No, the base is irrelevant; you can remove the log operations by replacing + with * and - with /. Then you get standard goniometric equivalences. What you can...
... Only logbase2 gives a difference of 1 though in the first two equations. Did you mean trigonometric equivalences? Does sin (theta) * cos (theta)= sin^2...
Geordan Mitchell, Danlee Mitchell's son, called me today to tell me to let everyone who might be interested know that Danlee will present the program...
I am studying bra and ket vectors, contravariant and covariant tensors, and "duals" - monzo and val vectors. If someone could summarize what all this means in...
hi Gene, would you please fill out the temperament template we've used before, with the data for atomic temperament? thanks. (if you can't find a copy of the...
I've recently heard that the physicist Oliver Heaviside (who invented vector calculus, discovered the Heaviside layer, simplified Maxwell's equations, etc.)...
... Oh, that looks like Hans Aberg's: http://tinyurl.com/5ouj4 """ So one might look for a two-dimensional keyboard having pitches 2^{k/12} 3^l. Looking for...
Happy to report that I have found a formula for 35 hexachords. (Sequences A006840 and A045629) A006840 is the same as A045611 for n=0 to n=7. n=6 is hexachords...
... (2n,n)- ... in ... ***This is the formula for A006840, which uses A045629, which reduces for complementation but not direction. There are 44 sets in...
... for ... sets ... vectors ... is ... reduces ... the ... am ... 35 is determined by: 1/2(44 + 1/2(C{6,3})+2^4) where 44 is determined by: SUM: 1/12...
A circulant graph is a graph on n nodes, which we can take to be numbers mod n. For every element of an index set (which without loss of generality we can take...
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...
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