... Myhill's property is another kind of MOS, but definitely assuming period=octave IIRC. There's an obvious link between MOS scales and propriety which I...
... in a ... Thanks. I will study these proofs. Is it true that subsets of the pentatonic and diatonic also have Myhill's property? Are there other interesting...
I've started to take an interest in the beatles 7-limit temperament [<1, 1, 5, 4], <0, 2, -9, -4]> TOP-MAX P = 1197.104145, G = 354.720338 TOP-RMS P =...
... After choosing symbols for magic tripod notation ... and getting it wrong ... I've decided that I don't like the Athenian ET notations. It's better to...
... Another thing to consider is the size of fifths in beatles temperament. The fifths at the far ends of the chain are far enough off that "B" sounds sharp...
... Sagittal ... step of ... interval in ... Hi Herman, As I recall, Dave & I chose symbols for the 27-equal notation that corresponded to the lowest primes...
... Yes, all of those are consistent with beatles. The full list of symbols my program came up with for the (-2, +7) interval is: )| '|) )/|\ .||) of which )|...
One of the things I've had some interest in, but not much success, is coming up with a notation system that might have developed in a musical culture where...
... That approximates as every other step of Negri10, or as the 5 note MOS of one of these no-fives "bug" type temperaments. It's not a very accurate...
... Well, that's an example of symmetrical notation. You can go 4 steps up and 5 steps down (or vice versa). ... You don't need both of them to be notated from...
As a first attempt, I'm starting with the assumption that the notation system I'm looking for will have names for 4/3 and 3/2 -- for simplicity I'll call the...
... how about http://launch.groups.yahoo.com/group/tuning/message/81808 as second approxiamtion with other useful properites? Represented in extended...
Question: Has anyone here studied any of these lattices, in relationship to musical tuning? 1. A2.12 sublattice of the Leech Lattice (one of 23 Neimeier...
Let's get this out of the other chain:) Question: Has anyone here studied any of these lattices, in relationship to musical tuning? 1. A2.12 sublattice of the...
WOLFGANG VON SCHWEINITZ REDCAT January 24th, 2009 http://redcat.org/season/0809/mus/schweinitz.php "[Plainsound Glissando Modulation is] one of the most...
... Or, to the contrary, we have the option to keep those accidentals. The 2401/2400 ratio is a very small interval, around 0.7212 cents, but it can be...
This may be of interest: http://www.science-bookmarks.com/2009/04/very-short-history-of-mathematics.html I don't see direct citations, and I don't quite agree ...
Here's a presentation on the mathematical equivalent of MOS scales: http://www-irma.u-strasbg.fr/~kassel/ChristoffelNJ0407.pdf So, they're old, and they're...
A great find. The author is apparently unaware of the music connection, citing biology and such but not music theory. I like the graphic method. I bet Erv...
... I agree. This is exactly the type of math I am looking for. I was daunted at first by the 123 pages, but actually, it's kind of a Powerpoint style piece,...
Here is an interesting find, a paper on "David Lewin and Maximally Even Sets". As a "pleasant by-product" of Lewin's work with the FFT (Fast Fourier...
THEORY IN A NUTSHELL 1. The 132 Steiner hexads comprise 1/7 of the 924 total hexads (hexachords), in fact they comprise 1/7 in every BW (Black and White)...
p. 154: Projective Planes and Difference Sets This Chapter is exciting to me for a couple reasons. They discuss 7-tET, 13t-ET and 31-tET. 43-tET unfortunately...
... A better way to state this would be to say: A Z-related difference set (pair, or triple, or whatever) operated upon by the affine group action will produce...
Hello everyone, My name's Rick and I'm a new member. Forgive me for starting a new thread but I haven't got my 'daily digest' yet and couldn't find an answer...
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