Request for advice on a Just tuning system

Hi Folks

I'm posting to both lists in the hope of finding some advice on a tuning
system I'm trying to set up.

For a start I have a "core" pentatonic : 1/1 8/7 4/3 3/2 7/4 2/1,
to which I have added 7/6 and 12/7 to give two more pentatonics :-

1/1 8/7 4/3 3/2 12/7 2/1 and 1/1 7/6 4/3 3/2 7/4 2/1.

As I'm interested in modal modulation I've expanded on the pentatonics
melodically by selecting 14 tetrachords I want to use, up to the
19-limit. I haven't yet fully explored the harmonic resources of all the
tetrachords taken together. Before I splatter the page with all these
ratios, I'd like to ask first if anyone has expanded Partch's successful
11 limit system through 13,17 and 19, and used the system in actual
melodic and harmonic music with acoustic instruments. Once I know this I
can get on to my next questions.

I notice in "The Just Intonation Primer" that the author is sceptical or
unsure as to the efficacy of ratios involving 17 and 19. I interpret
this as relating to harmonic music. I personally have no doubt as to
their usefulness in melodic music. Again I'd be interested to hear
from/of musicians who have used the higher primes successfully in
harmonic situations.

Many thanks in anticipation.

Kind Regards

hi Alison,

> From: Alison Monteith <alison.monteith3@which.net>
> To: <tuning@yahoogroups.com>
> Sent: Monday, March 04, 2002 10:08 AM
> Subject: [tuning] Request for advice on a Just tuning system
>
>
> Hi Folks
>
> I'm posting to both lists in the hope of finding some advice on a tuning
> system I'm trying to set up.
>
> For a start I have a "core" pentatonic : 1/1 8/7 4/3 3/2 7/4 2/1,
> to which I have added 7/6 and 12/7 to give two more pentatonics :-
>
> 1/1 8/7 4/3 3/2 12/7 2/1 and 1/1 7/6 4/3 3/2 7/4 2/1.
>
> As I'm interested in modal modulation I've expanded on the pentatonics
> melodically by selecting 14 tetrachords I want to use, up to the
> 19-limit. I haven't yet fully explored the harmonic resources of all the
> tetrachords taken together. Before I splatter the page with all these
> ratios, I'd like to ask first if anyone has expanded Partch's successful
> 11 limit system through 13,17 and 19, and used the system in actual
> melodic and harmonic music with acoustic instruments. Once I know this I
> can get on to my next questions.
>
> I notice in "The Just Intonation Primer" that the author is sceptical or
> unsure as to the efficacy of ratios involving 17 and 19. I interpret
> this as relating to harmonic music. I personally have no doubt as to
> their usefulness in melodic music. Again I'd be interested to hear
> from/of musicians who have used the higher primes successfully in
> harmonic situations.

i saw Jacky's response to this (i think it was on the MMM list)
and can pretty much agree with him. i've used primes up to 31,
and even that 31-limit piece was really just an experiment.

but i'm a strong believer in 19. i haven't done anything with
it on acoustic instruments ... only on the computer. but i
generally use acoustic-like timbres, if that makes a difference.
i really like the "periodicity buzz" that you get when you
include 19 in a nice meaty chord.

my piece _Theme from "Invisible Haircut"_ uses 19 and 13
prominently in some of the chords:
http://www.ixpres.com/interval/monzo/haircut/haircut.htm

you can view the javascript lattices for it at:
http://www.ixpres.com/interval/monzo/haircut/haircutlattices.htm

and there are also links on the main "haircut" page to some
old tuning-list posts that describe the harmony in more detail.

hope that helps.

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

Now we are cooking with some gas for a change!
David Beardsley, Darren Burgess and i easily and scuccesfully mapped 17 into
a tuning
with a 17/16 instead of a 10/9
and 17/15 17/14 17/13 and i think a 17/12 in there for an improvisation.
17 otonalities functioned as action points (for something to happen) and i
found if 17/16 became "the drone" it was much easier to "hit" the rest of
the 17 mode.

Pat Pagano, Director
South East Just Intonation Society
http://www.screwmusicforever.com/SHREESWIFT/
----- Original Message -----
From: Alison Monteith <alison.monteith3@which.net>
To: <tuning@yahoogroups.com>
Sent: Monday, March 04, 2002 1:08 PM
Subject: [tuning] Request for advice on a Just tuning system

> Hi Folks
>
> I'm posting to both lists in the hope of finding some advice on a tuning
> system I'm trying to set up.
>
> For a start I have a "core" pentatonic : 1/1 8/7 4/3 3/2 7/4 2/1,
> to which I have added 7/6 and 12/7 to give two more pentatonics :-
>
> 1/1 8/7 4/3 3/2 12/7 2/1 and 1/1 7/6 4/3 3/2 7/4 2/1.
>
> As I'm interested in modal modulation I've expanded on the pentatonics
> melodically by selecting 14 tetrachords I want to use, up to the
> 19-limit. I haven't yet fully explored the harmonic resources of all the
> tetrachords taken together. Before I splatter the page with all these
> ratios, I'd like to ask first if anyone has expanded Partch's successful
> 11 limit system through 13,17 and 19, and used the system in actual
> melodic and harmonic music with acoustic instruments. Once I know this I
> can get on to my next questions.
>
> I notice in "The Just Intonation Primer" that the author is sceptical or
> unsure as to the efficacy of ratios involving 17 and 19. I interpret
> this as relating to harmonic music. I personally have no doubt as to
> their usefulness in melodic music. Again I'd be interested to hear
> from/of musicians who have used the higher primes successfully in
> harmonic situations.
>
> Many thanks in anticipation.
>
> Kind Regards
>
>
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
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>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
>
>
>

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> Hi Folks
>
> I'm posting to both lists in the hope of finding some advice on a
tuning
> system I'm trying to set up.
>
> For a start I have a "core" pentatonic : 1/1 8/7 4/3 3/2 7/4
2/1,
> to which I have added 7/6 and 12/7 to give two more pentatonics :-
>
> 1/1 8/7 4/3 3/2 12/7 2/1 and 1/1 7/6 4/3 3/2 7/4 2/1.
>
> As I'm interested in modal modulation I've expanded on the
pentatonics
> melodically by selecting 14 tetrachords I want to use, up to the
> 19-limit.

hope my original reply to this gets posted.

in addition to everything i mentioned there, i notice that you will
find many of the pentatonics you're looking for, as well as ratios of
13, 15, 17, and implied ratios of 19 (via the 1216:1215 comma), in
the 22-tone tuning at the bottom of this page:

http://www.anaphoria.com/trans22.PDF

since this is designed for tubulong, gives frequency values, and has
a number of notes you're accustomed to working with, it may be just
the sort of think you're looking for . . .

i wrote,

> in addition to everything i mentioned there, i notice that you will
> find many of the pentatonics you're looking for, as well as ratios
of
> 13, 15, 17, and implied ratios of 19 (via the 1216:1215 comma), in
> the 22-tone tuning at the bottom of this page:
>
> http://www.anaphoria.com/trans22.PDF

it appears wilson is also using the 57:56 comma to construct the
tuning, though i'm sure he doesn't mean the 57:56 is to be ignored
(it's 30.6 cents while 1216:1215 is 1.4 cents) . . . perhaps kraig
can tell us whether erv really meant the evangelina tuning to have
different variants, one with 7/6 and another with 19/16?

--- In tuning@y..., "shreeswifty" <ppagano@b...> wrote:

/tuning/topicId_35212.html#35237

> Now we are cooking with some gas for a change!
> David Beardsley, Darren Burgess and i easily and scuccesfully
mapped 17 into
> a tuning
> with a 17/16 instead of a 10/9
> and 17/15 17/14 17/13 and i think a 17/12 in there for an
improvisation.
> 17 otonalities functioned as action points (for something to
happen) and i
> found if 17/16 became "the drone" it was much easier to "hit" the
rest of
> the 17 mode.
>
>
> Pat Pagano, Director
> South East Just Intonation Society
> http://www.screwmusicforever.com/SHREESWIFT/

***Isn't this the same tuning, Swifty, that you and Beardsley came up
with a couple of years ago? You probably have accumulated several
works in this tuning by now, I would imagine...

jp

yessir
i have a piece that will be being diffused at CCRMA next week.
spinal_chords uses the famous Pagano/Beardsley scale
it is a csound composition which attempts to make 60 or so chords from the
scale
using Chaosynth(linux) as a generator. It differs from the Mac/Win version
as it uses a csound score generation utility.
the Pc and Mac version is closed source and quite different - it seems more
like a granulator.

cheers

Pat Pagano, Director
South East Just Intonation Society
http://www.screwmusicforever.com/SHREESWIFT/
----- Original Message -----
From: jpehrson2 <jpehrson@rcn.com>
To: <tuning@yahoogroups.com>
Sent: Thursday, March 07, 2002 12:06 AM
Subject: [tuning] Re: Request for advice on a Just tuning system

> --- In tuning@y..., "shreeswifty" <ppagano@b...> wrote:
>
> /tuning/topicId_35212.html#35237
>
> > Now we are cooking with some gas for a change!
> > David Beardsley, Darren Burgess and i easily and scuccesfully
> mapped 17 into
> > a tuning
> > with a 17/16 instead of a 10/9
> > and 17/15 17/14 17/13 and i think a 17/12 in there for an
> improvisation.
> > 17 otonalities functioned as action points (for something to
> happen) and i
> > found if 17/16 became "the drone" it was much easier to "hit" the
> rest of
> > the 17 mode.
> >
> >
> > Pat Pagano, Director
> > South East Just Intonation Society
> > http://www.screwmusicforever.com/SHREESWIFT/
>
> ***Isn't this the same tuning, Swifty, that you and Beardsley came up
> with a couple of years ago? You probably have accumulated several
> works in this tuning by now, I would imagine...
>
> jp
>
>
>
>
>
> You do not need web access to participate. You may subscribe through
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>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
>
>
>

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

> I'd like to ask first if anyone has expanded Partch's successful
> 11 limit system through 13,17 and 19, and used the system in actual
> melodic and harmonic music with acoustic instruments.

the answer to that question involves the names "Cassandra" and "Erv
Wilson". a set of 53-tone (plus auxillaries) 13-limit designs, which
i believe are patterned after and include partch's 41-tone (plus two
auxillaries) 11-limit design.

btw, i even found some curious 49-tone 13-limit periodicity blocks
last night . . . and in the archives you'll find a string of 41-tone
13-limit systems i devised for justin white, if you're interested.

i'm certain gene could wave his mathemagical wand and provide some
even more compelling alternatives.

however, i'd first like to know what you mean by "modal modulation".
if you mean changing modes over a constant tonic, then this
particular tack, expanding partch's system, may not be the most
desirable one for you . . . of course you would know best.

> I notice in "The Just Intonation Primer" that the author is
sceptical or
> unsure as to the efficacy of ratios involving 17 and 19. I interpret
> this as relating to harmonic music. I personally have no doubt as to
> their usefulness in melodic music.

i agree -- any interval can work wonderfully in melodic music.

> Again I'd be interested to hear
> from/of musicians who have used the higher primes successfully in
> harmonic situations.

17 and 19 are very compelling harmonically in an otonal context. this
has been reported by ellis, carlos, and many others. if you have a
chance, look over my recent discussions with chris here and on
makemicromusic, you'll see how strongly we both felt, after
experiencing it, that 19-limit otonal chords were, in a certain
sense, the "true" or most root-defining tuning of a wide array of
modern, chromatic harmonies.

> From: shreeswifty <ppagano@bellsouth.net>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, March 05, 2002 6:52 PM
> Subject: Re: [tuning] Request for advice on a Just tuning system
>
>
> Now we are cooking with some gas for a change!
> David Beardsley, Darren Burgess and i easily and scuccesfully mapped 17
into
> a tuning
> with a 17/16 instead of a 10/9
> and 17/15 17/14 17/13 and i think a 17/12 in there for an
improvisation.
> 17 otonalities functioned as action points (for something to happen) and i
> found if 17/16 became "the drone" it was much easier to "hit" the rest of
> the 17 mode.

thanks for bringing that up, pat! i've had a webpage
about your 17-limit scale online for awhile, and forgot
about it.

"A 13-tone 7...17-limit scale of Pat Pagano and David Beardsley"
http://www.ixpres.com/interval/monzo/pagano-beardsley/7-17-limit.htm

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > From: shreeswifty <ppagano@b...>
> > To: <tuning@y...>
> > Sent: Tuesday, March 05, 2002 6:52 PM
> > Subject: Re: [tuning] Request for advice on a Just tuning system
> >
> >
> > Now we are cooking with some gas for a change!
> > David Beardsley, Darren Burgess and i easily and scuccesfully
mapped 17
> into
> > a tuning
> > with a 17/16 instead of a 10/9
> > and 17/15 17/14 17/13 and i think a 17/12 in there for an
> improvisation.
> > 17 otonalities functioned as action points (for something to
happen) and i
> > found if 17/16 became "the drone" it was much easier to "hit" the
rest of
> > the 17 mode.
>
>
> thanks for bringing that up, pat! i've had a webpage
> about your 17-limit scale online for awhile, and forgot
> about it.
>
> "A 13-tone 7...17-limit scale of Pat Pagano and David Beardsley"
> http://www.ixpres.com/interval/monzo/pagano-beardsley/7-17-limit.htm

what happened to the 17/15, 17/14, and 17/13 pat mentioned above?

He Paul
The Pag/Beard scale came afterwards using 17/16 as the "drone"
the scenario i was relating was a day previous improvisation. I did not
think mode 17 was my or david's own invention, but i do have so video/audio
of the piece which is rather nice.
It has Beardsley on lap steel , my monkiness on violin and darren on
modified Just ARP OMNI II.

cheers

Pat Pagano, Director
South East Just Intonation Society
http://www.screwmusicforever.com/SHREESWIFT/
----- Original Message -----
From: paulerlich <paul@stretch-music.com>
To: <tuning@yahoogroups.com>
Sent: Thursday, March 07, 2002 9:11 AM
Subject: [tuning] Re: Request for advice on a Just tuning system

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > > From: shreeswifty <ppagano@b...>
> > > To: <tuning@y...>
> > > Sent: Tuesday, March 05, 2002 6:52 PM
> > > Subject: Re: [tuning] Request for advice on a Just tuning system
> > >
> > >
> > > Now we are cooking with some gas for a change!
> > > David Beardsley, Darren Burgess and i easily and scuccesfully
> mapped 17
> > into
> > > a tuning
> > > with a 17/16 instead of a 10/9
> > > and 17/15 17/14 17/13 and i think a 17/12 in there for an
> > improvisation.
> > > 17 otonalities functioned as action points (for something to
> happen) and i
> > > found if 17/16 became "the drone" it was much easier to "hit" the
> rest of
> > > the 17 mode.
> >
> >
> > thanks for bringing that up, pat! i've had a webpage
> > about your 17-limit scale online for awhile, and forgot
> > about it.
> >
> > "A 13-tone 7...17-limit scale of Pat Pagano and David Beardsley"
> > http://www.ixpres.com/interval/monzo/pagano-beardsley/7-17-limit.htm
>
> what happened to the 17/15, 17/14, and 17/13 pat mentioned above?
>
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
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>
>
>
>

monz wrote:

>
> hi Alison,
>
> > From: Alison Monteith <alison.monteith3@which.net>
> > To: <tuning@yahoogroups.com>
> > Sent: Monday, March 04, 2002 10:08 AM
> > Subject: [tuning] Request for advice on a Just tuning system
> >
> >
> > Hi Folks
> >
> > I'm posting to both lists in the hope of finding some advice on a tuning
> > system I'm trying to set up.
> >
> > For a start I have a "core" pentatonic : 1/1 8/7 4/3 3/2 7/4 2/1,
> > to which I have added 7/6 and 12/7 to give two more pentatonics :-
> >
> > 1/1 8/7 4/3 3/2 12/7 2/1 and 1/1 7/6 4/3 3/2 7/4 2/1.
> >
> > As I'm interested in modal modulation I've expanded on the pentatonics
> > melodically by selecting 14 tetrachords I want to use, up to the
> > 19-limit. I haven't yet fully explored the harmonic resources of all the
> > tetrachords taken together. Before I splatter the page with all these
> > ratios, I'd like to ask first if anyone has expanded Partch's successful
> > 11 limit system through 13,17 and 19, and used the system in actual
> > melodic and harmonic music with acoustic instruments. Once I know this I
> > can get on to my next questions.
> >
> > I notice in "The Just Intonation Primer" that the author is sceptical or
> > unsure as to the efficacy of ratios involving 17 and 19. I interpret
> > this as relating to harmonic music. I personally have no doubt as to
> > their usefulness in melodic music. Again I'd be interested to hear
> > from/of musicians who have used the higher primes successfully in
> > harmonic situations.
>
> i saw Jacky's response to this (i think it was on the MMM list)
> and can pretty much agree with him. i've used primes up to 31,
> and even that 31-limit piece was really just an experiment.
>
> but i'm a strong believer in 19. i haven't done anything with
> it on acoustic instruments ... only on the computer. but i
> generally use acoustic-like timbres, if that makes a difference.
> i really like the "periodicity buzz" that you get when you
> include 19 in a nice meaty chord.
>
> my piece _Theme from "Invisible Haircut"_ uses 19 and 13
> prominently in some of the chords:
> http://www.ixpres.com/interval/monzo/haircut/haircut.htm
>
> you can view the javascript lattices for it at:
> http://www.ixpres.com/interval/monzo/haircut/haircutlattices.htm
>
> and there are also links on the main "haircut" page to some
> old tuning-list posts that describe the harmony in more detail.
>
> hope that helps.
>
> -monz
>
> It helps indeed. I'm still looking for epithets to describe 17 and 19, if this is possible.
> Thank you.

Regards

paulerlich wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> > I'd like to ask first if anyone has expanded Partch's successful
> > 11 limit system through 13,17 and 19, and used the system in actual
> > melodic and harmonic music with acoustic instruments.
>
> the answer to that question involves the names "Cassandra" and "Erv
> Wilson". a set of 53-tone (plus auxillaries) 13-limit designs, which
> i believe are patterned after and include partch's 41-tone (plus two
> auxillaries) 11-limit design.
>
> btw, i even found some curious 49-tone 13-limit periodicity blocks
> last night . . . and in the archives you'll find a string of 41-tone
> 13-limit systems i devised for justin white, if you're interested.
>
> i'm certain gene could wave his mathemagical wand and provide some
> even more compelling alternatives.
>
> however, i'd first like to know what you mean by "modal modulation".
> if you mean changing modes over a constant tonic, then this
> particular tack, expanding partch's system, may not be the most
> desirable one for you . . . of course you would know best.

The modal modulation I'm referring to in it's simplest form in 12 tet would be moving from C
ionian to D harmonic minor to wherever, exploiting common tones at the changeover and using only
the harmonic resources of the mode in use. Shostakovich used the technique and so do some jazz
players who like to think modally over the changes. All of which works well in equal temperaments.
I'd like to explore this with Just tetrachords (or larger structures) though I'm obviously asking
for trouble with extremely large numbers of pitches unless I think carefully and look for a well
related set of tones.

>
> > I notice in "The Just Intonation Primer" that the author is
> sceptical or
> > unsure as to the efficacy of ratios involving 17 and 19. I interpret
> > this as relating to harmonic music. I personally have no doubt as to
> > their usefulness in melodic music.
>
> i agree -- any interval can work wonderfully in melodic music.
>
> > Again I'd be interested to hear
> > from/of musicians who have used the higher primes successfully in
> > harmonic situations.
>
> 17 and 19 are very compelling harmonically in an otonal context. this
> has been reported by ellis, carlos, and many others. if you have a
> chance, look over my recent discussions with chris here and on
> makemicromusic, you'll see how strongly we both felt, after
> experiencing it, that 19-limit otonal chords were, in a certain
> sense, the "true" or most root-defining tuning of a wide array of
> modern, chromatic harmonies.
>

Thanks, I'll have a search.

Regards.

paulerlich wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> > Hi Folks
> >
> > I'm posting to both lists in the hope of finding some advice on a
> tuning
> > system I'm trying to set up.
> >
> > For a start I have a "core" pentatonic : 1/1 8/7 4/3 3/2 7/4
> 2/1,
> > to which I have added 7/6 and 12/7 to give two more pentatonics :-
> >
> > 1/1 8/7 4/3 3/2 12/7 2/1 and 1/1 7/6 4/3 3/2 7/4 2/1.
> >
> > As I'm interested in modal modulation I've expanded on the
> pentatonics
> > melodically by selecting 14 tetrachords I want to use, up to the
> > 19-limit.
>
> hope my original reply to this gets posted.
>
> in addition to everything i mentioned there, i notice that you will
> find many of the pentatonics you're looking for, as well as ratios of
> 13, 15, 17, and implied ratios of 19 (via the 1216:1215 comma), in
> the 22-tone tuning at the bottom of this page:
>
> http://www.anaphoria.com/trans22.PDF
>
> since this is designed for tubulong, gives frequency values, and has
> a number of notes you're accustomed to working with, it may be just
> the sort of think you're looking for . . .
>

I must have missed this one in my trawl through Anaphorian files. Most intriguing. Of course the
proof of the pudding is in the eating as they say and I'll have a good listen on the sampler. Many
thanks.

Kind regards

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

> > however, i'd first like to know what you mean by "modal
modulation".
> > if you mean changing modes over a constant tonic, then this
> > particular tack, expanding partch's system, may not be the most
> > desirable one for you . . . of course you would know best.
>
> The modal modulation I'm referring to in it's simplest form in 12
tet would be moving from C
> ionian to D harmonic minor to wherever, exploiting common tones at
the changeover and using only
> the harmonic resources of the mode in use.

i see . . . then, if you decide on a few types of modal modulation
schemes *a priori*, it's almost guaranteed that the corresponding
just intonation system would indeed have to have a very large number
of pitches to support what you're asking. i wonder if you'd consider
the possibility of using microtemperament to decrease the number of
pitches you'd be using?

then again, the evangelina system, just intonation with 22 tones
(plus substitute bars) would still give you a great variety of modal
modulations to choose from -- though most of the ones you might think
of *a priori* would be impossible. instead, the tuning would dictate
how your music flows -- which is not necessarily a bad thing!

> Shostakovich used the technique and so do some jazz
> players who like to think modally over the changes.

i can attest to this, but often this is a case of changing a lot more
mentally than changing the actual pitches one is using. the
distinction is an important one when choosing a tuning system.

> All of which works well in equal temperaments.
> I'd like to explore this with Just tetrachords (or larger
structures) though I'm obviously asking
> for trouble with extremely large numbers of pitches unless I think
carefully and look for a well
> related set of tones.

just want to reiterate that there is a *huge* middle ground between
equal temperaments and just intonation. particularly in the 19-limit.
since the primes 3, 5, 7, 11, 13, 17, and 19 are involved, equal
temperament and just intonation are both fairly extreme examples
(where one tempers out seven and zero commas, respectively). even
evangelista, as wilson presented it, implies a tempering-out of
1215:1216, though in this case a just implementation leaves little to
be desired (as a full, undistributed 1215:1216 is only 1.4 cents).

paulerlich wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> > > however, i'd first like to know what you mean by "modal
> modulation".
> > > if you mean changing modes over a constant tonic, then this
> > > particular tack, expanding partch's system, may not be the most
> > > desirable one for you . . . of course you would know best.
> >
> > The modal modulation I'm referring to in it's simplest form in 12
> tet would be moving from C
> > ionian to D harmonic minor to wherever, exploiting common tones at
> the changeover and using only
> > the harmonic resources of the mode in use.
>
> i see . . . then, if you decide on a few types of modal modulation
> schemes *a priori*, it's almost guaranteed that the corresponding
> just intonation system would indeed have to have a very large number
> of pitches to support what you're asking. i wonder if you'd consider
> the possibility of using microtemperament to decrease the number of
> pitches you'd be using?

I'm trying to keep to a Just system for the next project.

>
> then again, the evangelina system, just intonation with 22 tones
> (plus substitute bars) would still give you a great variety of modal
> modulations to choose from -- though most of the ones you might think
> of *a priori* would be impossible. instead, the tuning would dictate
> how your music flows -- which is not necessarily a bad thing!

Still studying Evangelina on the keyboard. Thanks for the advice.

Best Wishes

>