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?...
hi Carl. One reference to this issue occurs in Richard Parncutt's important 1988 "Revision of Terhardt's Psychoacoustical Model of the Root(s) of a musical...
Hi Kelly- ... There's nothing I can see here against harmonic entropy. ... "Tonal structure" sounds to me like it almost could be referring to functional...
... We all know that certain properties hold for mistunings. That's the whole point of temperament. What you said is that the precise tuning doesn't matter....
right..."since many aspcects of percetion are related to proportional change, logarithmic scales are common in psychophysics" (Sound and Hearing website, on...
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