... (this ... figured ... The usual generalization of the mediant gives the mediant of p1/q1, p2/q2, and p3/q3 as (p1+p2+p3)/(q1+q2+q3). So for 1/1, 5/4, 3/2...
genewardsmith@...
Sep 6, 2001 11:02 pm
508
... No. We need to divide the 2-D plane into mutually exclusive, exhaustive set of sub-regions. See the link in the "Eureka" post for more. But I think this ...
Paul H. Erlich
PERLICH@...
Sep 7, 2001 6:40 pm
509
Hello, This email message is a notification to let you know that a file has been uploaded to the Files area of the harmonic_entropy group. File :...
harmonic_entropy@yaho...
Oct 26, 2001 5:27 am
510
Paul, I believe that you have stated (and please do correct me if I am incorrect in my memory) that "Harmonic Entropy" is applicable to pure tone dyads (such...
Dave (if you are out there), or Paul (if you might know): Why the second derivative of the "Harmonic Entropy" function? What special significance is associated...
... Yes -- although the standard deviations typically used would only be applicable to such a case in a certain optimal frequency range, around 3000Hz. ... (a)...
... Well, there are variations. But it's always a function (meant to reflect one component of dissonance) of a precise specified input interval or chord. And...
... future ... rule ... p ... The ... The "actual input value" is a certain number of cents, so how can a normal curve be centered around it? The ... A "dyad"...
... Right. ... If the number of cents is c, the curve is y=1/(s*sqrt(2*pi))*exp((x-c)^2/2*s^2) where x is the position on the interval axis (have you looked at...
Hi Jacky, I think you asked this before, but it just popped into my mind again, so I thought I'd take another look. Monz, John de Laubenfels, Joseph, Margo and...
How 'bout it, Gene? I've made correction ... Invariant except for a constant, which it would good to be able to calculate. ... the ... Again up to an arbitrary...
http://groups.yahoo.com/group/harmonic_entropy/files/Erlich/fun.gif My guess that a triad l:m:n occupies an area proportional to (l*m*n)^ (1/3) seems to be...
... What a great chart! Obviously you selected a string of ratios that keeps the fifth just for the diagonal. What happens along the other spokes? and what are...
... The former. The cells shrink to zero, but the _ratios between their areas_ is what appears to be the same, and what would be key to having a meaningful...
That looks intriguing, Paul. I obviously missed the introduction, but I will certainly have a closer look at this issue. By the way: I finally got to add ...
... so close to the 3rd root of a million? and amounting to augmented triads? ... Well, I hope that most of my questions amount to: What changes from one point...
... Only in one particular region in the plot. The plot has points corresponding to all conceivable triads. ... I think it's all much simpler than you think --...
Thanks a lot. I think my idea of the triadic diagram is clear enough now. And yes, the diagram for the dyads also looks quite plausible. Then my "plausibility"...
... JG: Of one, the other, or both fundamental frequencies of the two tones from which the dyad is constructed? ... JG: Do you mean by this simply that the...
Paul, Is it your belief that a dyad constructed of two independent complex tones (each consisting of a fundamental as well as overtone frequencies of each of...
... sources ... each ... (complex) ... JG: Additionally, due to the nonlinear amplitude transfer function of perceived loudness levels [shown as approximately...
... I don't understand this question. What I'm trying to say is that, in the harmonic series, one finds certain intervals -- for example, if you go up throught...
Yes. Substantial psychoacoustic experiments have shown that phase changes have nearly no audible effect. In fact, the BBE Aural Enhancement products work by...
... Again, it would help. If one tone is much louder than the other, then the brain is more likely to disregard the quieter one, and simply use the louder one...
... changes ... JG: Paul, I thought that the experiments to which you refer above relate to assessing listener reaction to various "phase shift as a function...
... Well, by the time you hear it, the summation has already occured, unless the tones are presented to separate ears. There's probably some specific ...
... JG: Granted. ... JG: By "central" you mean "non-binaural", I presume? ... JG: By "phase-locking" you mean "static phase alignments resulting in significant...
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