Yahoo Tuning Groups Ultimate Backup tuning *BT* What is a Secor?

*BURIED TREASURE*
�What is a Secor?�
From: George Secor
January 8, 2002

A �secor� (lower case) is a generator, specifically
the interval that generates the scales of the Miracle
tuning.

A �Secor� (capitalized) is also a generator,
specifically the last name of the person writing this,
who has generated over the past 38 years a
considerable pile of paperwork containing notes and
sketches for a varied collection of original ideas
pertaining to alternative tonal systems, including the
aforementioned generating interval of a �secor� and
the keyboard geometry derived from it.

Hello, everyone! Judging from the number of times
that I was surprised to have found these two terms
appearing in the Tuning List postings of last year (a
selection of which I have read over the past several
weeks), I conclude that I need no further
introduction. In these postings, questions were
raised about how I made my discovery, inasmuch my
hastily written article in Xenharmonikon 3 (in the
spring of 1975) was necessarily brief due to an
impending deadline. It�s a rather complicated story,
but to put it briefly, I stumbled across these things
(working alone without a computer or even a scientific
calculator) while seeking ways in which to group EDO�s
into families according to generating intervals other
than the perfect fifth. I had no particular goal in
mind other than my own enlightenment, in contrast to
the very deliberate effort made by Dave Keenan and
Paul Ehrlich (and associates) to find a highly compact
or efficient organization of tones. I guess you could
call me the Leif Ericsson of a New World of tuning,
inasmuch as this information had �languished in
Xenharmonikon for some 26 years� (to quote message
25593 from Paul). As for which one of you gets to be
Christopher Columbus, I decline to make that call, so
if that�s of any importance to either of you, then you
two can duke it out (off list, please).

Margo Schulter managed to track me down and contacted
me the first week of September about a 17-tone well
temperament that I devised in 1978, which led to
considerable correspondence about some rather exciting
developments which will be published in the next issue
of Xenharmonikon. It was in her third e-mail
(9/25/01) that she offered the news:

<< There was a lot of excitement this Spring when some
people on the Alternate Tuning List came up with a
near-JI tuning using a generator of around 7/72 octave
-- and someone then discovered your article in
_Xenharmonikon_ 3 (Spring 1975), "A New Look at the
Partch Monophonic Fabric," describing an identical
keyboard scheme with a generator of 116.69 cents.

You might be amused to know that people have coined
the term "secor" (lowercase) for a generator of around
this size. For example, a 21-note tuning of this type
is said to "span 20 secors." >>

My reply of 9/28/01 included the following:

<< That has to be a first. As far as I knew, the only
intervals named after anyone, living or dead, were
commas, and those honored (i.e., Pythagoras and
Didymus) had to be dead for a very long time to
qualify. � Perhaps by dropping out of sight and lying
low for so many years I have given the impression of
being as good as dead, so that someone thought it
fitting to bestow the honor. >>

Anyway, I thank you all for this gesture, which is
warmly appreciated.

When I moved from Chicago to Los Angeles in 1979, I
expected that there would be more opportunities for
microtonal activity. However, the birth of my
daughter a year later required setting priorities that
resulted in quite the opposite (for which I have
absolutely no regrets). By the time our family moved
back to the Midwest in 1987, my microtonal activity
had virtually ceased.

About four years ago I realized that life was passing
by, and it seemed that all of the time and effort that
I had put into that pile of papers, still packed in a
couple of cardboard boxes, was going to be lost if I
didn�t start doing something soon. Within a year I
began work on a book, using my lunch time to type into
the computer between bites, and, at the present rate,
it will be at least another couple of years before it
will be completed.

Life is short, our days are numbered, and one never
knows what a day may bring forth, so I think it unwise
to wait until completion of the book to share some of
those nuggets of buried treasure that lie in that pile
of papers that I have produced. I will therefore be
digging through these and posting some of the things
that I uncover from time to time. (There is a
considerable amount of paper that deserves to remain
buried, and the perspective that comes with the
passage of time has made it a relatively simple matter
to separate the gems from the glass.) These postings
will be written in the style of a newspaper column and
will be easily identified by the subject line
beginning with the characters *BT* for the column
name, *Buried Treasure*.

In the next week or two I will also try to make some
comments and answer a few questions that were raised
in connection with my discovery of the Miracle tuning,
the secor generator, the decimal keyboard geometry (as
I now call it), and the mapping thereon of Harry
Partch�s monophonic fabric.

One of these can be dealt with immediately. It was
noted that I didn�t discover any of the moment of
symmetry (MOS) scales, such as �blackjack� and
�canasta,� that are associated with the Miracle
tuning. (May I commend you on the choice of such
colorful and memorable names.) The reason that I
didn�t mention any MOS scales is quite simple: The
term did not appear in print (to the best of my
knowledge) until Erv Wilson presented the concept in
two articles in the very same issue of Xenharmonikon
that contained my article about the Miracle generator
and keyboard.

I will also have a couple of major presentations to
make of ideas that I have come up with in the past
year. One of these is a first-rate 72-EDO practical
notation (5 months in the making and downwardly
compatible with both 31-EDO and 41-EDO) that I believe
is much better than anything any of us could ever have
hoped for. If there are any doubts, just ask Margo
Schulter, who kindly gave me feedback about it in
December, during the last month of its development.
(That�s your cue, Margo!)

Of course, now that I have officially joined the
Tuning List dialogue, any new questions or comments
will also be welcome.

And until next time, please stay tuned! (Pun
intended.)

--George

Love / joy / peace �

__________________________________________________
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🔗robert_wendell <BobWendell@technet-inc.com>

Wow! Welcome, George! What an honor and privilege (he said, waiting
with bated breath for bountiful buried treasures)! This is very
exciting indeed!

--- In tuning@y..., George Secor <gdsecor@y...> wrote:
> *BURIED TREASURE*
> "What is a Secor?"
> From: George Secor
> January 8, 2002
>
> A "secor" (lower case) is a generator, specifically
> the interval that generates the scales of the Miracle
> tuning.
>
> A "Secor" (capitalized) is also a generator,
> specifically the last name of the person writing this,
> who has generated over the past 38 years a
> considerable pile of paperwork containing notes and
> sketches for a varied collection of original ideas
> pertaining to alternative tonal systems, including the
> aforementioned generating interval of a "secor" and
> the keyboard geometry derived from it.
>
> Hello, everyone! Judging from the number of times
> that I was surprised to have found these two terms
> appearing in the Tuning List postings of last year (a
> selection of which I have read over the past several
> weeks), I conclude that I need no further
> introduction. In these postings, questions were
> raised about how I made my discovery, inasmuch my
> hastily written article in Xenharmonikon 3 (in the
> spring of 1975) was necessarily brief due to an
> impending deadline. It's a rather complicated story,
> but to put it briefly, I stumbled across these things
> (working alone without a computer or even a scientific
> calculator) while seeking ways in which to group EDO's
> into families according to generating intervals other
> than the perfect fifth. I had no particular goal in
> mind other than my own enlightenment, in contrast to
> the very deliberate effort made by Dave Keenan and
> Paul Ehrlich (and associates) to find a highly compact
> or efficient organization of tones. I guess you could
> call me the Leif Ericsson of a New World of tuning,
> inasmuch as this information had "languished in
> Xenharmonikon for some 26 years" (to quote message
> 25593 from Paul). As for which one of you gets to be
> Christopher Columbus, I decline to make that call, so
> if that's of any importance to either of you, then you
> two can duke it out (off list, please).
>
> Margo Schulter managed to track me down and contacted
> me the first week of September about a 17-tone well
> temperament that I devised in 1978, which led to
> considerable correspondence about some rather exciting
> developments which will be published in the next issue
> of Xenharmonikon. It was in her third e-mail
> (9/25/01) that she offered the news:
>
> << There was a lot of excitement this Spring when some
> people on the Alternate Tuning List came up with a
> near-JI tuning using a generator of around 7/72 octave
> -- and someone then discovered your article in
> _Xenharmonikon_ 3 (Spring 1975), "A New Look at the
> Partch Monophonic Fabric," describing an identical
> keyboard scheme with a generator of 116.69 cents.
>
> You might be amused to know that people have coined
> the term "secor" (lowercase) for a generator of around
> this size. For example, a 21-note tuning of this type
> is said to "span 20 secors." >>
>
> My reply of 9/28/01 included the following:
>
> << That has to be a first. As far as I knew, the only
> intervals named after anyone, living or dead, were
> commas, and those honored (i.e., Pythagoras and
> Didymus) had to be dead for a very long time to
> qualify. Perhaps by dropping out of sight and lying
> low for so many years I have given the impression of
> being as good as dead, so that someone thought it
> fitting to bestow the honor. >>
>
> Anyway, I thank you all for this gesture, which is
> warmly appreciated.
>
> When I moved from Chicago to Los Angeles in 1979, I
> expected that there would be more opportunities for
> microtonal activity. However, the birth of my
> daughter a year later required setting priorities that
> resulted in quite the opposite (for which I have
> absolutely no regrets). By the time our family moved
> back to the Midwest in 1987, my microtonal activity
> had virtually ceased.
>
> About four years ago I realized that life was passing
> by, and it seemed that all of the time and effort that
> I had put into that pile of papers, still packed in a
> couple of cardboard boxes, was going to be lost if I
> didn't start doing something soon. Within a year I
> began work on a book, using my lunch time to type into
> the computer between bites, and, at the present rate,
> it will be at least another couple of years before it
> will be completed.
>
> Life is short, our days are numbered, and one never
> knows what a day may bring forth, so I think it unwise
> to wait until completion of the book to share some of
> those nuggets of buried treasure that lie in that pile
> of papers that I have produced. I will therefore be
> digging through these and posting some of the things
> that I uncover from time to time. (There is a
> considerable amount of paper that deserves to remain
> buried, and the perspective that comes with the
> passage of time has made it a relatively simple matter
> to separate the gems from the glass.) These postings
> will be written in the style of a newspaper column and
> will be easily identified by the subject line
> beginning with the characters *BT* for the column
> name, *Buried Treasure*.
>
> In the next week or two I will also try to make some
> comments and answer a few questions that were raised
> in connection with my discovery of the Miracle tuning,
> the secor generator, the decimal keyboard geometry (as
> I now call it), and the mapping thereon of Harry
> Partch's monophonic fabric.
>
> One of these can be dealt with immediately. It was
> noted that I didn't discover any of the moment of
> symmetry (MOS) scales, such as "blackjack" and
> "canasta," that are associated with the Miracle
> tuning. (May I commend you on the choice of such
> colorful and memorable names.) The reason that I
> didn't mention any MOS scales is quite simple: The
> term did not appear in print (to the best of my
> knowledge) until Erv Wilson presented the concept in
> two articles in the very same issue of Xenharmonikon
> that contained my article about the Miracle generator
> and keyboard.
>
> I will also have a couple of major presentations to
> make of ideas that I have come up with in the past
> year. One of these is a first-rate 72-EDO practical
> notation (5 months in the making and downwardly
> compatible with both 31-EDO and 41-EDO) that I believe
> is much better than anything any of us could ever have
> hoped for. If there are any doubts, just ask Margo
> Schulter, who kindly gave me feedback about it in
> December, during the last month of its development.
> (That's your cue, Margo!)
>
> Of course, now that I have officially joined the
> Tuning List dialogue, any new questions or comments
> will also be welcome.
>
> And until next time, please stay tuned! (Pun
> intended.)
>
> --George
>
> Love / joy / peace
>
>
> __________________________________________________
> Do You Yahoo!?
> Send FREE video emails in Yahoo! Mail!
> http://promo.yahoo.com/videomail/

🔗jonszanto <JSZANTO@ADNC.COM>

🔗M. Schulter <MSCHULTER@VALUE.NET>

Hello, there, everyone, and I'd like for the moment to share a
seasonable and joyful word welcoming George Secor to our forum.

For many people here, George, I suspect that you're indeed known
especially for your original discovery and publication of the "Miracle
Tuning" with a generator of around 116.71 cents, or more precisely
with 19 such generators forming a 9:5-minor-seventh-plus-octave. How
wonderful to have this meeting of microtonal generations, a gathering
in which I joyously share even if some people might argue that my own
tastes are a few centuries off in one direction or another.

For me, while the excitement this last Spring certainly made me
interested in your xenharmonic adventures and contributions, it was
learning about your 17-note well-temperament of 1978 that especially
moved me to admiration and wonder: here was a system, devised 20 years
before I become involved with this microtonal community, which seemed
custom-designed for me.

Soon enough, I was not only delighting in your temperament at the
keyboard, but sharing that delight with you as we started to explore
the tuning together.

From my experience, I can predict that your "Buried Treasures" will
provide to our circle here a convivial feast of flavors -- or of
"moods" or "colors," to draw upon a tradition to which you and Ivor
Darreg and John Chalmers and others have helped to shape -- well
suited to accord with many diverse appetites for knowledge, wisdom,
and beauty.

Having had the opportunity to discuss some notational matters with
you, a most educative and ongoing seminar, as I might call it, I look
forward to contributing to any dialogue here from my own viewpoint,
only one of many.

While this outlook may not necessarily be representative -- at least
for people who aren't so passionate about mapping 14th-century
European cadences to 13-EDO appropriately "well-timbred" -- I hope
especially to address some questions about how a flexible notation
might be applied to a range of neo-medieval tunings.

One purpose of a better notation is to promote interchange between
different tunings and performance ensembles: for example, to borrow a
computer programming term, "porting" a piece composed in 31-EDO or a
31-note cycle of 1/4-comma meantone (maybe 31-NEDO, "Nearly Equal
Division of the Octave") to 72-EDO, or vice versa. How about porting a
neo-medieval piece designed for 29-EDO or 46-EDO or some comparable
regular temperament to 72-EDO -- what commas, maybe pointing in less
familiar directions, await the eager performers of our scenario?

Interchange issues aside, how might we approach the inflections and
step gradations of a really intricate system, whether from a
neo-medieval viewpoint, some 5-limit or 7-limit JI framework, or maybe
a xenharmonic take on atonality/pantonality or serialism?

One intriguing example might be 53-EDO, or what I call 53-NEDO, a
Pythagorean cycle with that charming asymmetry of 3.62 cents. That's
my style: two versions of the same interval differing by a few cents
is a mark of special distinction for a tuning. Whether we take it in
its precisely or "nearly" symmetrical form, 53 gives us no less than
nine commas or tuning steps for each whole-tone, or five for each
regular sharp or flat.

How might a 5-limit or 7-limit JI user of 53 -- or a neo-medievalist
who takes the regular Pythagorean intervals as a main point of
reference -- approach this intonational "embarrassment of riches"?

While I leave it to you, George, to share your ideas in the best way,
I can say that there are some exciting approaches you've shared with
me that really have me impressed, the kind of approaches which can
make less familiar tunings and styles more accessible as well as
facilitating more dialogue and interchange with fewer artificial
barriers.

As Willi Apel has written, there's a subtle interaction between music
and notation. In the era around 1400, six centuries or a bit more ago,
this meant all kinds of refinements regarding the expressing of
rhythmic variations and polymeters: everything from proportions like
those also used to express interval ratios, to red or blue notes and
ways of indicating free syncopation or "written out rubato."

While historians have sometimes stressed the sheer intellectual
complexity of some of this theory, we're also talking about a
tradition of beautiful music, with our intonational refinements of
today also linked to practice which an agreeable notation can help to
expedite as well as to clarify.

It isn't a question of either this or that "universal standard" --
we're too diverse a community for that -- but of more choices for
expressing the unique beauty and logic of a given tuning, possibly
adapted to the stylistic priorities and patterns in a given context,
or for "getting it all together" as xenharmonicists coming from
different outlooks or "notational customs" meet and seek accord,
literal or figurative.

This is an open seminar, because there are so many beautiful tunings
and questions to explore. With a system like 31-EDO or 31-NEDO, there
are a rich set of historical possibilities going back to Vicentino in
1555, while with neo-medieval systems or others with a large range of
steps and inflections, the precedents may be less abundant.

For any tuning, however, getting the best blend of new and old -- or
using and possibly translating between systems to accommodate
different types of instruments, notational traditions, or stylistic
outlooks -- is an ongoing project.

Considering a range of world musical traditions and literatures, rich
with many practices and theories for mapping "interval space," may
further diversify and enlighten our dialogue, making our colloquy an
exciting global classroom and celebration.

Ivor Darreg has wisely advised that, when in doubt, don't worry about
fine points of spelling -- make beautiful music. At the same time, a
"user-friendly" notation, or set of notations tailored to different
tastes or needs, can make the process yet more comprehensible and
rewarding.

This also raises another matter upon which you can comment with
special acumen and experience as one of the designers of the
Generalized Keyboard Scalatron (along with Erv Wilson and Dick
Harasek): how can the layout of a keyboard affect the way one
approaches both music and notation? People here have taken a special
interest in state-of-the-art keyboards at the opening of a new
century, and the right mixture of experience and enthusiasm could
carry a tradition of such musicians and xenharmonicists as Vicentino,
Colonna (1618), Bosanquet, Fokker, Hanson, and others to new heights.

What about notation and the building and playing of acoustical
instruments after the tradition of Harry Partch?

From the Miracle Tuning to your 17-note well-temperament to sundry
"buried treasures" and another outlook on notation, George, I can
predict that we're in for a real treat.

Welcome, George, to the Tuning List: let us revel together in the
tuneful concentus of music and community alike.

In peace, joy, and harmony,

Margo Schulter
mschulter@value.net

🔗monz <joemonz@yahoo.com>

> From: M. Schulter <MSCHULTER@VALUE.NET>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, January 09, 2002 11:36 PM
> Subject: [tuning] Re: *BT* What is a Secor?
>
>
> Hello, there, everyone, and I'd like for the moment to share a
> seasonable and joyful word welcoming George Secor to our forum.

I'm one of the people who corresponded with George privately
and encouraged him to join this group, so it's about time I
welcomed him here too! Glad to have you here, George, and
looking forward much to your contributions!! (And I totally
agree with Jon Szanto -- that was a fantastic introductory post!)

> As Willi Apel has written, there's a subtle interaction between music
> and notation. In the era around 1400, six centuries or a bit more ago,
> this meant all kinds of refinements regarding the expressing of
> rhythmic variations and polymeters: everything from proportions like
> those also used to express interval ratios, to red or blue notes and
> ways of indicating free syncopation or "written out rubato."
>
> While historians have sometimes stressed the sheer intellectual
> complexity of some of this theory, we're also talking about a
> tradition of beautiful music, with our intonational refinements of
> today also linked to practice which an agreeable notation can help to
> expedite as well as to clarify.
>
> It isn't a question of either this or that "universal standard" --
> we're too diverse a community for that -- but of more choices for
> expressing the unique beauty and logic of a given tuning, possibly
> adapted to the stylistic priorities and patterns in a given context,
> or for "getting it all together" as xenharmonicists coming from
> different outlooks or "notational customs" meet and seek accord,
> literal or figurative.

It's great to read all of this, Margo. Thanks so much for the
valuable input you give to medieval music topics.

While reading this, I couldn't get away from thoughts about my goals
for a more accurate representation of music. I've had many strong
arguments with Brian McLaren (in writing, and face-to-face) about the
relevance of lattice diagrams and the whole concept of representing
pitches in "ratio space", but ultimately the whole point of it is
to create an easier way for *me* (and like-minded others) to understand
what might be rather complex mathematical relationships among tones.

Bound up in this is my concept of finity, and while I'm very excited
about the developments in periodicity-block theory which have been
happening over at tuning-math lately (thanks, Gene!), it's nice to
know that musicians 600 years ago were successfully coming to terms
with this kind of thing, as well as with problems of rhythmic
notation! Thanks!

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
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Get your free @yahoo.com address at http://mail.yahoo.com

🔗paulerlich <paul@stretch-music.com>

Well, whatever the case may be, let be offer you a hearty welcome to
this list! I, for one, am overjoyed that you have joined us! And, a
fuller introduction, in fact an utterly self-indulgent one, would not
be at all out of place for you, given that we've been throwing around
your name for some time now. But thanks for the interesting tidbits
you have shared with us.

> In these postings, questions were
> raised about how I made my discovery, inasmuch my
> hastily written article in Xenharmonikon 3 (in the
> spring of 1975) was necessarily brief due to an
> impending deadline. It's a rather complicated story,
> but to put it briefly, I stumbled across these things
> (working alone without a computer or even a scientific
> calculator) while seeking ways in which to group EDO's
> into families according to generating intervals other
> than the perfect fifth. I had no particular goal in
> mind other than my own enlightenment, in contrast to
> the very deliberate effort made by Dave Keenan and
> Paul Ehrlich (and associates) to find a highly compact
> or efficient organization of tones. I guess you could
> call me the Leif Ericsson of a New World of tuning,
> inasmuch as this information had "languished in
> Xenharmonikon for some 26 years" (to quote message
> 25593 from Paul).

Strange, I don't recall every making this statement, nor do I see it
in said message. But whatever . . .

> As for which one of you gets to be
> Christopher Columbus, I decline to make that call, so
> if that's of any importance to either of you, then you
> two can duke it out (off list, please).

Everything's documented in Monz's webpages. BTW, would you care to
comment on this one:

http://www.ixpres.com/interval/dict/secor.htm

🔗gdsecor <gdsecor@yahoo.com>

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> Well, whatever the case may be, let be offer you a hearty welcome
to
> this list! I, for one, am overjoyed that you have joined us! And, a
> fuller introduction, in fact an utterly self-indulgent one, would
not
> be at all out of place for you, given that we've been throwing
around
> your name for some time now. But thanks for the interesting tidbits
> you have shared with us.

It was a little strange at first, seeing my name splashed around like
that. I guess my initial reaction to Margo's news was to joke about
it, because I felt a bit stunned, not knowing quite what to think.
One of the reasons why I waited so long to say something was that I
wanted to see first hand what all the fuss was about. Reviewing the
Tuning List e-mail is really spooky in this regard it allows you to
travel back through time, and once you get there, it lacks none of
the sensory impact of having been there when it actually happened.

The other reason I waited so long was because Margo and I we were in
the middle of a very exciting project, for which I was writing a
paper that I didn't complete until the end of November. And after
that, I had another one to do (which is still only about half
finished). I just didn't have the time both to write and to review
the postings.

Waiting has also made it easier by putting the events of last spring
a little farther into the past (for me especially). I almost howled
with laughter when I saw the subject line "Fun with secors" and
thought to myself, "Hmmm, no harm in a little fun." (Just so you
don't start taking my name in vain; now that's not funny.)

[GS:]
> > I guess you could
> > call me the Leif Ericsson of a New World of tuning,
> > inasmuch as this information had "languished in
> > Xenharmonikon for some 26 years" (to quote message
> > 25593 from Paul).
>
[PE:]
> Strange, I don't recall every making this statement, nor do I see
it
> in said message. But whatever . . .

Sorry. After looking at so many postings at once my eyes must have
started playing tricks on me. It was in Dave Keenan's message #25575
of Jun 25, 2001.

[GS:]
> > As for which one of you gets to be
> > Christopher Columbus, I decline to make that call, so
> > if that's of any importance to either of you, then you
> > two can duke it out (off list, please).
>
[PE:]
> Everything's documented in Monz's webpages.

Hey, I was just kidding! I usually can't resist a chance to put in a
joke when the opportunity presents itself.

[PE:]
> BTW, would you care to comment on this one:
>
> http://www.ixpres.com/interval/dict/secor.htm
>
> ?

Joe Monzo directed me to his website, so I saw that before I joined
the Tuning List and started reading the postings. It looks very
good! There is some new terminology over the past 10 years that I am
just beginning to become familiar with, so this has turned out to one
very helpful place to visit. Keep up the good work, all of you!

--George

🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:

> Reviewing the
> Tuning List e-mail is really spooky in this regard it allows you
to
> travel back through time, and once you get there, it lacks none of
> the sensory impact of having been there when it actually happened.

Except for the fact that you don't quite get the _timing_ of the
appearance of the messages. When the MIRACLE explosion occured, the
rate of posting increased to an all-time high on this list (due in no
small part to my extreme dorkiness), which then led to some acrimony,
which then led to a large number of spin-off lists . . . a very
turbulent time it was . . .
>
> Hey, I was just kidding! I usually can't resist a chance to put in
a
> joke when the opportunity presents itself.

In addition to extreme dorkiness, I am afflicted with a tendency to
take everything far too seriously. Please accept my apologies for
this in advance of any misunderstandings we might have in the
future . . .

> Keep up the good work, all of you!

Dave Keenan, Graham Breed, and Gene Ward Smith, with a little help
and prodding from yours truly, have been engaging in some ever-
deepening and ever-widening investigations into linear (and planar,
and equal, etc . . .) temperaments for approximating various sets of
just intervals. It will come as no surprise that your MIRACLE system
comes out as exceedingly accurate for its level of complexity for
both the 7-limit and the 11-limit, though perhaps not as stellar in
the 9-limit. Another system that shows up as "real special" (in the 7-
limit) for its level of complexity (a lower one) is one I published
in Xenharmonikon 17, which has a generator of about 708 cents and a
period of 600 cents -- and is thus expressed quite accurately in 22-
tET (I especially advocate certain 10-tone-per-octave subsets). If
you don't have access to a copy of XH17, you may view my paper here
(which, alas, has all the errors of the published version preserved
intact -- please ignore page 20 of the .pdf completely, for example):

http://www-math.cudenver.edu/~jstarret/22ALL.pdf

At the time I came up with the system mentioned here, my familiarity
with the field was limited to having read Partch, Helmholtz, and
Yasser. This, it seemed to me (at age 19, after a few years
of "searching"), was a "better way". I hope the paper appeals to you
in some small way, and perhaps as you read it, you will feel a
glimmer of "kindred spirits" that I feel nowhere but on this list,
and which keeps me here for hours upon hours, wasting my life
away . . . now approaching age 29.5 . . .

So, do you have any musical examples to share that use any of your
tuning systems?

Cheers,
Paul

🔗jpehrson2 <jpehrson@rcn.com>

🔗paulerlich <paul@stretch-music.com>

🔗unidala <JGill99@imajis.com>

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

> << . . . I am afflicted with a tendency to
> take everything far too seriously. Please accept my apologies for
> this in advance of any misunderstandings we might have in the
> future . . . >>

Paul,

I couldn't help empathizing with this "seriousness"
business, being prone myself to such intensity ...

It brought to mind some thoughts of one of my favorite
authors, James P Carse ("Finite and Infinite Games",
Ballantine, 1986):

<< To speak, or act, or think originally is to erase
the boundary of the self. It is to leave behind the
territorial personality. A genius does not have a mind
full of thoughts but is the thinker of thoughts, and
is the center of a field of vision. It is a field of
vision, however, that is recognizable as a field of
vision only when we see that it includes within itself
the original centers of other fields of vision.

This does not mean that I can see what you see. On the
contrary, *it is because I cannot see what you see that
I can see at all*. The discovery that you are the
unrepeatable center of your own vision is simultaneous
with the discovery that I am the center of my own. >>

<< Just as the titles of winners are worthless unless
they are visible to others, there is a kind of anti-
title which attaches to invisibility. To the degree
that we are invisible we have a past which has
condemned us to oblivion. It is as though we have
somehow been overlooked, even forgotten, by our chosen
audience. If it is the winners who are presently
visible, it is the losers who are invisibly past.

As we enter into finite play - not playfully, but
seriously - we come before an audience conscious
that we bear the antititles of invisibility. We feel
the need, therefore, to prove to them that we are not
what we think they think we are or, more precisely,
that we were not who we think the audience thinks
we were.

As with all finite play, an acute contradiction
quickly develops at the heart of this attempt.
As finite players we will not enter the game with
sufficient desire to win unless we are ourselves
convinced by the very audience we intend to convince.
That is, *unless we believe we actually are the losers
the audience sees us to be, we will not have the
necessary desire to win*. The more negatively we assess
ourselves, the more we strive to reverse the negative
judgement of others. The outcome brings the contra-
diction to perfection: by proving to the audience that
they were wrong, we prove to ourselves the audience was
right.

The more we are recognized as winners, the more we
know ourselves to be losers. That is why it is rare
for the winners of highly coveted and publicized prizes
to settle for their titles and retire. Winners,
especially celebrated winners, must prove repeatedly
that they are winners. The script must be played over
and over again. Titles must be defended by new contests.

So crucial is this power of the past to finite play
that we must find ways of remembering that we have
been forgotten to sustain our interest in the struggle.
There is a humiliating memory at the bottom of all
serious conflicts. "Remember the Alamo!", "Remember
the Maine!", "Remember Pearl Harbor!". These are the
cries that carried Americans into several wars. Having
once been insulted by Athens, the great Persian Emperor
Darius renewed his appetite for war by having a page
follow him about to whisper in his ear, "Sire, remember
the Athenians!".

Indeed, it is only remembering what we have forgotten
that we can enter into competition with sufficient
intensity to be able to forget we have forgotten
the character of all play: Whoever *must* play
cannot *play*. >>

Playfully, J Gill :)

🔗gdsecor <gdsecor@yahoo.com>

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
> Hello, there, everyone, and I'd like for the moment to share a
> seasonable and joyful word welcoming George Secor to our forum.
>
> For many people here, George, I suspect that you're indeed known
> especially for your original discovery and publication of
the "Miracle
> Tuning" with a generator of around 116.71 cents, or more precisely
> with 19 such generators forming a 9:5-minor-seventh-plus-octave. How
> wonderful to have this meeting of microtonal generations, a
gathering
> in which I joyously share even if some people might argue that my
own
> tastes are a few centuries off in one direction or another.
>
> For me, while the excitement this last Spring certainly made me
> interested in your xenharmonic adventures and contributions, it was
> learning about your 17-note well-temperament of 1978 that especially
> moved me to admiration and wonder: here was a system, devised 20
years
> before I become involved with this microtonal community, which
seemed
> custom-designed for me.
>
> Soon enough, I was not only delighting in your temperament at the
> keyboard, but sharing that delight with you as we started to explore
> the tuning together.
>
> From my experience, I can predict that your "Buried Treasures" will
> provide to our circle here a convivial feast of flavors -- or of
> "moods" or "colors," to draw upon a tradition to which you and Ivor
> Darreg and John Chalmers and others have helped to shape -- well
> suited to accord with many diverse appetites for knowledge, wisdom,
> and beauty.
>
> Having had the opportunity to discuss some notational matters with
> you, a most educative and ongoing seminar, as I might call it, I
look
> forward to contributing to any dialogue here from my own viewpoint,
> only one of many.
>
> While this outlook may not necessarily be representative -- at least
> for people who aren't so passionate about mapping 14th-century
> European cadences to 13-EDO appropriately "well-timbred" -- I hope
> especially to address some questions about how a flexible notation
> might be applied to a range of neo-medieval tunings.
>
> One purpose of a better notation is to promote interchange between
> different tunings and performance ensembles: for example, to borrow
a
> computer programming term, "porting" a piece composed in 31-EDO or a
> 31-note cycle of 1/4-comma meantone (maybe 31-NEDO, "Nearly Equal
> Division of the Octave") to 72-EDO, or vice versa. How about
porting a
> neo-medieval piece designed for 29-EDO or 46-EDO or some comparable
> regular temperament to 72-EDO -- what commas, maybe pointing in less
> familiar directions, await the eager performers of our scenario?
>
> Interchange issues aside, how might we approach the inflections and
> step gradations of a really intricate system, whether from a
> neo-medieval viewpoint, some 5-limit or 7-limit JI framework, or
maybe
> a xenharmonic take on atonality/pantonality or serialism?
>
> One intriguing example might be 53-EDO, or what I call 53-NEDO, a
> Pythagorean cycle with that charming asymmetry of 3.62 cents. That's
> my style: two versions of the same interval differing by a few cents
> is a mark of special distinction for a tuning. Whether we take it in
> its precisely or "nearly" symmetrical form, 53 gives us no less than
> nine commas or tuning steps for each whole-tone, or five for each
> regular sharp or flat.
>
> How might a 5-limit or 7-limit JI user of 53 -- or a neo-medievalist
> who takes the regular Pythagorean intervals as a main point of
> reference -- approach this intonational "embarrassment of riches"?
>
> While I leave it to you, George, to share your ideas in the best
way,
> I can say that there are some exciting approaches you've shared with
> me that really have me impressed, the kind of approaches which can
> make less familiar tunings and styles more accessible as well as
> facilitating more dialogue and interchange with fewer artificial
> barriers.
>
> As Willi Apel has written, there's a subtle interaction between
music
> and notation. In the era around 1400, six centuries or a bit more
ago,
> this meant all kinds of refinements regarding the expressing of
> rhythmic variations and polymeters: everything from proportions like
> those also used to express interval ratios, to red or blue notes and
> ways of indicating free syncopation or "written out rubato."
>
> While historians have sometimes stressed the sheer intellectual
> complexity of some of this theory, we're also talking about a
> tradition of beautiful music, with our intonational refinements of
> today also linked to practice which an agreeable notation can help
to
> expedite as well as to clarify.
>
> It isn't a question of either this or that "universal standard" --
> we're too diverse a community for that -- but of more choices for
> expressing the unique beauty and logic of a given tuning, possibly
> adapted to the stylistic priorities and patterns in a given context,
> or for "getting it all together" as xenharmonicists coming from
> different outlooks or "notational customs" meet and seek accord,
> literal or figurative.
>
> This is an open seminar, because there are so many beautiful tunings
> and questions to explore. With a system like 31-EDO or 31-NEDO,
there
> are a rich set of historical possibilities going back to Vicentino
in
> 1555, while with neo-medieval systems or others with a large range
of
> steps and inflections, the precedents may be less abundant.
>
> For any tuning, however, getting the best blend of new and old -- or
> using and possibly translating between systems to accommodate
> different types of instruments, notational traditions, or stylistic
> outlooks -- is an ongoing project.
>
> Considering a range of world musical traditions and literatures,
rich
> with many practices and theories for mapping "interval space," may
> further diversify and enlighten our dialogue, making our colloquy an
> exciting global classroom and celebration.
>
> Ivor Darreg has wisely advised that, when in doubt, don't worry
about
> fine points of spelling -- make beautiful music. At the same time, a
> "user-friendly" notation, or set of notations tailored to different
> tastes or needs, can make the process yet more comprehensible and
> rewarding.
>
> This also raises another matter upon which you can comment with
> special acumen and experience as one of the designers of the
> Generalized Keyboard Scalatron (along with Erv Wilson and Dick
> Harasek): how can the layout of a keyboard affect the way one
> approaches both music and notation? People here have taken a special
> interest in state-of-the-art keyboards at the opening of a new
> century, and the right mixture of experience and enthusiasm could
> carry a tradition of such musicians and xenharmonicists as
Vicentino,
> Colonna (1618), Bosanquet, Fokker, Hanson, and others to new
heights.
>
> What about notation and the building and playing of acoustical
> instruments after the tradition of Harry Partch?
>
> From the Miracle Tuning to your 17-note well-temperament to sundry
> "buried treasures" and another outlook on notation, George, I can
> predict that we're in for a real treat.
>
> Welcome, George, to the Tuning List: let us revel together in the
> tuneful concentus of music and community alike.
>
> In peace, joy, and harmony,
>
> Margo Schulter
> mschulter@v...

Margo, you¡¦re amazing! I expected a few kind words expressing how
really neat my new notation turned out, after I worked so long and so
hard on it to get all of the details just right, finally reaching the
point where I felt that I could improve it no further. (I guess
they¡¦re in there somewhere, if anyone looks hard enough.) Although I
do appreciate your noting the possibility of its being ¡§ported¡¨ from
one division of the octave to another (with the implication that many
things written in 72 could be sight-read directly into 31 or 41),
what happened to the sort of comments you made privately to me? Such
as:

12/4/01 ¡V << Although often the better part of valor is to defer
expressing opinions about tunings until I have actually tried them, I
would say that the idea of a new and unified notation for a Secorian
realization of Partch's system (or a subset) in 31-ET, 41-ET, or 72-
ET looks like a refreshing and very useful approach, a different way
of viewing the notes and the notation. Representing the Didymus' and
Archytas' [i.e., septimal, 64:63] commas by those flags is what I'd
call an elegant refinement. >>

And after I sent what has become the final version of the notation,
which incorporated a reworking of the symbols to make them much more
legible:

12/24/01 - << Please let me celebrate this Christmas Eve by letting
you know how beautiful your new sagittal notation is: it's coming
together for me, and the ingenuity of it is something that I'll write
about more in the next couple of days, including how intuitive it
looks to me for 1/4-comma meantone or 31-ET. >>

And, as promised, the comments a couple of days later:

12/26/01 - << I agree with your daughter: the bolder look is very
attractive, and readable, with very easy pattern recognition for the
regular sharps and flats, and also the semisharps and semiflats. ¡K
Most important here is that the main alterations (sharps, flats, and
semi-sharps or semi-flats) are very quickly recognizable. Being able
to pick out these principal forms quickly makes the notation
practical and also ¡§downward compatible¡¨ in a very pleasant way.

¡K This version maybe crossed a critical line for me: I find myself
thinking it a little, testing expectations and learning through the
process, and making it my own ¡X anyway, I'm on the other side of the
line now, not only admiring the system but drawn into it. I'd be
ready at any appropriate time to advocate this system on the Tuning
List, because it's coherent, unified, practical, and intuitive ¡X
maybe even more so for people who tend to focus on visual patterns
like those Bosanquet arrows rather than ¡§explain¡¨ them in terms of
the theory of commas.

To put the appeal into words, I'd say it's a very logical and
attractive map of 72-ET, with each semi-alteration of 3a72 [3
degrees of 72; that special character is a degree symbol] subdivided
into a Didymus and an Archytas comma. There's been some discussion on
the Tuning List about the idea that lots of musicians (at least
relatively speaking) are familiar with 24-ET and quartertones: the
comma signs could be taken as a further refinement. A key point is
that your basic semi-alteration signs provide a most engaging
standard in themselves, say for noting 17 in ¡§enharmonic¡¨ style, or,
of course, 31.

The argument I'd make [to those on the Tuning List about the approach
taken by this notation] is that if we really want a powerful 72-ET
notation, why not build it ¡§from the ground up,¡¨ while ingeniously
incorporating or paralleling lots of traditional symbols in the
process? There's a saying of Einstein that things should be made as
simple as possible, but no simpler. >>

After a testimonial like that, I wonder if is there anybody else out
there who might be interested in seeing it?

In closing, thanks for your warm welcome. I look forward to the rich
experience of sharing and encouragement with those who hold a common
hope and dream that someday our efforts just might have a chance of
becoming a part of the musical mainstream.

Until then, stay tuned!

--George

🔗paulerlich <paul@stretch-music.com>

🔗robert_wendell <BobWendell@technet-inc.com>

🔗jpehrson2 <jpehrson@rcn.com>

🔗paulerlich <paul@stretch-music.com>

🔗gdsecor <gdsecor@yahoo.com>

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> > After a testimonial like that, I wonder if is there anybody else
> out
> > there who might be interested in seeing it?
>
> Of course we would!

Good! First I would like to give a little background, after which I
have a question.

I began working on the saggital notation without knowing what
notations already existed for 72-EDO, so those had absolutely no
influence on its development. It's a practical (staff) notation that
consists completely of non-ASCII characters and requires no more than
one symbol to modify a note. I have read the postings discussing
notation, and absolutely everything that you disliked about the Sims
notation is avoided in the saggital notation, and everything that you
thought desirable in a 72-EDO notation is there. And more.

The symbols can be easily (and reasonably) simulated with ASCII
characters (used in combination, with the number of characters
varying, according to the symbol) for text documents and e-mail.
However, I don't expect that the simulated symbols will be suitable
for lattice diagrams, so you will probably need something else
(either instead or in addition), possibly along the lines of what you
are already using for that purpose (but I also have another
suggestion to make later).

The symbols work not only for 72, but also for 17, 19, 22, 24, 29,
31, 36, 41, and 48. (And there are other divisions that I haven't
mentioned that will probably work.) By bending the rules a little,
the notation will also work for 46, 53, and 96, unless we agree to
use an alternative approach to the positive tonal systems that will
treat them all in the same way, in which case the only rule-bending
would be for 96. (I have not completely thought through this
alternative approach, so I am not yet sure that I like it, but it is
something that we could all look at. This is so new, even to me,
that I haven't yet had time to consider all of the ramifications.)

Here's the question: If a majority of the group with an interest in
this really likes the saggital notation, might you all consider
changing the existing 72-EDO ASCII notation that you (except for
Monz) have agreed upon recently to something different in order to
make the agreement unanimous? (I'm trying my best to make us all
happy, Joe.)

In exchange for your agreeing to this, I would be happy to consider
any suggestions for improving the saggital notation, inasmuch as I
believe that there is always the possibility that someone else can
make something good into something even better.

One consideration is what to do about the Sims notation,
specifically, should there be two competing system? My answer is
that the two different notations don't serve the same constituency,
so they would not really be competing with one another. The Sims
notation is intended to be used by performers utilizing existing 12-
EDO instruments for music that is largely atonal (if I understand the
situation properly). The saggital notation is most suitable for
those who believe in building acoustic instruments specially designed
for alternate tunings or in creating computer-generated (pitch-bent)
MIDI files. Here we are interested principally in music using prime
numbers beyond the 5 limit. In cases where instrumentalists fluent
with the Sims notation desire to participate with those preferring
the saggital notation, all that woudl need to be done is to ensure
that each musician has a part available in one's notation of choice.
(In addition, we will find that with the saggital notation we can
maintain a link back to long-held notational precedents established
by the quartertone composers.)

It is a significant accomplishment that we have managed to agree that
72-EDO will be the system of choice on which to base our master
notation, whichever that may be. I feel that this should be a cause
for celebration and a common ground on which we can cooperate with
the Boston Microtonal Society, while continuing to respect each
other's individual differences, even as we respect and honor (and
should celebrate) diversity within our own ranks.

What do you think?

--George

🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:

> Here's the question: If a majority of the group with an interest
in
> this really likes the saggital notation, might you all consider
> changing the existing 72-EDO ASCII notation that you (except for
> Monz) have agreed upon recently to something different in order to
> make the agreement unanimous? (I'm trying my best to make us all
> happy, Joe.)

Perhaps . . . lay it on us!

> One consideration is what to do about the Sims notation,
> specifically, should there be two competing system? My answer is
> that the two different notations don't serve the same constituency,
> so they would not really be competing with one another. The Sims
> notation is intended to be used by performers utilizing existing 12-
> EDO instruments for music that is largely atonal (if I understand
the
> situation properly).

Sims (and perhaps the Dinosaur Annex) are somewhat interested in
emulating the higher reaches of the overtone series and summation
tones, while Maneri and the Boston Microtonal Society have no
interest in ratios, acoustics, or just intonation. The atonal/tonal
question is a separate and more difficult one.

> The saggital notation is most suitable for
> those who believe in building acoustic instruments specially
designed
> for alternate tunings or in creating computer-generated (pitch-
bent)
> MIDI files.

Hmm . . . then it may or may not satisfy composers like Joseph
Pehrson, who are equally, if not more, interested in writing for
existing acoustic instruments.

> It is a significant accomplishment that we have managed to agree
that
> 72-EDO will be the system of choice on which to base our master
> notation, whichever that may be.

What does this statement mean? Perhaps laying out the notation first
would be helpful.

> I feel that this should be a cause
> for celebration and a common ground on which we can cooperate with
> the Boston Microtonal Society,

So far, they have no interest in, or use for, anything we've been
doing. The one member of the BMS who heard a piece by one of
us "secorian" folks didn't understand it, and vice versa.

🔗robert_wendell <BobWendell@technet-inc.com>

🔗genewardsmith <genewardsmith@juno.com>

🔗paulerlich <paul@stretch-music.com>

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:

/tuning/topicId_32446.html#32587

> I began working on the saggital notation without knowing what
> notations already existed for 72-EDO, so those had absolutely no
> influence on its development.

*****Hello George!

Are you absolutely certain that's an *asset??* Isn't an approach like
that a little like "reinventing the wheel??"

>
> The symbols can be easily (and reasonably) simulated with ASCII
> characters (used in combination, with the number of characters
> varying, according to the symbol) for text documents and e-mail.

****Well, the ascii system we developed on this list to emulate the
Sims notation only uses *one* symbol per 72-tET pitch.

****Well, certainly I am always interested in new ideas, personally,
and I don't even know if I'm being asked my *personal* opinion on
this topic... probably not! :)

But, unless this system better emulates the Sims notation, which has
already an existing *performance practice* one of the most important
considerations for *any* notation, now or (I think) throughout
history, I, personally wouldn't be interested in changing.

Frankly, there are some things I don't like about the Sims notation,
but the fact that it is established is a *very* important factor.
There are players in New York and Boston who know it. I can name two
names right away: Ted Mook, renowned cellist here in NYC and Chris
Washburne, renowned trombonist... and many others.

> In exchange for your agreeing to this,

****Please see above! :)

>
> One consideration is what to do about the Sims notation,
> specifically, should there be two competing system? My answer is
> that the two different notations don't serve the same constituency,
> so they would not really be competing with one another.

*****The point is that we don't want to have many *different*
notations for 72-tET, in the event that it moves into
the "mainstream" as I hope it will...

Different notations for different constituencies is a concept that
does not interest me *at all.* And I will now be pompous and say
that I believe it doesn't serve *music* either! :)

What if somebody *else* new comes along with *his* method as well.
Should we have 3 different ones then, or 5 or 7 or 11??

The Sims
> notation is intended to be used by performers utilizing existing 12-
> EDO instruments for music that is largely atonal (if I understand
the situation properly).

*****I don't believe this is the case. Even some of Sims music
verges on the "tonal." I do admit the Bostonians tend to move
somewhat in that direction, but it's not *tacetly* tied to a style...

The saggital notation is most suitable for
> those who believe in building acoustic instruments specially
designed for alternate tunings or in creating computer-generated
(pitch-bent) MIDI files.

*****You mean using different notations for different *STYLES* of
music?? That would be absurd, if you will pardon my exuberance. :)

In that case, we could use a five line staff for Romantic music and,
maybe, a six line staff for Atonal music, or such like.

"Party down" sightreaders! :)

Here we are interested principally in music using prime
> numbers beyond the 5 limit.

*****I believe Sims music is concerned with this also. Monz??

In cases where instrumentalists fluent
> with the Sims notation desire to participate with those preferring
> the saggital notation, all that woudl need to be done is to ensure
> that each musician has a part available in one's notation of choice.

*****As opposed to having *one* notation that everybody knows?? I
much prefer this second option...

> (In addition, we will find that with the saggital notation we can
> maintain a link back to long-held notational precedents established
> by the quartertone composers.)
>

*****You mean simply the arrows going up and down that Monz is always
talking about?? Frankly, arrows were used in "classical
contemporary" music to signify just about *anything!* I've even seen
little arrows with big 4's attached at the bottom for quartertones...
in fact, I even used to use something like that 30 years ago...

> It is a significant accomplishment that we have managed to agree
that 72-EDO will be the system of choice on which to base our master
> notation, whichever that may be.

****Well, now here I am *entirely* with you, George!!! It's the only
thing I write in nowadays!

And, the best part is, if I go "regressive" and retreat back to 12-
tET (not in the immediate game plan) I will *still* be composing in
72-tET.

That's the kind of "consistency" that's for me! :)

best wishes,

Joseph Pehrson

🔗gdsecor <gdsecor@yahoo.com>

🔗genewardsmith <genewardsmith@juno.com>

🔗gdsecor <gdsecor@yahoo.com>

--- In tuning@y..., "robert_wendell" <BobWendell@t...> wrote:
> Hi, George! A reference to the above subject in an earlier post
> really caught my attention. I notice that 17 P5s come out with a
> comma of -66 cents and some change, so 17 fifths just under 4 cents
> sharp come right out on 10 octaves. What strikes me as curious
about
> this is the negative value of the comma as against the positive
value
> of the syntonic comma. In 17-EDO the thirds are almost neutral. I'm
> trying to see how the comma might be distributed in a productive
way
> in terms of getting nice thirds at least for part of the cycle of
> keys.
>
> I see that we could tune the fifths even sharper to reduce the 33+
> cent flatness of the thirds at four steps, and then swing back
toward
> flatness to compensate, but the 4-step thirds occur at 9 fifths
into
> the cycle, so we would need more than 9 fifths tuned sharper just
to
> get more than one third reduced to whatever the value we might
> propose and then it would swing back rather quickly toward greater
> flatness again as we included the somewhat flatted fifths.
>
> I wonder what I'm missing here. Is my familiarity with 12-tone well
> temperaments causing me to model after them inappropriately? Or is
> your 17-tone well temperament even attempting to move in the
> direction of approximating just thirds at all? If not, then what
> would well temperament mean in this context?
>
> Curiously,
>
> Bob

Hi Bob!

Great question! I have taken a very different approach in my 17-WT
in that I do not consider the ratios of 5 to be represented at all in
this division of the octave, so I treat it as a 13-lmit system that
skips over the fifth harmonic. The thirds of 4 and 6 degrees are
therefore considered subminor and supermajor intervals, and on the
near side of the circle of fifths I seek to approximate 7:6 and 9:7,
which on the other side of the circle tends to favor 13:11 and 14:11,
respectively, for these two intervals. Thirds of 5 degrees are all
neutral thirds, approximating 11:9 and 16:13 (and Margo Schulter even
finds 17:14 in there somewhere). In at least five different keys of
my 17-WT there are consonant ninth chords approximating 6:7:9:11:13.

Margo's involvement with my 17-WT has led to nothing less than a 17-
tone revolution for both of us, and a report of the many things we
have discovered will be appearing in Xenharmonikon 18, which should
be out this spring. My article will even include a description of
two different moment-of-symmetry (MOS) scales (buried treasure from
the winter of 1978) that contain multiple tempered 6:7:9:11 or
6:7:9:11:13 chords (generated by intervals of 11 and 2 degrees of 17,
respectively).

Your subsequent dialogue with Paul Erlich also included discussion
about a 19-WT. I worked on one for several years (experiencing
difficulty with the far side of the circle, as you noted), but I
finally came up with something with which I am really satisfied
("nothing short of amazing" would possibly be a more accurate
description), also in 1978, just before I tackled the 17-WT. This
looks like something that I should write up in a *Buried Treasure*
posting soon. Stay tuned!

--George

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗dkeenanuqnetau <d.keenan@uq.net.au>

🔗robert_wendell <BobWendell@technet-inc.com>

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> --- In tuning@y..., "robert_wendell" <BobWendell@t...> wrote:
> > Hi, George! A reference to the above subject in an earlier post
> > really caught my attention. I notice that 17 P5s come out with a
> > comma of -66 cents and some change, so 17 fifths just under 4
cents
> > sharp come right out on 10 octaves. What strikes me as curious
> about
> > this is the negative value of the comma as against the positive
> value
> > of the syntonic comma. In 17-EDO the thirds are almost neutral.
I'm
> > trying to see how the comma might be distributed in a productive
> way
> > in terms of getting nice thirds at least for part of the cycle of
> > keys.
> >
> > I see that we could tune the fifths even sharper to reduce the
33+
> > cent flatness of the thirds at four steps, and then swing back
> toward
> > flatness to compensate, but the 4-step thirds occur at 9 fifths
> into
> > the cycle, so we would need more than 9 fifths tuned sharper just
> to
> > get more than one third reduced to whatever the value we might
> > propose and then it would swing back rather quickly toward
greater
> > flatness again as we included the somewhat flatted fifths.
> >
> > I wonder what I'm missing here. Is my familiarity with 12-tone
well
> > temperaments causing me to model after them inappropriately? Or
is
> > your 17-tone well temperament even attempting to move in the
> > direction of approximating just thirds at all? If not, then what
> > would well temperament mean in this context?
> >
> > Curiously,
> >
> > Bob
>
>
> Hi Bob!
>
> Great question! I have taken a very different approach in my 17-WT
> in that I do not consider the ratios of 5 to be represented at all
in
> this division of the octave, so I treat it as a 13-lmit system that
> skips over the fifth harmonic. The thirds of 4 and 6 degrees are
> therefore considered subminor and supermajor intervals, and on the
> near side of the circle of fifths I seek to approximate 7:6 and
9:7,
> which on the other side of the circle tends to favor 13:11 and
14:11,
> respectively, for these two intervals. Thirds of 5 degrees are all
> neutral thirds, approximating 11:9 and 16:13 (and Margo Schulter
even
> finds 17:14 in there somewhere). In at least five different keys
of
> my 17-WT there are consonant ninth chords approximating 6:7:9:11:13.
>
> Margo's involvement with my 17-WT has led to nothing less than a 17-
> tone revolution for both of us, and a report of the many things we
> have discovered will be appearing in Xenharmonikon 18, which should
> be out this spring. My article will even include a description of
> two different moment-of-symmetry (MOS) scales (buried treasure from
> the winter of 1978) that contain multiple tempered 6:7:9:11 or
> 6:7:9:11:13 chords (generated by intervals of 11 and 2 degrees of
17,
> respectively).
>
> Your subsequent dialogue with Paul Erlich also included discussion
> about a 19-WT. I worked on one for several years (experiencing
> difficulty with the far side of the circle, as you noted), but I
> finally came up with something with which I am really satisfied
> ("nothing short of amazing" would possibly be a more accurate
> description), also in 1978, just before I tackled the 17-WT. This
> looks like something that I should write up in a *Buried Treasure*
> posting soon. Stay tuned!
>
> --George

Bob:
Fantastic, George! Thank you and I'm certainly tuned in for more when
you can get to it (he said, salivating shamelessly)!

🔗gdsecor <gdsecor@yahoo.com>

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> It's nice to have the uppercase Secor on the list as well as the
> lowercase. :-) Welcome George.

Dave Keenan, this is indeed an honor! Now that I have both of you on
the line, may I give you and Paul Erlich my heartiest congratulations
on your rediscovery of the Miracle tuning and the secor generating
interval. I regard your joint accomplishment as even more
significant than mine, inasmuch as this was only something that I
stumbled upon in the course of an investigation that had a different
objective, in contrast to your very deliberate effort that has every
indication of bearing some real fruit. (Paul, my apologies for
misspelling your name before, which makes a nice segue to:]

> By the way, how do you pronounce your name exactly
> see-kor
> sek-or
> say-kor
> empasis on first or last syllable?

It's see-kor, with the emphasis on the first syllable.

> It's very handy that it's spelled somewhat like "second" since it
_is_
> a kind of minor second.

Yes, I spent quite a bit of time reading a number of postings since
last April, and I saw the one with "SECond, minOR".

> I'm glad Margo was able to contact you to let you know about recent
> developments. I made some attempts myself ...

Erv Wilson, who originally informed you about my XH3 article, had my
address all along, but it seems that nobody ever thought to ask him.

> I'm wondering if you haven't fully appreciated the interactive
nature
> of this medium yet, since you seem to be trying to obtain
agreements
> and objections to a notation we haven't seen yet. It would be more
> usual that one would simply give the notation with minimal
explanation
> and then defend it against (or modify it to answer) any objections
> that may arise, and elaborate any descriptions which are found to
be
> unclear. You could otherwise spend a lot of time defending against
> objections that never arise or elaborating things that most find
> obvious.

I was just "testing the water" to see what everybody felt about yet
another notation, especially after you had just gone through a
prolonged process of settling on an ASCII version for 72-EDO. I felt
that giving everybody a chance to air their feelings about this
beforehand would allow us to lay the controversial aspect of the
topic aside at least temporarily, which would give us a chance to
devote our full concentration on the several levels of information
that are conveyed by the notation itself, which has a deceptively
simple appearance. There are many things about it that are not
immediately obvious, and even five months after I started working on
it I am still finding more. Don't misunderstand me -- it's not
really complicated; it just has a versatility that goes far beyond
what I expected. To put it in a nutshell, if there is any notation
that could literally "do it all," then I think I've discovered it.

I use the word "discovered" rather than "devised" because I have come
to the conclusion that this is one of those things -- for example,
the Bosanquet keyboard, the Miracle tuning, or the elegance of the
Tartini fractional sharps -- that, if nobody came up with it today,
somebody with enough persistence would eventually find.

> This is by way of saying that I'm dying to know how your notation
> system works, and I'm sure others are too. Particularly since I
have
> just read what seems like the definitive 'The notation of equal
> temperaments' by Paul Rapoport, 1995. (Thanks Manuel)

I haven't seen that, so it would probably be helpful if you were to
enlighten us on what you have read at the appropriate time. (Perhaps
I have just rediscovered something that was already out there, or a
variation of it, which wouldn't be the first time.)

Anyway, I would gather from the responses that I have seen up to this
point that we can all seek to understand this with an open mind, and,
once having done that, can then discuss what we should do at that
point in time. On that assumption, I will begin preparing a
presentation.

> I'm also looking forward to further "Buried Treasure" posts.

All in due time.

> Regards,
> -- Dave Keenan

And stay tuned!

--George

🔗jpehrson2 <jpehrson@rcn.com>

🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > It's nice to have the uppercase Secor on the list as well as the
> > lowercase. :-) Welcome George.
>
> Dave Keenan, this is indeed an honor! Now that I have both of you
on
> the line, may I give you and Paul Erlich my heartiest
congratulations
> on your rediscovery of the Miracle tuning and the secor generating
> interval. I regard your joint accomplishment as even more
> significant than mine, inasmuch as this was only something that I
> stumbled upon in the course of an investigation that had a
different
> objective, in contrast to your very deliberate effort that has
every
> indication of bearing some real fruit.

While I would in no way consider the more recent accomplishment more
significant, I feel that the subsequent understanding of the
diatonic, decatonic, and MIRACLE scales in terms of periodicity
blocks has led to (or at least dovetailed nicely with) something of a
revolution in tuning theory, mainly happening on the tuning-math list
and mainly due to Graham Breed and especially Gene Ward Smith.

If you don't understand what is meant by periodicity block, perhaps
this will help:

http://www.ixpres.com/interval/td/erlich/intropblock1.htm

Perhaps to pique your curiosity, does this make any sense to you:

* The JI diatonic scale (in any of its common 5-limit variants) is
the periodicity block defined by the pair 81:80 and 25:24;
* Treating 25:24 as a musically significant "chromatic alteration",
while tempering out 81:80, places this scale in a linear temperament
known as meantone, and makes it an MOS.

* The JI blackjack scale (in any of its common 7-limit variants --
search the archives for "BlackJust" to see examples) is the
periodicity block defined by the triplet 2401:2400, 225:224, and
36:35;
* Treating 36:35 as a musically significant "chromatic alteration",
while tempering out 2401:2400 and 225:224, places this scale in a
linear temperament known as MIRACLE, and makes it an MOS.

My decatonic scale in approximately 22-tET (if you've read my paper
yet) also follows this pattern, with 63:64 and 50:49 tempered out,
and 28:27 as a "chromatic alteration".

The same logic works for a vast array of tone-systems that have been
proposed, in various "limits" and other schemes (like the Bohlen-
Pierce world with an equivalence interval of 3 and a basic 'triad' of
3:5:7) . . .

🔗dkeenanuqnetau <d.keenan@uq.net.au>

🔗jpehrson2 <jpehrson@rcn.com>

🔗gdsecor <gdsecor@yahoo.com>

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> > ... I regard your joint accomplishment as even more
> > significant than mine, inasmuch as this was only something that I
> > stumbled upon in the course of an investigation that had a
> different
> > objective, in contrast to your very deliberate effort that has
> every
> > indication of bearing some real fruit.
>
> While I would in no way consider the more recent accomplishment
more
> significant, I feel that the subsequent understanding of the
> diatonic, decatonic, and MIRACLE scales in terms of periodicity
> blocks has led to (or at least dovetailed nicely with) something of
a
> revolution in tuning theory, mainly happening on the tuning-math
list
> and mainly due to Graham Breed and especially Gene Ward Smith.
>
> If you don't understand what is meant by periodicity block, perhaps
> this will help:
>
> http://www.ixpres.com/interval/td/erlich/intropblock1.htm
>
> Perhaps to pique your curiosity, does this make any sense to you:
>
> * The JI diatonic scale (in any of its common 5-limit variants) is
> the periodicity block defined by the pair 81:80 and 25:24; ...

After taking a couple of minutes to skim through part 1 and a little
bit of part 2 of your "gentle introduction," yes, it makes a lot of
sense. (I will read the rest later.)

> My decatonic scale in approximately 22-tET (if you've read my paper
> yet) also follows this pattern, with 63:64 and 50:49 tempered out,
> and 28:27 as a "chromatic alteration".

Right now the limiting factor is time, so I haven't read the paper
yet; but I have no trouble following the above.

> The same logic works for a vast array of tone-systems that have
been
> proposed, in various "limits" and other schemes (like the Bohlen-
> Pierce world with an equivalence interval of 3 and a basic 'triad'
of
> 3:5:7) . . .

This delves into the theoretical side more deeply than I (or most
others) ever cared to go, but I readily appreciate the importance of
what your whole Tuning Math Group or team (if I may call it that) is
doing. I am highly impressed by the wonderful spirit of cooperation,
unselfishness, and readiness -- no, eagerness that all of you have
demonstrated to give credit where credit is due, especially including

[Dave Keenan, #32782]
> We mustn't forget Joseph Pehrson's essential contribution, which
> was to ask the right question.

(As Socrates might have said: In order to get the right answers, you
have to ask the right questions.)

Anyway, thank you for correcting me about this, because I wouldn't
want anyone who had a part in any of this to feel slighted in any way.

By the way, I saw in the postings last year that you were discussing
publication of an article about these recent developments. I hope
that you still intend to do that.

--George

🔗paulerlich <paul@stretch-music.com>

🔗manuel.op.de.coul@eon-benelux.com

🔗gdsecor <gdsecor@yahoo.com>

🔗jpehrson2 <jpehrson@rcn.com>

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:

/tuning/topicId_32446.html#32972

> Joseph,
>
>
> You have inspired me to start composing,

****This is the best compliment I could ever receive from *anybody!*

Go for it, George! We'll be anxious to see what you come up with.

By the way, there are multiple opportunities for posting *real music*
files on Jon Szanto's group MakeMicroMusic:

/makemicromusic/messages

and I'm going to have to
> find out how one goes about generating those pitch-bent midi
files. I bought a Cakewalk program for my daughter, but I don't know
if she mislaid the documentation or what, because I can't find it.
Anyway, my attempt to achieve pitch bend with it was completely
unsuccessful
> (returning to the pitch-bend menu showed that my input hadn't even
> been accepted), and I wonder what I'm doing wrong. Since you guys
> are old hands at this, I would appreciate your directing me to
> whatever places I need to go to get some help with this.
>

****Joe Monzo is the "pitch bend maestro" so I'm sure he'll be able
to help you out. I use "tuning tables" myself in the synth, so I'm
really not very knowledgable about how to make the pitch bends work...

> By the way, congratulations on your success with the Blackjack
piece in the competition, and may the best be yet to come!
>

Thanks so much, George. I appreciate it. Now, of course, since I
mentioned the possibility of being on the recording to everybody it
probably will be jinxed and not happen. It pays to keep one's mouth
closed from time to time... :)

Anyway, sorry if I went a little hard on your recent notation
presentation.... I tried to put a little caveat at the beginning so
you'll take it all with a "grain of salt" and a sense of humor...
hopefully. (While still engaging in dialogue...)

best,

Joseph

*BT* What is a Secor?

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BT What is a Secor?