hi again, gene you mentioned in a post that it was not a good idea to try building scales from a selection of primes rather than all primes < p, why is that? ...
there is some stuff on diamonds () here http://anaphoria.com/lamb.PDF and http://anaphoria.com/dia.PDF more important than epimorphic intervals is to fill in...
... It's a perfectly fine idea, but not if you want superparticular ratio steps, where you will run into problems. ... That is the square numerator form, the...
... close to ... Epimorphic implies constant structure. Epimorphic is a good condition on JI scales, and requires a more coherent scale structure than simply ...
... i have found quite a lot of superparticular scales being selective with the primes, just not many of them make complete diamonds. ... have? ... okay. well...
The positive integers form a commutative monoid under multiplication: http://en.wikipedia.org/wiki/Monoid That is, there is a product which is commutative and...
Hey just an update of what I have been doing â€" Noticed that the 9 lim diamond can be achieved by the addition of the five different linear arrangements of...
... here is a .scl file note u may need to tweak depending on how much range ur keyboard has! it has 2 octaves for each harmonic space and goes backward from...
this is cheating - any diamond made of 5 elements you can call a pentatonic. although i see no reason not just to take pentatonics and make diamonds out of...
i dont understand what u are saying? the diamond has 19 tones, not 5 how is it cheating? who is it cheating? i am trying to say the 9lim diamond can be...
you say that you have a pentatonic scale generating a diamond. well a pentatonic by definition has 5 notes, how is this significant. couldn't this be said of...
... what do you mean by diamond made of 5 elements? ... yes of course ... i didnt realise this was how partch formed it but it makes sense if u rotate a series...
by 5 elements in the sense that you can have you can make a diamond out of any 5 harmonics or interval one chooses or likes the sound of. they needn't be...
... the same process applied to say the superparticular pentatonic (8/7)^2, (7/6)^2, 9/8, wont work. it has to be ascending superparticular intervals to...
... In general, (n+1)/n * (n+2)/(n+1) * ... * 2n/(n-1) = 2. The ratios between these give the commas (n+1)^2/((n+1)^2-1) .... (2*n-1)^2/((2*n-1)^2-1). If n is...
hey gene what i meant by linear rotations, was if u take the 6/5, 7/6, 8/7, 9/8, 10/9 as a circle and take each from a different starting point; that gives u 5...
these pentatonics oscillate (measure the periodic waveform of playing the whole scale as a chord) at the following ratios 6/5, 7/6, 8/7, 9/8, 10/9 -> 1/5 7/6,...
... hi there carl the keyboard mapping works like this, for each octave of the piano there is two octaves of a pentatonic scale they go in this order 8/7 * 9/8...
... You lost me. Are all four octaves the same, and if so can you show one of them? ... Which keys are those? ... Huh? ... I don't typically think of them...
... there are *five* distinct pentatonic modes to the 9lim diamond, each is achieved by multiplying the fifth to tenth harmonic like below ... this gives us...
... there are *five* distinct pentatonic modes to the 9lim diamond, each is achieved by multiplying the fifth to tenth harmonic like below ... this gives us...
... there are *five* distinct pentatonic modes to the 9lim diamond, each is achieved by multiplying the fifth to tenth harmonic like below ... this gives us...
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