretched TOP tuning has pure 7s, and the Kees tuning has the error of 3, over...
Suppose we have a linear temperament in the strict sense, so that the octave is the period. We then will have generator and period vals; suppose v is the val...
... Presumably the thing to do to generalize to any rank two temperament is to multiply by the number of periods to the octave. If we do that, we have both a...
Here is the same boring old list of 45 7-limit linear temperaments I keep reusing, this time sorted in terms of increasing badness, using the weighted kees...
Another idea we can try with this kees metric business is to refine the semistandard val. If v is a val, and if u has its p prime coordinate equal to the...
... complementible ... call ... then ... With the help of the Online Encyclopedia of Integer Sequences, here is the full grid for hendachords in 22-et: 110...
... Hendecachords ... 1 ... core ... partitions, ... found ... is ... because ... I realized that I am using the term "partition" in a non-orthodox way. What I...
... Just as 12-et has the Mathieu group M12 to go with it, 22-et has the (3-transitive) Mathieu group M22 to go with it. That might be worth exploring....
... <gwsmith@s...> ... <perlich@a...> ... for this ... What about the unstretched TOP tuning? That's what I was asking about. Recall that if *that* has pure...
... Okay I looked it up. It does correspond to the Steiner system S(3,6,22): (Summarizing) Out of 22 notes, each triple (triad) will appear in exactly one of...
... Because I'm defining a weighted linear complexity which depends on how many weighted steps it takes to get to an interval. Instead of "Kees complexity"...
... It seems to me the two measures should be proportional somehow. Or is your measure dependent on which interval you choose, rather than applying to the...
... It seems to me there are lots of possibilites. For instance, given any triad, there is a unique hexachord, and hence a unique complementary triad. That...
... I thought they wouldn't be, but apparently I'm wrong; for 5-limit temperaments based on a single comma, they seem to be in a proportion of log2(3)log2(5)....
I was discussing this a little on the tuning group: http://launch.groups.yahoo.com/group/tuning/message/60228 I didn't want to go into it more deeply there,...
... Yes...say does anyone know where I could get a listing of the 132 Steiner system blocks for S(5,6,12) and the 77 blocks for S(3,6,22)? (Both blocks of...
... <gwsmith@s...> ... be ... music... ... given any ... complementary ... Also, the order of each Mathieu group is a multiple of C(v,t) The remaining factors:...
Wilson's idea of having a recurrence relationship such that the ratios converge to a meantone with a particular brat, giving scales along the way, works if and...
Hello all, Brink showed me a tuning matrix, and i would like to create a Tonescape file of it. I'm interested in knowing what properties any of you might see...
... Whew! ... of ... Nice. So "comma complexity" and "generation complexity" do amount to the same thing after all. Are you with me that this is a significant ...
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