Hi All, I recently posted the following reply to Danny Wier's post on the Tuning List re: harmonicity rankings. My question is: Is there a tidy formula that...
The problem with Euler's function, and apparently with yours, is that they're based on factoring. While this comes into play when harmonies are generated from...
Hi Carl, When you say you put 5/3 above 5/4, do you mean that 5/3 is more, or less consonant? As far as N*D goes: That would make a 7/5 more consonant than an...
... More. Don't you think so? ... That's the classical counterexample / trouble spot with n*d. It's a hard judgement to make, and they're really pretty close ...
... Dears Carl & Robin, ... 5*3 = 15 ... 5*4 = 20 ... Some people conclude from that for triads respectively: 3:4:5 = G:C:E with 3*4*5=60 would sound even...
Well.. no, not really. I have been opening up Scala and listening to a lot of ratios of late. I hear 5/4 and 5/3 more or less equally consonant. And, I hear...
Hi Andreas, ... I did leave out the notion of taking the log of the result, which according to Paul Erlich is the right way to scale the scores. I left this...
Hi Andreas, Thank you. I appreciate the insight into this from the viewpoint of extrapolating the concepts into triads. I'm interested in focusing on diads...
Here's how they sound on my system: http://lumma.org/stuff/75.wav http://lumma.org/stuff/85.wav To me the sound of the first one *is* more consonant in a...
In 1999, I thought Archimedean tilings might offer a nice way to look at tonespace. I came up with: http://lumma.org/stuff/4.8.8.png There's enough room here...
Thanks, Carl, Interesting voicing on those... what is that? To my ear, 8/5 is more consonant. Robin ... listening ... equally ... think ... and ... an ... 8/5?...
Straightforward voicing... they both share a common root pitch. Same timbre, duration, and amplitude envelope. Before passing final judgement, you should also...
... I agree that the 8/5 sounds more consonant than the 7/5 ... with that particular voicing. On listening closely, I notice that the shared harmonic of the...
Hi Carl, I have been thinking about the 5/4 and 5/3 and think that a food example is appropriate. Apricot jam and strawberry jam are equally sweet. They just...
... Actually glucose is substantially less sweet than cane sugar. And cane and beet sugar are both sucrose. Is that what you meant? Some advocate ranking...
Hi, No.. I had a feeling that that comparison might not work out.. Sweetness (most to least): 2/1,3/2,4/3 Thanks, Robin ... equally ... train ... 4/3...
... I think a 2/1 is really pretty flavorless; at least not a sweet sort of flavor. Sweet would be a pretty good word to describe the 5-colored intervals,...
Hi Herman, Good suggestions. There are what, six categories of taste? Sweet, sour, bitter, salty, hot (spicy), and savory (umami)are the ones that come to...
... Simply by playing an http://en.wikipedia.org/wiki/Natural_horn you can taste the flavour of the: http://en.wikipedia.org/wiki/Harmonic_series_%28music%29 ...
I've mentioned scalar complexity here before but it still isn't in my errors and complexities PDF. One definition is that it's the size of the wedge product...
... According to my PDF, he used the sum-abs of the weighted wedgie. That's proportional to the Tenney harmonic distance of a single unison vector, and...
One more thing on this: the formula I was using before is actually a special case for the rank 2 case. The correct one is sqrt(det(MTM)/n**r) where sqrt is...
Here's the simplification you're after. First a recap. The Perry harmonic complexity or Perry complexity (PC) of a ratio n/d was defined by Robin Perry as the...
Thank you very much, Dave. That is simple, elegant, brilliant. I'm still looking at patterns in the process to refine the definition for primes higher than...
Since my 26 hexachord system uses A - Z, it could also be used as a code (a la "Enigma" for example) Since I am studying Crytography as part of my career, I...
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