... Okay, well, a just intonation point is at the bottom of a basin of a dissonance graph. But so is the point where one basin meets another. So a zero first...
hi Paul (for when you come back), or others. I can't locate the old thread, but thanks for suggesting the above spelling for the chord d4- f#-b4-E5. I don't...
Hi Kelly, ... Exactly! ;-) ... The tetrad am : bm : cn : dn has the property that dn/am = n/m if and only if a = d. (Here juxtaposition means multiplication:...
Hello. For chords such as 3:7:10, and 4:6:10, where the difference tones land on the chord tones (ie, 10-7=3, 10-6-4; Helmholtz commented on these, and I like...
Hi Yahya ... Hmmm...I'm not sure if I would include the latter two chords in the same category as the one I cited. And 4:6:7:14 has an octave in it, which may...
Hello Harmonic Entropy List. 5:16:21:25, ...another chord which, I think, sounds interesting and unique, and which has an interesting number feature. Among...
... But there is a correlation between the 'height' of the interval in the series (ie, eg, 5/4 x 3 = 15/12) and the difference tone, so there could be a...
Hi Kelly, ... You do *very* strange arithmetic! ;-) You often write things like: 5/4 x 3 = 15/12 This should be, instead, 5/4 x 3/3 = 15/12 since a) you can...
Hi again Kelly, ... [snip] ... Errata: in the above, I should have written: 45/36 = (5 x 9) / (4 x 9) = 5/4 80/60 = (4 x 20) / (3 x 20) = 4/3 80/36 = (4 x 20)...
... Not laughing, Kelly; it's an interesting pattern. Let's take your first example: Sequence: 4, 5, 6 Double the middle term: Sequence : 4, 10, 6 Rearrange:...
... hi Yahya - thanks for the math correction. I'm terrible at it, though love numbers... By 'height', I was referring to how, for example, the major third in...
... Hi Yayha, ... Sorry. You guys really keep me on my toes. I just chose very small ... Personally, I find the interval of a major seventh more consonant...
hi Yahya, ... Yes. ... Chords of the type 3:7:10 have the coherant difference tones --which is pertinant to the list, yes?--- and are useful ways to arrange ...
Kelly, ... [snip] ... Good! ... Did you follow this reasoning? Do you see that it means that "double the middle term in an arithmetic progression is always...
The radio premiere of David Beardsley's (http://biink.com/db/index.htm) 30-minute 2004 string quartet "as beautiful as a crescent of a new moon on a cloudless...
A leading Psychoacoustician wrote "I had a look at "Harmonic Entropy" and was immediately put off by the idea that intervals are frequency ratios (which ratio?...
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