Yahoo Tuning Groups Ultimate Backup tuning Personal e-mail problems

Hello, there, everyone, and my apologies for using this public forum to
report some private e-mail problems which might be affecting people here
who have been trying to reach me. Since some of the matters for these
e-mails do relate to our tuning community, I hope this won't be too much
of a license.

Please let me explain that I am unable to download any files from the
Yahoo site because some months ago, they put in a Sign-In Web page
requiring a browser with support for secure log-in (HTTPS). There's a line
of the text on this Sign-In screen suggesting that there _should_ be a
menu item for a "Standard" login, without the security barrier, but I
might guess that the intended HTML could be broken, since I can't find any
such link in Lynx, including a possible hidden link.

The Yahoo FAQ helpfully explains why the secure mode might fail, and
mentions the option of Standard mode, but doesn't explain how to access
the latter option. This suggests to me that "Standard" _should_ be a
self-evident link, and that something could be wrong with the HTML.

I've tried following their technical support or "Customer Care" procedure
to report this problem, using their Web forms and e-mail followups, but
have gotten no response -- this has been going on for some months. It
means that I can't login, download files with links posted here, or do
other things requiring a Sign-in.

As to e-mail, I've recently tried to get in touch with George Secor and
John Chalmers. A recent response here from George Secor suggests that one
of my outgoing private messages got through, but I haven't received any
new incoming mail from either George or John, and have been unable, as
explained above, to access the file of previously sent e-mails at Yahoo. I
have pretty confidently figured out the password, George, and if that file
could be played at some other Web site, I could download it.

If someone had the clout to get Yahoo to straighten out the "Standard
mode" login with Lynx, I could download it there too; so far, that hasn't
happened.

Anyway, I'm very concerned about this problem with some of my incoming
e-mail -- I'm not sure if outgoing e-mail is being affected, although
Tuning List posts have been showing up in the Digests I get (no problem
there) and at Yahoo (fortunately, I don't need to Sign-in to read the
archives or latest posts).

Since other people here could also conceivably have tried to reach me, I
am reporting the problem here. Earlier this week I had my ISP remove a new
e-mail filtering system which I was unable to access, which was meant to
intercept "suspicious" e-mail (junk mail, viruses), but might be
intercepting other legitimate personal e-mail as well. I was unable to
access the Web site for viewing, screening, and downloading these
"suspicious" messages, for reasons very similar to the Yahoo problem. I
hope that removing this filtering might help with the incoming e-mail
problem; I was told that it had been removed later on the same day that I
made the request.

My concern is to keep up essential communications, and also to let anyone
affected know what has been happening. Thank you for your patience and
your understanding as to why I am posting this information here.

Most appreciatively,

Margo Schulter
mschulter@value.net

🔗jonszanto <JSZANTO@ADNC.COM>

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
> Hello, there, everyone, and my apologies for using this public
> forum to report some private e-mail problems which might be
> affecting people here who have been trying to reach me.

We owe you a lot, Margo, so don't apologize.

> Since other people here could also conceivably have tried to reach
> me, I am reporting the problem here. Earlier this week I had my
> ISP remove a new e-mail filtering system which I was unable to
> access, which was meant to intercept "suspicious" e-mail (junk
> mail, viruses), but might be intercepting other legitimate
> personal e-mail as well.

I suspect that even if you are having problems with Yahoo, your ISP may be a problem as well. I sent you an email yesterday, the 13th, at about 9:00 am, as relayed from George Secor. This was done from my own email acct, and if you haven't received it then your ISP is at fault.

I hope that you/we can get it resolved (though I give virtually no chance to Yahoo, and you may have to alter *your* email/web habits to accomodate), and I hope that our forum will not be bugged if you need to occasionally post a public note such as the one I'm replying to.

Very best,
Jon

🔗M. Schulter <MSCHULTER@VALUE.NET>

Hello, there, Alison and everyone.

Thank you for raising questions about your 7-based pentatonic or
slendro-like scale which made me realize some special reasons to use
some JI tunings I have based on or including factors of 2-3-7-9.

Like you, I'm enthusiastic about both JI systems and temperaments; for
me, they are different ways approaching the open continuum of
intervals, each with its own charms. It's true that a given tuning in
either approach _could_ be approximated, more or less, by a tuning
using the other; but why not enjoy the variety of both, as we seem to
do quite happily?

For your septimal pentatonic, I would say that the simple arithmetic
of the septimal comma at 64:63, or about 27.26 cents, suggests that
for a five-note scale, the alternatives are either JI or some very
appreciable "compromise" of the fifths and fourths, the 7-based
intervals, or both.

You _could_, of course, do this in 22-tET with the fifths about 7
cents wide, or also in George Secor's fine 17-note well-temperament
with the fifths a bit more than 5 cents wide.

You _could_ also, of course, take those five notes of your instrument
from some "near-just" system designed to use lots more notes,
including some of the ones I use.

However, for both of us, simply tuning it in JI is a very appealing
solution. While there's a potential "bug" in this solution, that bug
could also be a very valuable feature in the right musical context.
Here I'll arbitrarily use D for the lowest note of your pentatonic:

D F G A C D
1/1 7/6 4/3 3/2 7/4 2/1
0 267 498 702 969 1200

Here the potential "complication" is the narrow 21:16 fourth between G
and C, about 471 cents.

However, that same narrow fourth can take part in some fine "crunchy"
sonorities of a kind celebrated by Keenan Pepper, who discussed the
use of 16:21:24:27. Here, if your instrument has a second octave, that
would be, for example, G3-C4-D4-F4 (with C4 as middle C).

If the instrument has only one octave, you could still do G3-C4-D4, or
16:21:24.

An advantage of JI is that it often generates new and unexpected
intervals of this kind, which can be seen not as "flaws" but as
stimulating resources.

The usefulness of these intervals depends, of course, on style and
taste. In a 5-limit JI system used for conventional 16th-century
European music, fifths or thirds of other than the expected size are
often simply "navigational hazards": but in a septimal pentatonic,
something like 16:21:24:28 could be an invigorating touch.

This has become one of my favorite special effects in 3-7 JI systems,
which I like to emulate in temperaments with intervals near 16:21
also.

If I were going to bring up the question of any possible "refinement"
of your beautiful JI tuning, however hypothetically or playfully
(since it changes the terms of the problem a bit), I might mention the
idea of an instrument with an extra sixth string, which could be tuned
to 16/9, thus "fixing" the 21:16 "problem" -- when you want it fixed,
that is -- while still leaving that interval available when you choose
to use it:

D F G A C1 C2 D
1/1 7/6 4/3 3/2 7/4 16/9 2/1
0 267 498 702 969 996 1200

This is an approach I take in some of my own 3-7 tunings; it means a
bit more complication, but keeps an uncompromising JI approach while
increasing the range of musical intervals and options. Now we have
available either the pure fourth G-C2, or the 21:16 at G-C1.

There's also a 27-cent step C1-C2, a real "microinterval" that might
have interesting melodic uses.

Anyway, your JI scale made me realize that often I tend to use JI
systems where the 7-based intervals are "auxilliary" degrees, so that
even if I play in parallel sonorities like 12:14:18:21 or 14:18:21:24,
the melodies often move mostly in Pythagorean steps (apart from
cadences, where 28:27 semitones or thirdtones are routine).

While this kind of arrangement is ideal for lots of my music in three
or four parts, your post made me realize that to play a scale like
yours, I would typically find myself moving between the two manuals to
get the basic five notes.

This made me realize a special advantage of some tunings I have with
2-3-7-9 JI where I can simply play D-F-G-A-C-D, or whatever, and get
your pentatonic scale. I want to try it, for example, over a drone,
where it should be really delightful.

Specifically, a bit more than a year and half ago, I set up a 3-7 JI
tuning based on the diatonic of Archytas, where D-A is wide by a 64:63
-- but haven't used it much. Your scale gives me a great reason to get
better acquainted with that tuning -- thank you!

Most appreciatively,

Margo Schulter
mschulter@value.net

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:

/tuning/topicId_37751.html#37764

>>
> D F G A C1 C2 D
> 1/1 7/6 4/3 3/2 7/4 16/9 2/1
> 0 267 498 702 969 996 1200
>
> This is an approach I take in some of my own 3-7 tunings; it means a
> bit more complication, but keeps an uncompromising JI approach while
> increasing the range of musical intervals and options. Now we have
> available either the pure fourth G-C2, or the 21:16 at G-C1.
>
> There's also a 27-cent step C1-C2, a real "microinterval" that might
> have interesting melodic uses.
>

***Hello Margo...

This is an interesting concept to me since it seems a bit reflective
of the Blackjack scale in which there is a small interval of 33
cents... It seems almost as though the small interval in Blackjack
is a Just Intonation "correction" in a way, and helps provide the
larger number of quasi just (wafso-just... within a fair sense of
just) that we find in Blackjack.

Maybe Paul can either back me up on this, or provide counter
argument... Paul??

Thanks!

Joseph

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗emotionaljourney22 <paul@stretch-music.com>

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
>
> /tuning/topicId_37751.html#37764
>
> >>
> > D F G A C1 C2 D
> > 1/1 7/6 4/3 3/2 7/4 16/9 2/1
> > 0 267 498 702 969 996 1200
> >
> > This is an approach I take in some of my own 3-7 tunings; it
means a
> > bit more complication, but keeps an uncompromising JI approach
while
> > increasing the range of musical intervals and options. Now we have
> > available either the pure fourth G-C2, or the 21:16 at G-C1.
> >
> > There's also a 27-cent step C1-C2, a real "microinterval" that
might
> > have interesting melodic uses.
> >
>
>
> ***Hello Margo...
>
> This is an interesting concept to me since it seems a bit
reflective
> of the Blackjack scale in which there is a small interval of 33
> cents... It seems almost as though the small interval in Blackjack
> is a Just Intonation "correction" in a way, and helps provide the
> larger number of quasi just (wafso-just... within a fair sense of
> just) that we find in Blackjack.
>
> Maybe Paul can either back me up on this, or provide counter
> argument... Paul??
>
> Thanks!

well, the 27 cent interval in question is 64:63, and yes, blackjack
represents the 64:63 with the 33 cent step . . . but 33 cent steps in
blackjack can also represent lots of other ratios, like 56:55 . . . i
made a whole post just listing these once . . .

🔗Alison Monteith <alison.monteith3@which.net>

"M. Schulter" wrote:

> Hello, there, Alison and everyone.
>
> Thank you for raising questions about your 7-based pentatonic or
> slendro-like scale which made me realize some special reasons to use
> some JI tunings I have based on or including factors of 2-3-7-9.
>
> Like you, I'm enthusiastic about both JI systems and temperaments; for
> me, they are different ways approaching the open continuum of
> intervals, each with its own charms. It's true that a given tuning in
> either approach _could_ be approximated, more or less, by a tuning
> using the other; but why not enjoy the variety of both, as we seem to
> do quite happily?
>
> For your septimal pentatonic, I would say that the simple arithmetic
> of the septimal comma at 64:63, or about 27.26 cents, suggests that
> for a five-note scale, the alternatives are either JI or some very
> appreciable "compromise" of the fifths and fourths, the 7-based
> intervals, or both.
>
> You _could_, of course, do this in 22-tET with the fifths about 7
> cents wide, or also in George Secor's fine 17-note well-temperament
> with the fifths a bit more than 5 cents wide.
>

Yes, I forgot to mention that the slendros in particular can be reasonably approximated in 22 tet,
and I have a 22tet guitar I've found that the cents difference between JI and 22 tet doesn't
bother me, particularly if I use ostinatos and other linear structures.

>
> You _could_ also, of course, take those five notes of your instrument
> from some "near-just" system designed to use lots more notes,
> including some of the ones I use.
>
> However, for both of us, simply tuning it in JI is a very appealing
> solution. While there's a potential "bug" in this solution, that bug
> could also be a very valuable feature in the right musical context.
> Here I'll arbitrarily use D for the lowest note of your pentatonic:
>
> D F G A C D
> 1/1 7/6 4/3 3/2 7/4 2/1
> 0 267 498 702 969 1200
>
> Here the potential "complication" is the narrow 21:16 fourth between G
> and C, about 471 cents.
>
> However, that same narrow fourth can take part in some fine "crunchy"
> sonorities of a kind celebrated by Keenan Pepper, who discussed the
> use of 16:21:24:27. Here, if your instrument has a second octave, that
> would be, for example, G3-C4-D4-F4 (with C4 as middle C).

Yes, I prefer sonority to dissonance here. Sounds more appealing somehow. To my ears the timbre of
a slightly "zingy" stretched string makes the 21:16 most appealing. I have a second octave and
with the careful use of contrary motion in simple counterpoint the interval can be used as a
particularly fine suspension.

>
>
> If the instrument has only one octave, you could still do G3-C4-D4, or
> 16:21:24.
>
> An advantage of JI is that it often generates new and unexpected
> intervals of this kind, which can be seen not as "flaws" but as
> stimulating resources.
>
> The usefulness of these intervals depends, of course, on style and
> taste. In a 5-limit JI system used for conventional 16th-century
> European music, fifths or thirds of other than the expected size are
> often simply "navigational hazards": but in a septimal pentatonic,
> something like 16:21:24:28 could be an invigorating touch.
>
> This has become one of my favorite special effects in 3-7 JI systems,
> which I like to emulate in temperaments with intervals near 16:21
> also.
>
> If I were going to bring up the question of any possible "refinement"
> of your beautiful JI tuning, however hypothetically or playfully
> (since it changes the terms of the problem a bit), I might mention the
> idea of an instrument with an extra sixth string, which could be tuned
> to 16/9, thus "fixing" the 21:16 "problem" -- when you want it fixed,
> that is -- while still leaving that interval available when you choose
> to use it:
>
> D F G A C1 C2 D
> 1/1 7/6 4/3 3/2 7/4 16/9 2/1
> 0 267 498 702 969 996 1200
>
> This is an approach I take in some of my own 3-7 tunings; it means a
> bit more complication, but keeps an uncompromising JI approach while
> increasing the range of musical intervals and options. Now we have
> available either the pure fourth G-C2, or the 21:16 at G-C1.

What a fine idea. A very simple but effective elaboration. I can actually do this with my
marimbas, and now that you've pointed this out I'm keen to look at other such refinements,
especially in the very uneven pelog type scales that I use.

>
> There's also a 27-cent step C1-C2, a real "microinterval" that might
> have interesting melodic uses.
>
> Anyway, your JI scale made me realize that often I tend to use JI
> systems where the 7-based intervals are "auxilliary" degrees, so that
> even if I play in parallel sonorities like 12:14:18:21 or 14:18:21:24,
> the melodies often move mostly in Pythagorean steps (apart from
> cadences, where 28:27 semitones or thirdtones are routine).
>
> While this kind of arrangement is ideal for lots of my music in three
> or four parts, your post made me realize that to play a scale like
> yours, I would typically find myself moving between the two manuals to
> get the basic five notes.
>
> This made me realize a special advantage of some tunings I have with
> 2-3-7-9 JI where I can simply play D-F-G-A-C-D, or whatever, and get
> your pentatonic scale. I want to try it, for example, over a drone,
> where it should be really delightful.

I use the pedal a lot, either as a drone or inverted drone which gives depth and meaning to the
mode in use. I also like to modulate to other modes with two or three common tones, either on the
same drone or on one of the tones of my basic slendro. I'm still working through the cadential
possibilities and produce sets of "rules" for these and for melodic movement and counterpoint,
influenced in part by the work of Dufay, Ockeghem, Obrecht and others. Often I bend the rules or
do the opposite of what is required.

>
> Specifically, a bit more than a year and half ago, I set up a 3-7 JI
> tuning based on the diatonic of Archytas, where D-A is wide by a 64:63
> -- but haven't used it much. Your scale gives me a great reason to get
> better acquainted with that tuning -- thank you!
>
> Most appreciatively,
>
> Margo Schulter
> mschulter@value.net
>

And thank you for your inspiration. Your work on cadential patterns in three and four parts in
particular has been an excellent source for my compositional method. I find that the modal harmony
of the High Middle Ages is much more easily translated into an abstract modal method of JI
composition than is the common practice tonal system.

Kind Regards

🔗jpehrson2 <jpehrson@rcn.com>

🔗M. Schulter <MSCHULTER@VALUE.NET>

Hello, there, Alison and also Kraig; thank you both for your responses
and ideas as people realizing these JI tunings with custom acoustical
instruments. It's good to be reminded of the biases that I have as
someone relying on digital technologies, as well as to get the benefit
of your ideas and experiences.

Kraig, your point about a six-note scale for ratios of 3-7 resembling
a pentatonic plus one of its transpositions made me look at this in
one of my 3-7 tunings, where indeed I could combine these two scales
to get a six-note set. Here I'll use "v" to show a note lowered a
64:63, or comma of Archytas as George Secor has aptly named it, from
Pythagorean, taking E as a reference:

E4 Gv4 A4 B4 Dv4 E4
1/1 7/6 4/3 3/2 7/4 2/1

A4 Cv4 D4 E4 Gv4 A4
1/1 7/6 4/3 3/2 7/4 2/1

Here's the six-note set with 7/4 and 16/9 with reference to E:

E4 Gv4 A4 B4 Dv4 D4 E4
1/1 7/6 4/3 3/2 7/4 16/9 2/1

Have I interpreted your comment about "modulations" or transpositions
correctly?

Now for some of your remarks, Alison:

> Yes, I forgot to mention that the slendros in particular can be
> reasonably approximated in 22 tet, and I have a 22tet guitar I've
> found that the cents difference between JI and 22 tet doesn't bother
> me, particularly if I use ostinatos and other linear structures.

Maybe we could look at this as a kind of approach somewhere between
3-7 JI and a typical gamelan tuning with fifths at around 720 cents.

> Yes, I prefer sonority to dissonance here. Sounds more appealing
> somehow. To my ears the timbre of a slightly "zingy" stretched
> string makes the 21:16 most appealing. I have a second octave and
> with the careful use of contrary motion in simple counterpoint the
> interval can be used as a particularly fine suspension.

I'd love to hear how this sounds on your instrument. On keyboard, I
find that it often has the effect of an "energetic consonance," more
or less -- in a suspension, or note against note. I could ask more
about your style, but maybe a recording would explain best (or a live
performance best of all, if I were in your neighborhood).

> A very simple but effective elaboration. I can actually do this with
> my marimbas, and now that you've pointed this out I'm keen to look
> at other such refinements, especially in the very uneven pelog type
> scales that I use.

This suggests to me that we might share a liking for something like
this, one of Lou Harrison's pelog-style pentatonics:

E4 Fv4 A4 B4 Cv5 E5
1/1 28/27 4/3 3/2 14/9 2/1
0 63 498 702 765 1200
28:27 9:7 9:8 28:27 9:7
63 435 204 63 435

I love this scale, and also a variant I use with Gv4 (7/6). It can
encourage some energetic patterns, with the uneven steps maybe lending
encouraging (although Javanese/Balinese pelogs can also get energetic
with quite different steps).

> I use the pedal a lot, either as a drone or inverted drone which
> gives depth and meaning to the mode in use. I also like to modulate
> to other modes with two or three common tones, either on the same
> drone or on one of the tones of my basic slendro. I'm still working
> through the cadential possibilities and produce sets of "rules" for
> these and for melodic movement and counterpoint, influenced in part
> by the work of Dufay, Ockeghem, Obrecht and others. Often I bend the
> rules or do the opposite of what is required.

The inverted drone is something I should try. Your synthesis sounds
really exciting, and experience indeed seems the best education in
finding the "rules" for such a style.

One of the things which really drew me into listening to gamelan, and
especially slendro, is the slow counterpoint on the instrument called
_gender_, with lots of fifths or fourths and octaves, a bit like "down
home Gothic" for me, and yet different. You remind me of some old
listening moments -- and your style could bring some new ones to lots
of people. I'm trying to imagine what your rules and patterns might be
like, reflecting a unique musical vision realized with the love of
handcrafted instruments. Thank you for sharing this process with us!

> I find that the modal harmony of the High Middle Ages is much more
> easily translated into an abstract modal method of JI composition
> than is the common practice tonal system.

One of the wonderful things is that this kind of outlook has lots of
room for a range of fertile approaches -- illumined by your custom
instruments.

Most appreciatively,

Margo

🔗Alison Monteith <alison.monteith3@which.net>

"M. Schulter" wrote:

The inverted drone is something I should try. Your synthesis sounds

> really exciting, and experience indeed seems the best education in
> finding the "rules" for such a style.
>
> One of the things which really drew me into listening to gamelan, and
> especially slendro, is the slow counterpoint on the instrument called
> _gender_, with lots of fifths or fourths and octaves, a bit like "down
> home Gothic" for me, and yet different. You remind me of some old
> listening moments -- and your style could bring some new ones to lots
> of people. I'm trying to imagine what your rules and patterns might be
> like, reflecting a unique musical vision realized with the love of
> handcrafted instruments. Thank you for sharing this process with us!

> I start from the point of view that all harmonic rules rely on a pre-compositional definition of
> consonance and dissonance. The "Franconian rule" - 'a consonance is essential at the beginning
> of a measure in all modes' invites me to define my consonances from the outset. I could define
> consonances differently for each piece, section, line of text or measure. If I was writing for
> voices, and I often imagine that I am in microtonality, I could use consonance as an emotional
> factor by describing states of mind with more fewer consonances, a form of word painting.

> Tinctoris recommends that in simplex no dissonances are permitted at all. Again this begs to be
> contextually defined in a xenharmonic context. Or the warning not to return to the same
> consonance after a dissonance. This rules out auxiliaries, but what if I return to one of the
> crunchy variants that you talked about?

The treatment of melody likewise invites a similar approach, particularly if I adopt some of the
many rules that have arisen by the time of Palestrina. For my part, I find it easier to get
started if I limit my resources - Xeno-Gothic post-minimalism anyone?

Thanks for your wisdom and insights Margo.

Kind Regards

🔗M. Schulter <MSCHULTER@VALUE.NET>

Hello, there, Alison, and please let me comment a bit on some of your
points.

> I start from the point of view that all harmonic rules rely on a
> pre-compositional definition of consonance and dissonance. The
> "Franconian rule" - 'a consonance is essential at the beginning of a
> measure in all modes' invites me to define my consonances from the
> outset. I could define consonances differently for each piece,
> section, line of text or measure. If I was writing for voices, and I
> often imagine that I am in microtonality, I could use consonance as
> an emotional factor by describing states of mind with more fewer
> consonances, a form of word painting.

This is a very creative and fertile way to approach the Franconian
rule -- and it's interesting that some 13th-14th century theorists have
different views on the degree of consonance or dissonance to be
accorded to certain intervals.

For now, I might just add that there's another formulation of the kind
of pattern that Franco suggests in a 13th-century treatise
traditionally dated maybe a generation or so earlier: generally
sonorities on primary beats should be more concordant, or less
discordant, than those on secondary beats.

Of course, then as now, theory can only express a part of the music
itself, and your own response is the best guide.

> Tinctoris recommends that in simplex no dissonances are permitted at all.

Yes, this is a typical 15th-16th century rule for note-against-note
writing.

> Again this begs to be contextually defined in a xenharmonic context.

This is very true, and your statement could apply to historical
practice also. For example, the major second (Pythagorean 9:8) and
minor seventh (Pythagorean 16:9) are regarded as having some degree of
"concord" or "compatibility" by some medieval musicians, but treated
cautiously as discords in usual Renaissance styles.

> Or the warning not to return to the same consonance after a
> dissonance. This rules out auxiliaries, but what if I return to one
> of the crunchy variants that you talked about?

Here I might have two quick replies, which might lead to a conclusion
about like this: "Do what seems right in a given piece or style, and
feel free to experiment with rules and interpretations."

First, the rule you quote might come from a Renaissance theorist like
Tinctoris; dissonance treatment in the 15th-16th century era is
relatively strict. Even in this era, however, auxiliary tones or the
like certainly occur, for example something like this in an ornamented
passage:

B4 A4 B4 C5 D5 ...
G4 G4 ...
3 2 3 4 5
-------

This isn't to say that you might not choose to avoid auxilliaries as a
stylistic choice, of course -- if an interpretation of a rule you see
leads to a musically pleasing result, or a fruitful line of
creativity, historical precedents or interpretations shouldn't get in
the way.

With "crunchy variants," one approach would be to regard them as
relatively "concordant" sonorities, following the approach you
describe above of defining concord and discord to fit a given piece or
style.

It's easy to say, "Let the rules serve the music rather than vice
versa" -- but, of course, sometimes sticking to a given rule could be
a creative way of reaching a result that you might not find otherwise.

> The treatment of melody likewise invites a similar approach,
> particularly if I adopt some of the many rules that have arisen by
> the time of Palestrina. For my part, I find it easier to get started
> if I limit my resources - Xeno-Gothic post-minimalism anyone?

Thank you for sharing this process, and your approach of setting some
rules and applying them to different schemes of "concord/discord"
could give you a special mixture of direction and freedom. Of course,
adopting "some of the many rules that have arisen by the time of
Palestrina" also involves a lot of choice and discernment, for example
as to which rules might fit together for a given piece.

> Thanks for your wisdom and insights Margo.

Thank you, Alison, for the same, and especially for sharing a
formative process like this woven of your musical wisdom and loving
craft as a designer as well as player of instruments.

Most appreciatively,

Margo

🔗Kraig Grady <kraiggrady@anaphoria.com>

Hello Margo!
I will try to illustrate how one can apply what would actually be the Marwa permutations and
not the Purvi modulation to a pentatonic as opposed to the heptatonic that Erv uses to illustrate
in his XEN. 9 article.
http://www.anaphoria.com/xen9mar.PDF
fig 8 (bottom of page 6) being the closest illustration

If we take your scale

1/1 7/6 4/3 3/2 7/4 2/1

and present it as a linear series we have the following

3/2 1/1 4/3 7/4 7/6 (3/2)

which we can see as a cycle of the following intervals

4/3 4/3 21/16 4/3 (9/7 as our closing disjunction)

now the Marwa will keep the disjunction at the end but will cycle through the previous 4
intervals in such manner

21/16 4/3 4/3 4/3 (9/7 as our closing disjunction)
4/3 21/16 4/3 4/3 (9/7 as our closing disjunction)
4/3 4/3 21/16 4/3 (9/7 as our closing disjunction)
4/3 4/3 4/3 21/16 (9/7 as our closing disjunction)

The six tone scale is generated by the last two.

B4 E4 A4 Dv4 Gv4
4/3 4/3 21/16 4/3 (9/7 as our closing disjunction)

B4 E4 A4 D4 Gv4
4/3 4/3 4/3 21/16 (9/7 as our closing disjunction)

if we had the preceding two (just because it is easier to notate here) we would have

B4 Ev4 Av4 Dv4 Gv4
21/16 4/3 4/3 4/3 (9/7 as our closing disjunction)

B4 E4 Av4 Dv4 Gv4
4/3 21/16 4/3 4/3 (9/7 as our closing disjunction)

B4 E4 A4 Dv4 Gv4
4/3 4/3 21/16 4/3 (9/7 as our closing disjunction)

B4 E4 A4 D4 Gv4
4/3 4/3 4/3 21/16 (9/7 as our closing disjunction)

"M. Schulter" wrote:

> Kraig, your point about a six-note scale for ratios of 3-7 resembling
> a pentatonic plus one of its transpositions made me look at this in
> one of my 3-7 tunings, where indeed I could combine these two scales
> to get a six-note set. Here I'll use "v" to show a note lowered a
> 64:63, or comma of Archytas as George Secor has aptly named it, from
> Pythagorean, taking E as a reference:
>
> E4 Gv4 A4 B4 Dv4 E4
> 1/1 7/6 4/3 3/2 7/4 2/1
>
> A4 Cv4 D4 E4 Gv4 A4
> 1/1 7/6 4/3 3/2 7/4 2/1
>
> Here's the six-note set with 7/4 and 16/9 with reference to E:
>
> E4 Gv4 A4 B4 Dv4 D4 E4
> 1/1 7/6 4/3 3/2 7/4 16/9 2/1
>
> Have I interpreted your comment about "modulations" or transpositions
> correctly?
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

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