Yahoo Tuning Groups Ultimate Backup tuning-math 2d-(2,3,7,11) temperaments (was: [MMM] bottle band ...)

This is in reply to MMM #9220:
--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <paul@s...>
wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
>
> > I think the 11-limit-non-5 scale (14, 17, 31, 48 family) with
> > generator between 11:14 and 7:9 (~425 cents) should have a name,
> > too. As long as we have all those colorful names for 5- and 7-
limit
> > families of temperaments, we ought to get non-5 on the list (and
> > perhaps generate more interest in both 17 and 31). Suggestions,
> > anyone? Paul, Gene?
>
> I suggest you ask Gene on the tuning-math list for a nice big
survey
> of 2-dimensional temperaments of {2,3,7,11}-JI (this may already
have
> been done and be in the archives of the tuning-math list -- I can't
> recall for sure). Then maybe part 3 of my _Middle Path_ paper (the
> one I'm sending part 1 of to everyone now) will cover this topic.
> More important than naming, though, will be the new systems -- I'm
> willing to bet that the survey will bring to your attention good
> systems that you hadn't thought of before.

Okay, I'm asking! Gene?

--George

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> --- In tuning-math@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:
>
> > Okay, I'm asking! Gene?
>
> Here. Why 11-limit no fives in particular?

Because that's the kind of scale (11-note subset of 31-ET) that Jacob
Barton used in "Sentinel" for bottle band:

/makemicromusic/topicId_9132.html#9132

As it turns out, Jacob rediscovered a scale that I originally found
in 1978 (as the 14, 17, 31, 48 family, generator ~425c):

/makemicromusic/topicId_9132.html#9141
/makemicromusic/topicId_9132.html#9218

Jacob thought that the 6:7:9:11 chord should have a simple name, and
I replied that I thought that the scale that he used should also have
a name. I thought that 17 and 31 could probably use a boost, as
evidenced by recent comments by Paul Erlich (indicating a lack of
interest in 31-ET) and Igliashon Jones (indicating a lack of interest
in the 6:7:9 triad, and by implication, 6:7:9:11 and 17-ET).

Does it already happen to have a name, and if not, do you have any
suggestions?

--George

🔗Paul Erlich <perlich@aya.yale.edu>

--- In tuning-math@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:

> Igliashon Jones (indicating a lack of interest
> in the 6:7:9 triad,

Huh? I happen to know that Igliashon is very much a fan of the 6:7:9
chord, and ordered a 22-equal guitar because he wanted a septimal
diatonic based on such triads with no wolves (which is impossible in
31-equal). Where did you get the idea that Igliashon has a lack of
interest in the 6:7:9 triad, George?

> Does it already happen to have a name, and if not, do you have any
> suggestions?

I'd be much more interested in the full list, particularly to see if
there are systems with lower complexity *and* error than the one
George mentions . . .

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
>
> --- In tuning-math@yahoogroups.com, "George D. Secor"
<gdsecor@y...>
> wrote:
>
> > Igliashon Jones (indicating a lack of interest
> > in the 6:7:9 triad,
>
> Huh? I happen to know that Igliashon is very much a fan of the
6:7:9
> chord, and ordered a 22-equal guitar because he wanted a septimal
> diatonic based on such triads with no wolves (which is impossible
in
> 31-equal). Where did you get the idea that Igliashon has a lack of
> interest in the 6:7:9 triad, George?

Perhaps I should have said a *relative* lack of interest, as
evidenced by the scales he wished to favor with a keyboard design.
Search for "6:7:9" in this message:

/makemicromusic/topicId_8475.html#8627

So another reason I'd like to have a name for Jacob's "Bottle" scale
is to make others aware of how 6:7:9 can be used in a non-diatonic or
non-pentatonic context.

> > Does it already happen to have a name, and if not, do you have
any
> > suggestions?
>
> I'd be much more interested in the full list, particularly to see
if
> there are systems with lower complexity *and* error than the one
> George mentions . . .

Fair enough, but don't forget the other scale I mentioned: the 9-tone
scale (the 17, 26, 43 family) with ~140-cent generator that gives
three 6:7:9:11 tetrads (or better yet, three 6:7:9:11:13 pentads).
I've been working on a composition using this one.

Go to it, Gene!

--George

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Paul Erlich <perlich@aya.yale.edu>

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> --- In tuning-math@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:
>
> > Does it already happen to have a name, and if not, do you have
any
> > suggestions?
>
> I know of no name for it--should we name it after Barton, as for
> instance Bartonic?

We already have "Hanson", so why not just "Barton"?

First I think we ought to take a look at this discussion between Mats
Oljare and Robert Valentine about MOS in 17-ET:

/tuning/topicId_32163.html#32163

The one that Mats actually used in the piece "Fafner" is described as:

ssLssLsL L=4 s=1 (8.3)

Bob lists seven scales in all, including these two, with 3deg17
generator:

LLsLLLs L=3 s=1 (7.2 = seven pitches, two chunks)
sssLsssLssL L=3 s=1 (11.3)

The 9-tone scale corresponds to Jacob's, with 11deg31 generator. So
who gets the name?

For the record, I found this scale (for both 17 and 31) way back in
1978, but didn't formally write about it until around late November
or early December 2001, when I was finishing up my 17-tone paper for
Xenharmonikon 18 (which is still awaiting publication). So I guess
I'm entitled to choose the name.

Now it's one thing to list a bunch of scales, generators, or commas
and quite another thing to single out one of those in the list and
use it in some practical application, e.g., in a piece of music (as
Jacob has done), as the basis for a keyboard (as I did with the
Miracle generator/Decimal keyboard), or as the linchpin for a
notation (as I did with 4095:4096 in Sagittal). As you well know,
anyone with a computer and a sufficient amount of know-how can churn
out a massive list of scales, but it takes a person with a measure of
artistic sensibility to discover or identify the ones that are most
valuable. And often such a person will stumble upon these things
almost unwittingly or haphazardly.

Hey, I had already graphed the error of each 9-limit consonance as a
function of the Hanson generator and identified its minimax value at
least several years before I ever heard of (and met) Larry Hanson (or
even Erv Wilson, for that matter), but I only considered it as one
possibility among many (instead singling out the Miracle generator as
the basis for a new keyboard). And even though I found the 9-tone
scale with 11:14~7:9 generator and multiple 6:7:9:11 tetrads over 25
years ago, I didn't think it important enough even to attempt to
write anything using it. And although I valued 22-ET enough to have
it hard-wired as one of the preset tunings on my Scalatron, I never
explored it sufficiently to discover such gems as Porcupine or Paul's
decatonic scales. So many scales, so little time -- alas, one must
pick and choose those most to treasure with one's time and attention.

So on the basis of this principle of "significant use" (taking Jacob
at his word that we can expect "other movements", etc.), "Barton"
gets my vote.

--George

🔗George D. Secor <gdsecor@yahoo.com>

🔗Paul Erlich <perlich@aya.yale.edu>

I'm pretty sure every time I named a tuning after someone, it was
because they advocated or used that system primarily or considered
it "best" for some purpose. If it's just one system out of several
the person used, I didn't name it after them, even if they were the
first to discover it.

--- In tuning-math@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...>
> wrote:
> >
> > --- In tuning-math@yahoogroups.com, "George D. Secor"
> <gdsecor@y...> wrote:
> >
> > > Does it already happen to have a name, and if not, do you have
> any
> > > suggestions?
> >
> > I know of no name for it--should we name it after Barton, as for
> > instance Bartonic?
>
> We already have "Hanson", so why not just "Barton"?
>
> First I think we ought to take a look at this discussion between
Mats
> Oljare and Robert Valentine about MOS in 17-ET:
>
> /tuning/topicId_32163.html#32163
>
> The one that Mats actually used in the piece "Fafner" is described
as:
>
> ssLssLsL L=4 s=1 (8.3)
>
> Bob lists seven scales in all, including these two, with 3deg17
> generator:
>
> LLsLLLs L=3 s=1 (7.2 = seven pitches, two chunks)
> sssLsssLssL L=3 s=1 (11.3)
>
> The 9-tone scale corresponds to Jacob's, with 11deg31 generator.
So
> who gets the name?
>
> For the record, I found this scale (for both 17 and 31) way back in
> 1978, but didn't formally write about it until around late November
> or early December 2001, when I was finishing up my 17-tone paper
for
> Xenharmonikon 18 (which is still awaiting publication). So I guess
> I'm entitled to choose the name.
>
> Now it's one thing to list a bunch of scales, generators, or commas
> and quite another thing to single out one of those in the list and
> use it in some practical application, e.g., in a piece of music (as
> Jacob has done), as the basis for a keyboard (as I did with the
> Miracle generator/Decimal keyboard), or as the linchpin for a
> notation (as I did with 4095:4096 in Sagittal). As you well know,
> anyone with a computer and a sufficient amount of know-how can
churn
> out a massive list of scales, but it takes a person with a measure
of
> artistic sensibility to discover or identify the ones that are most
> valuable. And often such a person will stumble upon these things
> almost unwittingly or haphazardly.
>
> Hey, I had already graphed the error of each 9-limit consonance as
a
> function of the Hanson generator and identified its minimax value
at
> least several years before I ever heard of (and met) Larry Hanson
(or
> even Erv Wilson, for that matter), but I only considered it as one
> possibility among many (instead singling out the Miracle generator
as
> the basis for a new keyboard). And even though I found the 9-tone
> scale with 11:14~7:9 generator and multiple 6:7:9:11 tetrads over
25
> years ago, I didn't think it important enough even to attempt to
> write anything using it. And although I valued 22-ET enough to
have
> it hard-wired as one of the preset tunings on my Scalatron, I never
> explored it sufficiently to discover such gems as Porcupine or
Paul's
> decatonic scales. So many scales, so little time -- alas, one must
> pick and choose those most to treasure with one's time and
attention.
>
> So on the basis of this principle of "significant use" (taking
Jacob
> at his word that we can expect "other movements", etc.), "Barton"
> gets my vote.
>
> --George