I wrote, ... Oops -- should be 49:48, of course!...
Paul Erlich
paul@...
May 25, 2001 6:59 pm
29
... unison ... A unison vector defines an equivalence relation in the lattice. Hence the name "unison". A periodicity block results from N independent unison...
Paul Erlich
paul@...
May 25, 2001 6:54 pm
28
In-Reply-To: <9ejj0r+mrao@eGroups.com> ... They're intervals used to specify the temperament that aren't being tempered out. I thought this was the definition...
graham@...
May 25, 2001 5:25 pm
27
... Paul, I started a response to this but it is getting long and interesting. I'll post it tonight. -monz...
monz
joemonz@...
May 25, 2001 4:47 pm
26
Oh, Monz . . . you're not expecting the result to be a stretched or squashed 72-tET, are you? 'Cause if you are, then it's a one- parameter optimization --...
Paul Erlich
paul@...
May 24, 2001 7:29 pm
25
... Still confused. Since when are octaves and twelfths "chromatic"?...
Paul Erlich
paul@...
May 24, 2001 6:14 pm
24
I wrote, ... Oops! That should be 104:99, not 143:128! ... Really? So ratios such as 16:9 would have fallen outside it?...
Paul Erlich
paul@...
May 24, 2001 6:11 pm
23
In-Reply-To: <9ehp0r+cb7i@eGroups.com> ... It defines 12-equal, but must contain 24 notes. ... That's that one disposed of ... ... The top of the equation will...
graham@...
May 24, 2001 1:10 pm
22
In-Reply-To: <9ehtrn+iaeg@eGroups.com> ... Hey, this *is* tuning-math, you know! ... Oh, alright then. The periodicity block could be F\--C\--G\--D\ / \ / \ /...
graham@...
May 24, 2001 1:10 pm
21
... http://groups.yahoo.com/group/tuning-math/message/20 ... Damn, Paul! Duh again! I had signed off for the night, and just realized this error and came back...
monz
joemonz@...
May 24, 2001 6:16 am
20
... Umm . . . I thought that explanation used a _prime-limit_ of 13, not an _integer-limit_ of 12. In particular, Partch showed that Schoenberg's two...
Paul Erlich
paul@...
May 24, 2001 5:17 am
19
... http://groups.yahoo.com/group/tuning-math/message/18 ... Of course... duh! I knew all this. Guess it's just information overload. ... Sure! Guess...
monz
joemonz@...
May 24, 2001 5:09 am
18
... I might try and then give up. ... Oh yes . . . Dave Keenan has been thinking 11-limit all along. He posted some 7-limit and 11-limit optimization results,...
Paul Erlich
paul@...
May 24, 2001 4:08 am
17
... Hi Monz. What we're discussing here is the 24-tone periodicity block you came up with to derive the 22-shruti system of Indian music. The unison vectors of...
Paul Erlich
paul@...
May 24, 2001 4:03 am
16
... Monz wrote, ... OK -- we now have to do a two-parameter optimization, where the two parameters are the size of the generator (let's call it G), and the ...
monz
joemonz@...
May 24, 2001 3:45 am
15
... http://groups.yahoo.com/group/tuning-math/message/14 ... Can you guys please illustrate all this with lattices and other tables and diagrams? My math...
monz
joemonz@...
May 24, 2001 3:06 am
14
... up with ... I think the problem is that, as you said before, the scale really has 12 pitch classes, not 24, due to the syntonic comma squared vanishing. ...
Paul Erlich
paul@...
May 24, 2001 1:44 am
13
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. ...
graham@...
May 23, 2001 11:22 am
12
... http://groups.yahoo.com/group/tuning-math/message/11 ... This is a really cool Tuning List, but so far, there is very little math on it... not that I would...
jpehrson@...
May 23, 2001 3:09 am
11
Hey Paul, I *LOVE* THIS LIST!!!!!! Thanks for being wise enough to create it! -monz http://www.monz.org "All roads lead to n^0"...
monz
joemonz@...
May 23, 2001 1:41 am
10
... 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
9
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
8
... 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
7
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
6
... 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
5
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
4
... 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
3
... 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
2
Paul, thanks for inviting me to join this new list. Thank you also for not banning me from it :)...
Orphon Soul, Inc.
tuning@...
May 21, 2001 6:41 am
1
No one responded to my Hypothesis on the tuning list. Search for "hypothesis"....
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