--- In tuning-math@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning-math@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> > Doesn't the fact that meantone, (the single most popular 5-limit
> > temperament of all time), doesn't even make the top-ten, mean that
> > there is something very wrong with our figure of demerit?
>
> Very wrong. Very, very wrong.
When I wrote the above I hadn't got around to converting all Graham's
decimal octaves into something I could understand. Here they are.
Min Gens
Num of MA per Figure
chains Gen err compl of
per oct (cents)(cents) otonal demerit
---------------------------------------
15-limit
29 15.93 4.7 29 3948
1 497.24 10.0 23 5269
1 351.71 7.8 28 6089
3 83.02 2.8 48 6426
1 497.89 4.8 37 6619
2 83.16 3.1 52 8431
1 83.42 6.4 38 9190
1 116.72 5.0 45 10111
1 234.41 5.8 42 10162
2 165.81 3.9 52 10575
... When I wrote the above I hadn't got around to converting all Graham's decimal octaves into something I could understand. Here they are. Min Gens Num of...
Dave Keenan
D.KEENAN@...
May 29, 2001 12:16 am
This follows from http://groups.yahoo.com/group/tuning-math/message/59 I listed the temperaments in the order that Graham ranked them but I gave a different...
Dave Keenan
D.KEENAN@...
May 29, 2001 7:01 am
... into ... Exactly what I was thinking (with a generalized definition of MOS) . . . and of course, the more complete otonalities, the better. ... 10c ... ...
Paul Erlich
paul@...
May 29, 2001 8:12 pm
Notice how 16.6 cents (approx one step of 72-EDO) is by far the best "generator generator". i.e. the vast majority of top-10 generators are very close to a...
Dave Keenan
D.KEENAN@...
May 29, 2001 7:13 am
... Holy $#!% -- totally missed that. And how did MIRACLE end up on the _bottom_ for 9-limit? ... MA optimization is hard. Go with RMS. ... Paultone. Yes. ... ...
Paul Erlich
paul@...
May 28, 2001 9:23 am
... It's moved up now. ... I used that algorithm *because* it's easy. If you have another one, write the code and plug it in. ... AIUI, this wouldn't affect...
graham@...
May 28, 2001 12:54 pm
... ?? ... Yup -- the 6:5 and 5:3 are kinda hairy at your value. ... Yay! By the way, your Blackjack chord progression totally blew away and inspired Joseph...
Paul Erlich
paul@...
May 28, 2001 5:05 pm
... As I Understand It ... But I'm only doing the optimization in order to compare temperaments. The way I'm doing it is good enough for that. The real...
graham@...
May 28, 2001 7:55 pm
... http://groups.yahoo.com/group/tuning-math/message/56 ... Me too!!!! I could tell by looking at it that I simply *had* to hear it... that's exactly why *I*...
monz
joemonz@...
May 29, 2001 3:18 am
... You deserve a lot of credit also for the voice-leading (which Joseph and I meticulously reproduced on the keyboard) and for such a good choice of timbre....
Paul Erlich
paul@...
May 29, 2001 8:08 pm
... http://groups.yahoo.com/group/tuning-math/message/68 ... Joseph ... The first time I heard that progression, I was literally paralyzed with...
jpehrson@...
Jun 3, 2001 4:14 pm
... than the ... The generator doesn't have to be greater than _half_ the period (equivalence interval). But yes, it's still O(n^2)....
Dave Keenan
D.KEENAN@...
May 27, 2001 6:41 am
... is that ... Well, I usually think of diaschismic as having a ~3:2 generator and a half-octave "by-generator". But yes, replacing the ~3:2 with an ...
Paul Erlich
paul@...
May 28, 2001 9:09 am
... That isn't what I found by playing the Bohlen-Pierce and O'Connell scales with the matching timbres. I'll keep looking for alternative periods until my...
graham@...
May 28, 2001 7:55 pm
In-Reply-To: <9ev4ed+ntv4@eGroups.com> ... Which progression are we talking about here? The one I worked out by improvising and posted notation and an MP3...
graham@...
May 29, 2001 9:04 am
... by ... out on ... equivalence? ... The latter. I must have missed the former -- where it it?...
Paul Erlich
paul@...
May 29, 2001 8:13 pm
... <http://www.microtonal.co.uk/miracle/>. You complained about it ending with a neutral triad IIRC. Graham...
graham@...
Jun 2, 2001 7:13 am
... Oops -- I forgot to listen to this on good speakers. On the speakers I was listening to it on, there was so much distortion that I didn't even know it was...
Paul Erlich
paul@...
Jun 2, 2001 8:52 pm
In-Reply-To: <9evi4u+e5pu@eGroups.com> In article <9evi4u+e5pu@eGroups.com>, D.KEENAN@... (Dave Keenan) ... If you look down my tables, you should see...
graham@...
May 29, 2001 9:04 am
In-Reply-To: <9evhgg+5rf0@eGroups.com> ... Oh, I thought the difference would be the other way. ... I don't know about that, it sounds suspiciously like fixing...
graham@...
May 29, 2001 9:04 am
In-Reply-To: <9evhgg+5rf0@eGroups.com> ... I've updated the files at <http://www.microtonal.co.uk/temper.html> with a few changes: Simpler ETs are listed. The...
graham@...
May 29, 2001 1:15 pm
I don't think it's essential to make meantone look like the best 5- limit linear temperament. Meantone is important for other reasons, outside the scope of...
Paul Erlich
paul@...
May 29, 2001 9:37 pm
... I looked at the 7-limit results and they're fascinating. While I don't see paultone, I see a 5/11 oct. generator with a half-octave interval of repetition....
Paul Erlich
paul@...
May 29, 2001 10:00 pm
... _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at http://mail.yahoo.com...
Joe Monzo
joemonz@...
May 29, 2001 8:19 pm
... Thanks for doing that Graham. Much appreciated. Here's how to calculate the notes per octave of the smallest MOS containing a complete otonality. In pseudo...
David C Keenan
D.KEENAN@...
May 30, 2001 10:47 am
In-Reply-To: <9f166e+2vcv@eGroups.com> ... There was a bug in the program when I generated the exp files. The routine for optimizing the minimax was ignoring...
graham@...
May 30, 2001 12:48 pm
In-Reply-To: <3.0.6.32.20010530034550.00a72d90@...> ... I've updated that. It's showing 22 as a schismic MOS, which is wrong. Graham...
graham@...
May 30, 2001 12:48 pm
... wrong. I disagree. I think it's correct. With a period of an octave won't any generator in the range 489 to 492 cents generate a proper MOS? 490.9 c will...
Dave Keenan
D.KEENAN@...
May 30, 2001 10:27 pm
... MOS ... any ... 490.9 c ... a ... still ... But it's not _schismic_!...
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