No one responded to my Hypothesis on the tuning list. Search for "hypothesis"....
paul@...
May 21, 2001 4:54 am
... for "hypothesis". If you accidentally hit Ctrl-W in IE, the window you're typing in disappears. What a crock! So, I'll have to start this again. ...
Graham Breed
graham@...
May 21, 2001 11:32 am
... Not necessarily -- I was thinking more along the lines of, the form of the periodicity block with the most consonances. ... It might not be a linear...
paul@...
May 21, 2001 5:43 pm
In-Reply-To: <9ebk3d+5dqs@eGroups.com> ... How would that relate to the unison vectors? ... One fewer unison vectors than you need for an ET will always give a...
graham@...
May 21, 2001 5:59 pm
... form ... For example, the melodic minor scale and the major scale are both periodicity blocks of the unison vectors 25:24 and 81:80, with the 81:80...
paul@...
May 21, 2001 6:33 pm
... like an ... I might try, but first I need some definitions. :)...
genewardsmith@...
Aug 18, 2001 5:09 am
... Joe Monzo's dictionary is chock full of definitions: http://www.ixpres.com/interval/dict/index.htm...
John Starrett
jstarret@...
Aug 18, 2001 3:29 pm
... A sketch of the proof of the Hypothesis is provided in post #591 on this list. Hopefully, all the terminology in that post should be self-explanatory, or...
Paul Erlich
paul@...
Aug 18, 2001 7:13 pm
... I looked at CLAMPITT.pdf, and it seems to me the argument that there is something interesting about WF scales is extremely unconvincing. Can anyone...
genewardsmith@...
Aug 19, 2001 8:13 pm
... There are a tremendous number of arguments as to why there is something interesting about WF or MOS scales in the literature. Personally, I buy very few of...
Paul Erlich
paul@...
Aug 20, 2001 2:46 am
... Unless I am missing something (highly likely at this point!) the pentatonic and diatonic scales are WF in mean tone intonation but not in just intonation....
genewardsmith@...
Aug 20, 2001 3:39 am
... not ... serve ... Strict, fixed-pitch just intonation has almost never been used in actual music with these scales. This is because of the so- called...
Paul Erlich
paul@...
Aug 20, 2001 6:44 pm
... It seems to me the comma problem is less of a problem if you are only interested in melody, and this whole business is justified in terms of melody. Is it...
genewardsmith@...
Aug 21, 2001 12:33 am
... been ... the ... only ... In terms of harmony? ... Probably Pythagorean is everyone's favorite melodic tuning. And yes, I do dislike the melodic jaggedness...
Paul Erlich
paul@...
Aug 21, 2001 1:09 am
... I don't know--to my ears, melodically Pythagorean is brighter and more aggressive, (and actually not too much different from 12 ET), but JI diatonic melody...
genewardsmith@...
Aug 21, 2001 4:18 am
... You like JI diatonic melody even when there is a direct leap of 40:27? ... the ... at ... Even when there is a direct leap of 40:27? P.S. The only culture...
Paul Erlich
paul@...
Aug 21, 2001 7:06 pm
... ET), ... my ... 40:27? I see what you are saying--I was assuming the JI melody was something appropriate to the scale. Of course if you translate something...
genewardsmith@...
Aug 21, 2001 9:57 pm
... Do you have an example of an actual diatonic melody that sounds good to you in JI? Most classical melodies, say Mozart for example, sound bad to me in JI...
Paul Erlich
paul@...
Aug 21, 2001 7:07 pm
... Howdy, Gene! I doubt the "synechdochic property" (the "self-similarity" at the center of the Carey and Clampitt article) is significant, except maybe in...
carl@...
Aug 20, 2001 4:26 am
... Did you get this from me? 'Cause you know I agree. But see the message I just posted about why MOSs appear to be _harmonically_ special for the class of...
Paul Erlich
paul@...
Aug 20, 2001 6:49 pm
... Absolutely -- I've long credited you with it, even in a pre-send version of that post. ... I didn't catch the why, but I am of course familiar with the ...
carl@...
Aug 20, 2001 7:23 pm
I wrote... ... I mean, I caught that they are non-parallelpiped PBs, but not why this should translate into fewer harmonic structures (do you mean only...
carl@...
Aug 20, 2001 7:26 pm
... See the last post. ... I'm thinking both, but I suppose the latter might do if we're trying to mathematize this....
Paul Erlich
paul@...
Aug 20, 2001 8:35 pm
... Roughly, the reasoning is that slicing the lattice with parallel, hyperplanar slices is likely to minimize the number of "wolves" or broken consonances...
Paul Erlich
paul@...
Aug 20, 2001 8:34 pm
Thanks, Paul, for inviting me to participate in your new group! Good luck with it! Joseph ... _________________________________________________________________...
Joseph Pehrson
jpehrson@...
May 21, 2001 7:03 pm
... http://groups.yahoo.com/group/tuning-math/message/1 ... for "hypothesis". I remember this interesting hypothesis mentioned on the Tuning List... So, I can...
jpehrson@...
May 21, 2001 7:11 pm
In-Reply-To: <9ebn2i+9ksu@eGroups.com> ... Does it matter which major scale we take? Or are we contracting the lattice to one dimension? ... It is, the...
graham@...
May 22, 2001 10:41 am
... the ... the ... the ... When the 81:80 is tempered out, the lattice curls into a cylinder. Then all major scales are identical. ... give a ... definitions....
Paul Erlich
paul@...
May 22, 2001 6:59 pm
In-Reply-To: <9eecso+amc3@eGroups.com> ... You should always be able to define a linear temperament using two intervals. Finding the right two can be tricky. ...
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