... <jdl@a...> ... Believe it or not, I actually did impress a beautiful woman with tuning math the other day! Of course it is a lot easier in a mathematics...
John Starrett
jstarret@...
Oct 1, 2000 3:52 pm
21
(Oops!! Sent this first to the tuning list by mistake! Oh well, they'll figure it out...) [John Starrett:] ... You rogue! She loved it when you used the...
John A. deLaubenfels
jdl@...
Oct 1, 2000 5:26 pm
22
Hi! This is interesting stuff! I couldn't find a webpage by her, but the most recent notice about her is at: http://www.ece.uci.edu/colloquia/00w.html#Dabby ...
Allan Myhara
amyhara@...
Oct 1, 2000 6:59 pm
23
Hi John -- I was wondering if you could help in understanding your triangular tetrachord graphs. I would like to use the same thing for triads but of course...
Paul H. Erlich
PERLICH@...
Oct 1, 2000 8:17 pm
24
... it, "entropy" ... Yup! ... for ... From http://www.ixpres.com/interval/td/entropy.htm: [In a Farey or other series of fractions, representing dyads from...
Paul Erlich
PERLICH@...
Oct 1, 2000 8:23 pm
25
Disclaimer: these results are not personally endorsed by Bill yet . . . but the ranking that his program indicates for the tetrads is: most concordant 502...
Paul H. Erlich
PERLICH@...
Oct 1, 2000 9:47 pm
26
... Well... it is a very interesting article... but I only have time to do the last paragraph... but it 'sums up" the attitude of the writer: Im letzten...
Joseph Pehrson
pehrson@...
Oct 2, 2000 2:54 pm
27
Ed Borasky wrote, ... Hi Ed. Bill e-mailed me off-list to tell me that the "amplitudes" are in dB and not really amplitudes at all. The conversion from...
Paul H. Erlich
PERLICH@...
Oct 2, 2000 6:24 pm
28
Hi Bill. ... hmm . . . but the results will be very different depending on whether you normalize to "1" or to some other constant . . . and what about negative...
Paul H. Erlich
PERLICH@...
Oct 2, 2000 7:05 pm
29
... From: William Sethares [mailto:sethares@...] Sent: Monday, October 02, 2000 3:20 PM To: PErlich@... Cc:...
Paul H. Erlich
PERLICH@...
Oct 2, 2000 7:28 pm
30
... I assume you had a point in using 120-degree rather than 90-degree angles in your tetrachord plots, didn't you? The reasons I see are (a) symmetry, and (b)...
Paul H. Erlich
PERLICH@...
Oct 2, 2000 11:56 pm
31
Thanks, Paul, for the re- over-view. That clears things up for me for now. -- David J. Finnamore Nashville, TN, USA ...
David J. Finnamore
daeron@...
Oct 3, 2000 3:51 am
32
... Well, among the 36 tetrads I made for Joseph Pehrson, which used timbres with harmonic partials, Joseph found chords like 4:5:6:7 to be among the most...
Paul H. Erlich
PERLICH@...
Oct 3, 2000 6:00 pm
33
... http://www.egroups.com/message/harmonic_entropy/32 As Paul mentioned, I had a problem with the sequential ordering of the supposedly increasing discordance...
Joseph Pehrson
pehrson@...
Oct 3, 2000 7:54 pm
34
Joseph Pehrson wrote, ... But Joseph, you yourself said that the chords 0 302 502 1004 0 502 702 1004 were more...
Paul H. Erlich
PERLICH@...
Oct 3, 2000 8:03 pm
35
... wrote: http://www.egroups.com/message/harmonic_entropy/34 ... method seemed more suitable to describing the gradual progression and, in fact, NONE of the...
Joseph Pehrson
pehrson@...
Oct 3, 2000 8:12 pm
36
... But you agreed that 9:11:13:15, which Monz made a version of, _would_ seem out of place in it . . . ... When you've got as great a desire to find out the...
Paul H. Erlich
PERLICH@...
Oct 3, 2000 8:36 pm
37
... wrote: http://www.egroups.com/message/harmonic_entropy/36 ... chords were really in JI anyway, so if I were to treat these chords as rough approximations...
Joseph Pehrson
pehrson@...
Oct 3, 2000 8:57 pm
38
... Wouldn't you say, though, that they should be somewhat _higher_ in the ranking? Based solely on your previous comments on these chords, it would seem so ....
Paul H. Erlich
PERLICH@...
Oct 3, 2000 9:21 pm
39
John, I'm really confused. Can you tell me the formula used in your triangular plots? I need to be able to calculate x and y values for any point (to place it...
Paul H. Erlich
PERLICH@...
Oct 3, 2000 10:18 pm
40
I think I figured it out -- it's x=i1 y=i1/sqrt(3)+2*i2/sqrt(3) right??? So the axes _are_ at 60-degree angles, after all!...
Paul H. Erlich
PERLICH@...
Oct 3, 2000 11:19 pm
41
Or rather, the axes are at 120-degree angles but the normals to the axes are at 60-degree angles. ? This is so confusing . . ....
Paul H. Erlich
PERLICH@...
Oct 3, 2000 11:38 pm
42
This is what it looks like, with integer limit 24: http://www.egroups.com/files/harmonic_entropy/chalmers.jpg...
Paul H. Erlich
PERLICH@...
Oct 4, 2000 12:42 am
43
If you want to see something pretty, go to http://www.egroups.com/files/tuning/perlich/triads36.jpg. It's a triangular (like Chalmers' tetrachordal graphs)...
Paul H. Erlich
PERLICH@...
Oct 4, 2000 7:53 am
44
In-Reply-To: <CE80F17667E4D211AE530090274662729C54D6@...> ... I seem to be only getting half of Paul's conversations. Can replies please be...
graham@...
Oct 4, 2000 11:37 am
45
In-Reply-To: <CE80F17667E4D211AE530090274662729C54DF@...> ... That's the stuff. I was only thinking of drawing one diagram. So the ratio...
graham@...
Oct 4, 2000 11:37 am
46
... Bugged, which I assume came about as you tried to make the function names more sensible or consistent. I do this all the time. ... This is called several...
William S. Annis
wsannis@...
Oct 4, 2000 1:04 pm
47
In-Reply-To: <200010041304.IAA29253@...> ... Specifically as I try to make them shorter:) ... Okay, change from ratioWithin... to isWithin......
graham@...
Oct 4, 2000 2:15 pm
48
... wrote: http://www.egroups.com/message/harmonic_entropy/43 ... triads with integer limit 36. There are six identical sextants, each one the mirror image of...
Joseph Pehrson
pehrson@...
Oct 4, 2000 5:19 pm
49
... in the sequence determined by your method above, and I was quite happy with them. They seemed to fit into the increasingly discordant array with no...
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