some tracks from MidwestMicrofest concert 01

http://www.midwestmicrofest.org/concert01_audio

The 'pratt' track is by Ryan Pratt, not a member here.

the 'tarantella' track is a studio realization--ultimately I wasn't happy
enough with the live execution to release it.

all other tracks are live.

more to come...including Joel Mandelbaum, J.L. Smith, Chris Bailey. The
other things which were played live by "La'ood S. Peakers" (Juggler, and
Blackwood's etude in 19) I assume you've all heard already, and the only
thing different is to hear people clapping.

Best,
Aaron.

Thanks for uploading the tracks, Aaron. If it isn't too much hassle, I'd
like to hear Juggler and Blackwood's etude. Actual acoustic realizations are
a different thing, and I haven't actually heard the Blackwood.

On 10/31/07, aaron@... <aaron@...> wrote:
>
> http://www.midwestmicrofest.org/concert01_audio
>
> The 'pratt' track is by Ryan Pratt, not a member here.
>
> the 'tarantella' track is a studio realization--ultimately I wasn't happy
> enough with the live execution to release it.
>
> all other tracks are live.
>
> more to come...including Joel Mandelbaum, J.L. Smith, Chris Bailey. The
> other things which were played live by "La'ood S. Peakers" (Juggler, and
> Blackwood's etude in 19) I assume you've all heard already, and the only
> thing different is to hear people clapping.
>
> Best,
> Aaron.
>
>
>

[Non-text portions of this message have been removed]

--- In MakeMicroMusic@yahoogroups.com, "Cody Hallenbeck"
<codyhallenbeck@...> wrote:
>
> Thanks for uploading the tracks, Aaron. If it isn't too much hassle, I'd
> like to hear Juggler and Blackwood's etude. Actual acoustic
realizations are
> a different thing, and I haven't actually heard the Blackwood.

They weren't actual acoustic realizations...they were electronic, over
speakers.

I'll post the Blackwood later...Juggler can be heard from
www.akjmusic.com/works.html

-A.

> On 10/31/07, aaron@... <aaron@...> wrote:
> >
> > http://www.midwestmicrofest.org/concert01_audio
> >
> > The 'pratt' track is by Ryan Pratt, not a member here.
> >
> > the 'tarantella' track is a studio realization--ultimately I
wasn't happy
> > enough with the live execution to release it.
> >
> > all other tracks are live.
> >
> > more to come...including Joel Mandelbaum, J.L. Smith, Chris
Bailey. The
> > other things which were played live by "La'ood S. Peakers"
(Juggler, and
> > Blackwood's etude in 19) I assume you've all heard already, and
the only
> > thing different is to hear people clapping.
> >
> > Best,
> > Aaron.
> >
> >
> >
>
>
> [Non-text portions of this message have been removed]
>

Cheers for posting this Aaron! I love the medley, and the other pieces are very well done as well. I hope there will be more concerts like this!
/ magnus

On Wed, 31 Oct 2007 aaron@... wrote:

> http://www.midwestmicrofest.org/concert01_audio
>
> The 'pratt' track is by Ryan Pratt, not a member here.
>
> the 'tarantella' track is a studio realization--ultimately I wasn't happy
> enough with the live execution to release it.
>
> all other tracks are live.
>
> more to come...including Joel Mandelbaum, J.L. Smith, Chris Bailey. The
> other things which were played live by "La'ood S. Peakers" (Juggler, and
> Blackwood's etude in 19) I assume you've all heard already, and the only
> thing different is to hear people clapping.
>
> Best,
> Aaron.
>
>
>
>

--- In MakeMicroMusic@yahoogroups.com, aaron@... wrote:
>
> http://www.midwestmicrofest.org/concert01_audio
>
> The 'pratt' track is by Ryan Pratt, not a member here.
>
> the 'tarantella' track is a studio realization--ultimately I wasn't
> happy enough with the live execution to release it.
>
> all other tracks are live.
>

Great stuff! Thanks once more for organizing all this! (And for
playing my piece!)
The tarantella is real fun... As for the medley, it keeps sounding
slightly out of tune to me - that large semitone... I got to say 19EDO
is not my favorite tuning at the moment - at least for classical music.

> more to come...including Joel Mandelbaum, J.L. Smith, Chris Bailey.

Looking forward!
--
Hans Straub

Awesome. THANK YOU FOR DOING THIS.

It sounds great. My main criticism would be around the timbre
of the pianos. Tarantella is awesome.

-Carl

At 03:49 PM 10/31/2007, you wrote:
>http://www.midwestmicrofest.org/concert01_audio
>
>The 'pratt' track is by Ryan Pratt, not a member here.
>
>the 'tarantella' track is a studio realization--ultimately I wasn't happy
>enough with the live execution to release it.
>
>all other tracks are live.
>
>more to come...including Joel Mandelbaum, J.L. Smith, Chris Bailey. The
>other things which were played live by "La'ood S. Peakers" (Juggler, and
>Blackwood's etude in 19) I assume you've all heard already, and the only
>thing different is to hear people clapping.
>
>Best,
>Aaron.

Hans Straub wrote...

>As for the medley,

I think it's a set, not a medley, right? Since there are pauses
between pieces?

>it keeps sounding
>slightly out of tune to me - that large semitone...

1/4-comma sounds more natural, yes, but I've always thought 1/3-comma
is a nice color.

-Carl

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> Hans Straub wrote...
>
> >As for the medley,
>
> I think it's a set, not a medley, right? Since there are pauses
> between pieces?

Yes you are absolutely right---I should change the link title though.

> >it keeps sounding
> >slightly out of tune to me - that large semitone...
>
> 1/4-comma sounds more natural, yes, but I've always thought 1/3-comma
> is a nice color.

One thing about 19 is that it's more practical.

But I'm getting tired of it, and find I'm more attracted to 31 and 53
these days. I guess 41 and 43, too.

If I had to pick one tuning for the rest of my life, it might be 31,
or a cool well-temp of 12 (shoot me now). I find 31 just gorgeous, and
I don't have the same problem with the fifth that others do, or even
the ninth. I can definately live with it for the relatively fewer # of
tones, and the delicious 5 and 7 limit. It even has nice strange
possibilities (11- and 13-, etc.).

I think I like novelty, but I'm enough of a traditionalist that I want
to say new things within more established diatonic framworks more. So
I couldn't be happy without the meantone ideal, where there are
more-or-less equal diatonic step sizes (sorry, Kraig!)

I go back and forth on this, though. 17 and ilk are fun for just being
wack. And things like 3and7 based scales (Michael Harrison stuff) are
just fun. I have to admit, I don't find myself all that attracted to
things beyond the 7- limit that I feel that I *must* have them to say
what I want to say.

-A.

On Fri, 2 Nov 2007, Carl Lumma wrote:

> Hans Straub wrote...
>
>> it keeps sounding
>> slightly out of tune to me - that large semitone...
>
> 1/4-comma sounds more natural, yes, but I've always thought 1/3-comma
> is a nice color.

I agree with both of you :)

19-edo semitone (126 cents) is right between 16/15 (112 cents) and 13/12 (138 cents), so it has both 5-limit feel and quartertone feel. In fact
C-F# (568 cents) is closer to 11/8 (551 cents) than to 45/32 (590 cents), so you may well hear a semitone as a 11/12 step harmonically. For example, in the key of C, B may be heard as the 11/8 above F, the subdominant. If you want an 11-limit kind of sound then 19-edo is great for its compactness. But I don't usually want 11-limit sound so I usually prefer a milder temperament between around 2/7 commas and 1/6 commas.

>One thing about 19 is that it's more practical.

Ja.

>But I'm getting tired of it, and find I'm more attracted to 31 and 53
>these days. I guess 41 and 43, too.

I don't see the appeal of 43 over 31. And don't forget 22 and 46!

>If I had to pick one tuning for the rest of my life, it might be 31,

31 is a very good one.

>or a cool well-temp of 12 (shoot me now).

Bang!

>I find 31 just gorgeous, and
>I don't have the same problem with the fifth that others do, or even
>the ninth.

Then you're set. Unfortunately, the 5ths and 9ths really bother
me in 31. Even the power chord is pretty harsh.

>I go back and forth on this, though. 17 and ilk are fun for just being
>wack.

Yeah. 15 and 26 are nice wackage points. Then again, some say
that 18 is Blackwood's best etude.

-Carl

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> >One thing about 19 is that it's more practical.
>
> Ja.

Ja wohl...

> >But I'm getting tired of it, and find I'm more attracted to 31 and 53
> >these days. I guess 41 and 43, too.
>
> I don't see the appeal of 43 over 31. And don't forget 22 and 46!

yeah...i guess I agree, you lose 7th partial stuff quite a bit, but
some people prefer 1/5 comma triad to 1/4-comma ones.

I'm not fond (overly) of 22. It strikes me as bland for some reason.
46 seems intriguing, but I guess I feel like a want a prime mumber (or
at least odd #), cause I don't care for the 12-eq tritone enough to
want to keep it around.

Let's not forgot 53, which is an all around great tuning. I don't mind
the slight beating of the 7th harmonic stuff.

> >If I had to pick one tuning for the rest of my life, it might be 31,
>
> 31 is a very good one.
>
> >or a cool well-temp of 12 (shoot me now).
>
> Bang!
>
> >I find 31 just gorgeous, and
> >I don't have the same problem with the fifth that others do, or even
> >the ninth.
>
> Then you're set. Unfortunately, the 5ths and 9ths really bother
> me in 31. Even the power chord is pretty harsh.

For some...31 with adaptive fifths might just be heaven.

> >I go back and forth on this, though. 17 and ilk are fun for just being
> >wack.
>
> Yeah. 15 and 26 are nice wackage points. Then again, some say
> that 18 is Blackwood's best etude.

That's the Messiaen sounding one, right?

15 is great. it's like east meets west, and it's wacky...Mizarian
Porcupine is a legend.

Aaron,
These four tracks are terrific. I found each one to have that
wonderful 19-on-edge, about-to-fall-off-a-cliff sound. The Tarantella
was really well done, my congrats to the great Dr. La'oud S. Peekers.
He's my favorite performer at the time also.

But the live duos were also great. I wish I could have experienced the
dynamics of moving melodies from one keyboard to another in person.
All very well done.

I anxiously await some more.

Prent Rodgers

--- In MakeMicroMusic@yahoogroups.com, aaron@... wrote:
>
> http://www.midwestmicrofest.org/concert01_audio
>

> Best,
> Aaron.
>

>> >But I'm getting tired of it, and find I'm more attracted to 31 and 53
>> >these days. I guess 41 and 43, too.
>>
>> I don't see the appeal of 43 over 31. And don't forget 22 and 46!
>
>yeah...i guess I agree, you lose 7th partial stuff quite a bit, but
>some people prefer 1/5 comma triad to 1/4-comma ones.
>
>I'm not fond (overly) of 22. It strikes me as bland for some reason.

The tetrads sound about as rough as triads do in 12. However, like
12, 22 does more in fewer notes than, well, just about any tuning
besides 12.

>46 seems intriguing, but I guess I feel like a want a prime mumber (or
>at least odd #), cause I don't care for the 12-eq tritone enough to
>want to keep it around.

46 has more accurate tritones. The presence of the half octave
does mean you can perform the "tritone substitution" without comma
shifts.

>Let's not forgot 53, which is an all around great tuning. I don't mind
>the slight beating of the 7th harmonic stuff.

Yes, 53 is great.

>> >I go back and forth on this, though. 17 and ilk are fun for just being
>> >wack.
>>
>> Yeah. 15 and 26 are nice wackage points. Then again, some say
>> that 18 is Blackwood's best etude.
>
>That's the Messiaen sounding one, right?

Yes, I think so.

>15 is great. it's like east meets west, and it's wacky...Mizarian
>Porcupine is a legend.

As I keep saying, I'm also extremely fond of Blackwood's 15-tone
etude, and as well of his 15-tone guitar suite.

-Carl

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> >> >But I'm getting tired of it, and find I'm more attracted to 31
and 53
> >> >these days. I guess 41 and 43, too.
> >>
> >> I don't see the appeal of 43 over 31. And don't forget 22 and 46!
> >
> >yeah...i guess I agree, you lose 7th partial stuff quite a bit, but
> >some people prefer 1/5 comma triad to 1/4-comma ones.
> >
> >I'm not fond (overly) of 22. It strikes me as bland for some reason.
>
> The tetrads sound about as rough as triads do in 12. However, like
> 12, 22 does more in fewer notes than, well, just about any tuning
> besides 12.

True. I think it's interesting for all the reasons Paul mentioned,
too, that it's not meantone, so it can bring music to new directions,
the decatonic scale, etc.

One problem is perhaps there are very few pieces in 22 I've flipped
for. What's the repertoire in 22 that bowls you over?

> >46 seems intriguing, but I guess I feel like a want a prime mumber (or
> >at least odd #), cause I don't care for the 12-eq tritone enough to
> >want to keep it around.
>
> 46 has more accurate tritones. The presence of the half octave
> does mean you can perform the "tritone substitution" without comma
> shifts.

Yes...and again, it's on the "other side of twelve" from 19, 31, etc.
so little has been done with it.

> >Let's not forgot 53, which is an all around great tuning. I don't mind
> >the slight beating of the 7th harmonic stuff.
>
> Yes, 53 is great.

And whatever works in it works in at least 5 limit JI, and sometimes
the reverse. I know JI purists wouldn't like the beating, but in most
music, I think it's barely noticeable. I'm with Gene---a little
beating, quasi-JI, is fine with me.

> As I keep saying, I'm also extremely fond of Blackwood's 15-tone
> etude, and as well of his 15-tone guitar suite.

Since you reintroduced me to it, I like the 15-etude the best, too.
The 19-etude has it's fine moments, but mostly sounds a bit
traditional in a less than exciting way to me.

-A.

--- In MakeMicroMusic@yahoogroups.com, "Prent Rodgers"
<prentrodgers@...> wrote:
>
> Aaron,
> These four tracks are terrific. I found each one to have that
> wonderful 19-on-edge, about-to-fall-off-a-cliff sound. The Tarantella
> was really well done, my congrats to the great Dr. La'oud S. Peekers.
> He's my favorite performer at the time also.
>
> But the live duos were also great. I wish I could have experienced the
> dynamics of moving melodies from one keyboard to another in person.
> All very well done.
>
> I anxiously await some more.

Thanks, Prent. Glad you liked em! I'll put up Chris Bailey's 'Ditty'
next---it's an amazing piece, and he and Jacob did a great, energetic
performance of it.

-A.

>One problem is perhaps there are very few pieces in 22 I've flipped
>for. What's the repertoire in 22 that bowls you over?

It's a massively underused ET. I like Paul's pieces.

>> >Let's not forgot 53, which is an all around great tuning. I don't mind
>> >the slight beating of the 7th harmonic stuff.
>>
>> Yes, 53 is great.
>
>And whatever works in it works in at least 5 limit JI, and sometimes
>the reverse. I know JI purists wouldn't like the beating, but in most
>music, I think it's barely noticeable. I'm with Gene---a little
>beating, quasi-JI, is fine with me.

Even in lab conditions, it's quite hard to hear the triads aren't
just.

-Carl

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> >One problem is perhaps there are very few pieces in 22 I've flipped
> >for. What's the repertoire in 22 that bowls you over?
>
> It's a massively underused ET.
>

So we should organize a 22-tone piano project next?
22edo is actually a candidate to be my favorite tuning.
--
Hans Straub

At 07:05 AM 11/5/2007, you wrote:
>--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@...> wrote:
>>
>> >One problem is perhaps there are very few pieces in 22 I've flipped
>> >for. What's the repertoire in 22 that bowls you over?
>>
>> It's a massively underused ET.
>>
>
>So we should organize a 22-tone piano project next?
>22edo is actually a candidate to be my favorite tuning.

In the chat room when the concert that just happenned was
being planned, I voted for 22, but was outnumbered.

-Carl

I've been experimenting and found 7tet and 8tet are the most natural sounding scales to play pure sine waves with (ironically 5tet, for example, which you'd think would sound much purer because notes are spread much further apart, actually sounds more dissonant in mood).

Multiples of 7 or 8tet, IE 24tet, provide an extra degree of expression by playing notes slightly above or below any 7tet subset of it.

Do any of you have any clue why this (7tet is more consonant than 5tet) phenomena happens and/or how to manipulate it to make more expressive music and open more tonal degrees of freedom?

Carl Lumma <carl@...> wrote: At 07:05 AM 11/5/2007, you wrote:
>--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@...> wrote:
>>
>> >One problem is perhaps there are very few pieces in 22 I've flipped
>> >for. What's the repertoire in 22 that bowls you over?
>>
>> It's a massively underused ET.
>>
>
>So we should organize a 22-tone piano project next?
>22edo is actually a candidate to be my favorite tuning.

In the chat room when the concert that just happenned was
being planned, I voted for 22, but was outnumbered.

-Carl

__________________________________________________
Do You Yahoo!?
Tired of spam? Yahoo! Mail has the best spam protection around
http://mail.yahoo.com

[Non-text portions of this message have been removed]

--- In MakeMicroMusic@yahoogroups.com, "Aaron Krister Johnson"
<aaron@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@> wrote:
> >
> > Hans Straub wrote...
> >
> > >As for the medley,
> >
> > I think it's a set, not a medley, right? Since there are pauses
> > between pieces?
>
> Yes you are absolutely right---I should change the link title
though.
>
> > >it keeps sounding
> > >slightly out of tune to me - that large semitone...
> >
> > 1/4-comma sounds more natural, yes, but I've always thought 1/3-
comma
> > is a nice color.
>
> One thing about 19 is that it's more practical.
>
> But I'm getting tired of it, and find I'm more attracted to 31 and
53
> these days. I guess 41 and 43, too.
>
> If I had to pick one tuning for the rest of my life, it might be 31,
> or a cool well-temp of 12 (shoot me now).
>
> I find 31 just gorgeous, and
> I don't have the same problem with the fifth that others do, or even
> the ninth. I can definately live with it for the relatively fewer #
of
> tones, and the delicious 5 and 7 limit. It even has nice strange
> possibilities (11- and 13-, etc.).
>
> I think I like novelty, but I'm enough of a traditionalist that I
want
> to say new things within more established diatonic framworks more.
So
> I couldn't be happy without the meantone ideal, where there are
> more-or-less equal diatonic step sizes (sorry, Kraig!)
>
> I go back and forth on this, though. 17 and ilk are fun for just
being
> wack. And things like 3and7 based scales (Michael Harrison stuff)
are
> just fun. I have to admit, I don't find myself all that attracted to
> things beyond the 7- limit that I feel that I *must* have them to
say
> what I want to say.
>
> -A.

Hi Aaron,

How about a cool well-temp of 19? If you construct a chain of fifths
(of ~695.6304cc) from F to E#, the major triads from F to C# will
have equal-beating intervals (5th, M3, & m3 beat at the same rates as
one another (Wilson's metameantone). There will also be three nearly-
exact 7:9's, giving you three nice 6:7:9 (subminor) triads (on C, G,
and D). (It also improves 13 in the most common keys, particularly
9:13.) The temperament is completed by renaming E# as Fb and
constructing a chain of same-size fifths from Fb to F.

A Scala file listing is given here, for your convenience:

! secor_19wt.scl
!
George Secor's 19-tone proportional-beating (5/17-comma) well
temperament
19
!
69.41306
131.54971
191.26088
260.67394
317.95963
382.52175
451.93481
504.36956
573.78263
638.34474
695.63044
765.04350
824.75467
886.89131
956.30438
1011.16460
1078.15219
1145.13978
2/1

For starters, why don't you try this out on those selections from the
Fitzwilliam Virginal Book with which you so ably opened the MW
Microfest concert?

Best,

--George

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@...> wrote:
> In the chat room when the concert that just happenned was
> being planned, I voted for 22, but was outnumbered.

Out-voted, or outnumbered? :)

Thanks George, this looks interesting.

I can verify in my spreadsheet that the major triads beat equally with
the fifth size given, but I'm interested in more of the theory behind
how meta-meantone was developed by Wilson as well, apparantly from a
limiting process of rationals...I couldn't really make sense of what I
saw in Kraig Grady's 'Wilson archives'....can anyone give a math summary?

-A.

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor" <gdsecor@...>
wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "Aaron Krister Johnson"
> <aaron@> wrote:
> >
> > --- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@> wrote:
> > >
> > > Hans Straub wrote...
> > >
> > > >As for the medley,
> > >
> > > I think it's a set, not a medley, right? Since there are pauses
> > > between pieces?
> >
> > Yes you are absolutely right---I should change the link title
> though.
> >
> > > >it keeps sounding
> > > >slightly out of tune to me - that large semitone...
> > >
> > > 1/4-comma sounds more natural, yes, but I've always thought 1/3-
> comma
> > > is a nice color.
> >
> > One thing about 19 is that it's more practical.
> >
> > But I'm getting tired of it, and find I'm more attracted to 31 and
> 53
> > these days. I guess 41 and 43, too.
> >
> > If I had to pick one tuning for the rest of my life, it might be 31,
> > or a cool well-temp of 12 (shoot me now).
> >
> > I find 31 just gorgeous, and
> > I don't have the same problem with the fifth that others do, or even
> > the ninth. I can definately live with it for the relatively fewer #
> of
> > tones, and the delicious 5 and 7 limit. It even has nice strange
> > possibilities (11- and 13-, etc.).
> >
> > I think I like novelty, but I'm enough of a traditionalist that I
> want
> > to say new things within more established diatonic framworks more.
> So
> > I couldn't be happy without the meantone ideal, where there are
> > more-or-less equal diatonic step sizes (sorry, Kraig!)
> >
> > I go back and forth on this, though. 17 and ilk are fun for just
> being
> > wack. And things like 3and7 based scales (Michael Harrison stuff)
> are
> > just fun. I have to admit, I don't find myself all that attracted to
> > things beyond the 7- limit that I feel that I *must* have them to
> say
> > what I want to say.
> >
> > -A.
>
> Hi Aaron,
>
> How about a cool well-temp of 19? If you construct a chain of fifths
> (of ~695.6304cc) from F to E#, the major triads from F to C# will
> have equal-beating intervals (5th, M3, & m3 beat at the same rates as
> one another (Wilson's metameantone). There will also be three nearly-
> exact 7:9's, giving you three nice 6:7:9 (subminor) triads (on C, G,
> and D). (It also improves 13 in the most common keys, particularly
> 9:13.) The temperament is completed by renaming E# as Fb and
> constructing a chain of same-size fifths from Fb to F.
>
> A Scala file listing is given here, for your convenience:
>
> ! secor_19wt.scl
> !
> George Secor's 19-tone proportional-beating (5/17-comma) well
> temperament
> 19
> !
> 69.41306
> 131.54971
> 191.26088
> 260.67394
> 317.95963
> 382.52175
> 451.93481
> 504.36956
> 573.78263
> 638.34474
> 695.63044
> 765.04350
> 824.75467
> 886.89131
> 956.30438
> 1011.16460
> 1078.15219
> 1145.13978
> 2/1
>
> For starters, why don't you try this out on those selections from the
> Fitzwilliam Virginal Book with which you so ably opened the MW
> Microfest concert?
>
> Best,
>
> --George
>

--- In MakeMicroMusic@yahoogroups.com, "Aaron Krister Johnson"
<aaron@...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, "George D. Secor" <gdsecor@>
wrote:
> > ...
> > How about a cool well-temp of 19? If you construct a chain of
fifths
> > (of ~695.6304cc) from F to E#, the major triads from F to C# will
> > have equal-beating intervals (5th, M3, & m3 beat at the same
rates as
> > one another (Wilson's metameantone). There will also be three
nearly-
> > exact 7:9's, giving you three nice 6:7:9 (subminor) triads (on C,
G,
> > and D). (It also improves 13 in the most common keys,
particularly
> > 9:13.) The temperament is completed by renaming E# as Fb and
> > constructing a chain of same-size fifths from Fb to F.
>
> Thanks George, this looks interesting.

My original version of this had the fifths slightly different in
size, so that a diminished 4th was exactly 7:9. A few years ago I
happened to notice that the intervals in the best major triads beat
at approximately the same rate, so I altered the size of the fifth
slightly in order to make them exactly the same.

One great advantage of a 19-tone well temperament over the equal
division is a significant improvement in the 7ths (both minor and
major, but particularly the harmonic 7th). Because 19-ET represents
both 6:7 and 7:8 with a single interval of 4deg, that interval tends
to sound ambiguous: is it a small 3rd or a large 2nd? The well
temperament remedies that problem such that, e.g., G-A# sounds like a
small 3rd (~6:7), A#-C sounds like a large 2nd (~7:8), and Ab-B
sounds ambiguous (~13:15), just as you'd want them to sound as
members of a harmonic series built on C.

> I can verify in my spreadsheet that the major triads beat equally
with
> the fifth size given, but I'm interested in more of the theory
behind
> how meta-meantone was developed by Wilson as well, apparantly from a
> limiting process of rationals...I couldn't really make sense of
what I
> saw in Kraig Grady's 'Wilson archives'....can anyone give a math
summary?
>
> -A.

While I can't speak for Erv, I _can_ give my own reasons for why I
find this tuning so attractive. In 1/4- or 1/3-comma meantone (and
also 31-ET and 19-ET) the rather quick beating of the minor or major
3rds (respectively) make the sound less restful than we would like.
In meta-meantone both 3rds beat much more slowly, and the lack of
rapid beating tends to make an instrument sound more like
it's "singing." (Much the same could be said for 34-ET, BTW.)

So I guess you could say that the rationale behind meta-meantone is
to minimize the fastest beat rate in a major triad, where the major
3rd is arrived at via a chain of four 5ths.

Best,

--George