Inspired by Harold Fortiun's group generated by the thirds {7/6, 6/5, 11/9, 5/4, 9/7} I thought it would be interesting to look at note groups generated by...
Two generator groups: I found 42 of these generated by consonances in the octave; the octave-containing groups are [2, c] for c a consonance, and the full list...
Finite index means there is an integer n such that 1/n of the 7-limit intervals belong to the subgroup. Below I took integer generators up to 50 and looked at...
Meantone can be described as the 19&31 system; if we take h19 = <19 30 44 53| and h31 = <31 49 72 87| then the meantone 2-division val is j2 = 5 h19 - 3 h31 =...
The meantone-superpythagorean co-tuning is the pair of tunings for meantone and superpythagorean such that the 7-limit is a linear combination of the meantone...
... What that tends to do is screw things up, especially for the less accurate temperament. I looked at 53 co-fifths for meantone, and most were good to...
... 6/5, ... more ... I've met Dr. Harold Fortuin. He invented the "Clavette", a microtonal keyboard (it uses hexagons over buttons and can be programmed for ...
I am studying the different counting methods of Polya. The first I learned about on this newsgroup, the second, by way of conversations with contributors to...
Here's a paper by a Slovenian electrical engineer, where he calculates succesively higher values of |Z(t)|. He also notices that these come near octave...
This is a rather far-fetched connection, since it involves JI scales as the number of notes to the octave goes to infinity. It's about Farey sequences, but you...
... conversations ... as ... is ... in a ... been ... generate ... question ... bunch ... Mathematics ... Smith ... the ... Well, I have been studying the...
The phenomenon of the peak values of zeta(1/2+it) being dominated by near integers n = ln(2)t/(2 pi) turns out to be even more apparent when you look at...
... far. ... Yes. Actually, the article is from the 1961 Illinois Journal of Mathematics. "Symmetry Types of Periodic Sequences" by E. N. Gilbert and John...
... Here's an explanation of the relationship between looking at zeta peaks and the derivative. We have zeta(1/2+it) = exp(i theta(t))Z(t) where Z is the Z...
... I've uploaded a plot of |zeta| in green and |zeta'|/theta in red to the zeta derivatives folder, under zeta, in Photos. It's quite illuminating....
... This is what first got me interested in the tuning-math group. Unfortunately, in spite of reading 2 popular books on the RZH ("Prime Obsession" and "The...
I am trying to contact Brian Lee about the scores of Elsie Hamilton's music that we located in England and at the Anthroposophy world headquarters in Dornach, ...
I found these links on usenet: http://www.titanmusic.com/papers/public/ps-cmmr2004.pdf http://gsd.ime.usp.br/sbcm/2001/papers/rEmilios_Cambouropoulos.pdf ...
... Interesting, though somewhat frustrating. The first paper didn't do a very good job of explaining the algorithms. The second wasn't claiming as much...
I always considered enharmonic-spelling to be a burden with musical notation software. Is there any program that actually understands that a certain note in a...
hi Ozan, ... yes ... Tonalsoft's Musica does. it clearly differentiates all "enharmonically-equivalent" sets of notes. (release 1.0 now planned for summer...
... ... well, of course, *how* it differentiates between enharmonics depends on exactly how the particular tuning works. for example, if the user is working in...
... Which chart? The first one corresponds with what Erv Wilson called Mavila, in that Meta-Mavila is constructed analogously to Meta-Meantone in terms of how...
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