Another beautiful Secor tuning -- Note for Heinz Bohlen

Hello, there, Heinz Bohlen and everyone.

Thank you for your latest response, at once gracious and most
encouraging, which I regret noticing only last night -- maybe not so
surprising, given the volume of some recent digests and also some
musical and other distractions I have encountered over the past days.

Your remark that the "Musical Animal" article provides a kind of
philosophical grounding for the Bohlen-Pierce scale does not at all
surprise me, and very much fits my own reading of this piece.

More generally, your most poetic statement about the "gestalt" of a
scale has moved me to an essay on this topic, which I hope to have
finished in the next few days, including an introduction on how the
"Musical Animal" piece has had an influence on some of my own
attitudes in approaching a new or different tuning.

Today I experienced for the first time a tuning which I've been
meaning to try for some months: George Secor's 17-note
well-temperament, in which I promptly felt right at home, even while
seeking out some "special" intervals he notes, specifically a few
virtually just 11:6's. In my usual terms, these would be "augmented
sixths" such as Eb-C# -- a kind of sound, in a tempered version, that
I much relish in something like 17-tET. I likewise found myself
enjoying the near-11:6 intervals, and would like better to become
acquainted with their nuances of "justness."

Secor also notes the presence of some pure 11:7 intervals, familiar to
me as regular minor sixths in a tuning with pure 14:11 major thirds --
which, of course, are also available in what I might term the more
"remote" portion of the tuning circle.

His beautiful temperament has nine of the fifths (Ab-B) at about
707.220 cents, and the other eight at around 704.377 cents.

While I'm not sure about the kind of stylistic setting which may have
inspired Secor's tuning, I correctly guessed that it would be a
wonderful choice for neo-Gothic music growing largely out of 13th-14th
century Western European styles.

In the "Puff Pipes" timbre I used, the major thirds in the nearer part
of the tuning circle at ~428.88 cents had a very pleasantly "bright"
or sunny quality, at once relatively concordant and providing a most
satisfying cadential resolution. They can be points of motion, or
places to pause now and then.

There are five remote thirds at a pure 14:11 (~417.51 cents), the
octave complements of Secor's pure 11:7's, and in this gestalt -- to
borrow your term -- these major thirds seemed quite "mellow," lending
a note of "modal color," while still providing very nice cadences.

As expected on the basis of experience with other tunings, I liked the
pure 11:7 minor sixths also: they have a bit of a pleasantly "languid"
flavor for me.

A feature of Secor's tuning circle is that the brightest major thirds,
and also the most narrow or compact diatonic semitones, are located in
the nearest transpositions -- with steps such as E-F or B-C at around
63.90 cents, quite close to 28:27. As we move to the remote portion of
the circle, these semitones gently increase in size to around 78.11
cents -- identical to those of a regular tuning with pure 14:11 major
thirds, and very close to 46-tET.

I very much like this touch, which gives the tuning its own character
and pattern. Of course, I experience that pattern in the setting of
the musical style I happen to be exploring, and would emphasize that
Secor's tuning and its wealth of intervals and sonorities could fit
many kinds of styles both known and yet to be discovered.

As it happens, I only learned of this superb well-temperament in the
last few months, more or less, while looking at a post by Brian
McLaren from a Tuning List archive for July, 1994. McLaren quotes from
an article by Secor in the first issue of _Interval_ (1978).[1]

Just about a year ago, not yet aware of Secor's tuning, I came up with
a 17-note well-temperament taking as the first 12 notes a regular
tuning with pure 14:11 major thirds (Eb-G#). Five of the remaining
fifths were tempered at about 708.77 cents to produce two pure 9:7
major thirds in the far portion of the circle, with the remaining
"odd" fifth at about 708.00 cents to fill out the circle, and produce
another near-9:7 third.

In this scheme, the largest major thirds and narrowest diatonic
semitones occur at the far portion of circle. Together with pure 14:11
major thirds and 11:7 minor sixths, the more "usual" 12-note range
from Eb to G# has "alternative thirds" (augmented seconds and
diminished fourths) with a "supraminor/submajor" quality near 17:14
and 21:17, shading toward neutrality as one moves into more remote
regions.

Secor's tuning, in contrast, offers a rich palette of neutral thirds,
shading toward the supraminor/submajor range in the remote portion of
the circle.

For some reason, approaching the problem of a 17-note well-temperament
at 22 years or more apart (Secor's tuning was published in 1978), we
both hit on having some fifths at ~704.377 cents to obtain a set of
11:7 or 14:11 intervals.

The two schemes seem in some ways mirror images of one another, and
I would mainly say that my own experience at devising such a
well-temperament seems immensely richer now that I know Secor's
beautiful solution.

Here I am moved to conclude by quoting some words you have written:

"Their images can blend into each other, as
their sounds can..., like a sweeter and a
dryer version of wine from the same variety
of grapes."[2]

-----
Notes
-----

1. George Secor, "17-Tone Well Temperament," _Interval_ Volume 1,
Number 1 (Spring 1978), pp. 4-5, quoted in article by Brian McLaren,
"Secor well temperament," as posted by Gary Morrison, "Post from Brian
McLaren," 13 July 1994.

2. Heinz Bohlen, "The Musical Animal's Acoustic Adventures" article in
_Xenharmonikon_ 17 (Spring 1998), pp. 41-56, at 50. Here the Musical
Animal is comparing the 4:5:6 triad with the Bohlen-Pierce triad in
its just version at 3:5:7.

Most appreciatively,

Margo Schulter
mschulter@value.net

Hi,

I've just had the chance to read your article and the 11/6 interval
immediately attracted my attention as it's the inversion of 12/11,
which is -maybe- the most important 'neutral second' interval in
Eastern/Turkish 17 interval tone system.

Being almost in the middle of a minor third (6/5), this interval
serves as the balance factor in the cadancial sections of pieces
composed in makams ending with Uşşák genus (12/11, 6/5, 4/3).

I have observed that the genus gains its balance within a minor third
harmonic span at the finalis and just then the second degree becomes
lower as 12/11. The strong attraction of the minor third causes the
fourth become -what's called "kapalı nevâ" and the genus completes in
the written form.

Best regards,
Ertugrul

PS: Because of the extremely high traffic at the list, I don't get
either messages or digests with e-mail. That's why, private
conversation will be appreciated, however I'll browse the group in -
hopefully- regular basis, too.

---
Decode address to reply:
ertugrulinanc-at-yahoo-dot-com

--- In tuning@y..., mschulter <MSCHULTER@V...> wrote:
> Hello, there, Heinz Bohlen and everyone.
>
> Thank you for your latest response, at once gracious and most
> encouraging, which I regret noticing only last night -- maybe not so
> surprising, given the volume of some recent digests and also some
> musical and other distractions I have encountered over the past
days.
>
> Your remark that the "Musical Animal" article provides a kind of
> philosophical grounding for the Bohlen-Pierce scale does not at all
> surprise me, and very much fits my own reading of this piece.
>
> More generally, your most poetic statement about the "gestalt" of a
> scale has moved me to an essay on this topic, which I hope to have
> finished in the next few days, including an introduction on how the
> "Musical Animal" piece has had an influence on some of my own
> attitudes in approaching a new or different tuning.
>
> Today I experienced for the first time a tuning which I've been
> meaning to try for some months: George Secor's 17-note
> well-temperament, in which I promptly felt right at home, even while
> seeking out some "special" intervals he notes, specifically a few
> virtually just 11:6's. In my usual terms, these would be "augmented
> sixths" such as Eb-C# -- a kind of sound, in a tempered version,
that
> I much relish in something like 17-tET. I likewise found myself
> enjoying the near-11:6 intervals, and would like better to become
> acquainted with their nuances of "justness."
>
> Secor also notes the presence of some pure 11:7 intervals, familiar
to
> me as regular minor sixths in a tuning with pure 14:11 major
thirds --
> which, of course, are also available in what I might term the more
> "remote" portion of the tuning circle.
>
> His beautiful temperament has nine of the fifths (Ab-B) at about
> 707.220 cents, and the other eight at around 704.377 cents.
>
> While I'm not sure about the kind of stylistic setting which may
have
> inspired Secor's tuning, I correctly guessed that it would be a
> wonderful choice for neo-Gothic music growing largely out of 13th-
14th
> century Western European styles.
>
> In the "Puff Pipes" timbre I used, the major thirds in the nearer
part
> of the tuning circle at ~428.88 cents had a very pleasantly "bright"
> or sunny quality, at once relatively concordant and providing a most
> satisfying cadential resolution. They can be points of motion, or
> places to pause now and then.
>
> There are five remote thirds at a pure 14:11 (~417.51 cents), the
> octave complements of Secor's pure 11:7's, and in this gestalt -- to
> borrow your term -- these major thirds seemed quite "mellow,"
lending
> a note of "modal color," while still providing very nice cadences.
>
> As expected on the basis of experience with other tunings, I liked
the
> pure 11:7 minor sixths also: they have a bit of a
pleasantly "languid"
> flavor for me.
>
> A feature of Secor's tuning circle is that the brightest major
thirds,
> and also the most narrow or compact diatonic semitones, are located
in
> the nearest transpositions -- with steps such as E-F or B-C at
around
> 63.90 cents, quite close to 28:27. As we move to the remote portion
of
> the circle, these semitones gently increase in size to around 78.11
> cents -- identical to those of a regular tuning with pure 14:11
major
> thirds, and very close to 46-tET.
>
> I very much like this touch, which gives the tuning its own
character
> and pattern. Of course, I experience that pattern in the setting of
> the musical style I happen to be exploring, and would emphasize that
> Secor's tuning and its wealth of intervals and sonorities could fit
> many kinds of styles both known and yet to be discovered.
>
> As it happens, I only learned of this superb well-temperament in the
> last few months, more or less, while looking at a post by Brian
> McLaren from a Tuning List archive for July, 1994. McLaren quotes
from
> an article by Secor in the first issue of _Interval_ (1978).[1]
>
> Just about a year ago, not yet aware of Secor's tuning, I came up
with
> a 17-note well-temperament taking as the first 12 notes a regular
> tuning with pure 14:11 major thirds (Eb-G#). Five of the remaining
> fifths were tempered at about 708.77 cents to produce two pure 9:7
> major thirds in the far portion of the circle, with the remaining
> "odd" fifth at about 708.00 cents to fill out the circle, and
produce
> another near-9:7 third.
>
> In this scheme, the largest major thirds and narrowest diatonic
> semitones occur at the far portion of circle. Together with pure
14:11
> major thirds and 11:7 minor sixths, the more "usual" 12-note range
> from Eb to G# has "alternative thirds" (augmented seconds and
> diminished fourths) with a "supraminor/submajor" quality near 17:14
> and 21:17, shading toward neutrality as one moves into more remote
> regions.
>
> Secor's tuning, in contrast, offers a rich palette of neutral
thirds,
> shading toward the supraminor/submajor range in the remote portion
of
> the circle.
>
> For some reason, approaching the problem of a 17-note well-
temperament
> at 22 years or more apart (Secor's tuning was published in 1978), we
> both hit on having some fifths at ~704.377 cents to obtain a set of
> 11:7 or 14:11 intervals.
>
> The two schemes seem in some ways mirror images of one another, and
> I would mainly say that my own experience at devising such a
> well-temperament seems immensely richer now that I know Secor's
> beautiful solution.
>
> Here I am moved to conclude by quoting some words you have written:
>
> "Their images can blend into each other, as
> their sounds can..., like a sweeter and a
> dryer version of wine from the same variety
> of grapes."[2]
>
> -----
> Notes
> -----
>
> 1. George Secor, "17-Tone Well Temperament," _Interval_ Volume 1,
> Number 1 (Spring 1978), pp. 4-5, quoted in article by Brian McLaren,
> "Secor well temperament," as posted by Gary Morrison, "Post from
Brian
> McLaren," 13 July 1994.
>
> 2. Heinz Bohlen, "The Musical Animal's Acoustic Adventures" article
in
> _Xenharmonikon_ 17 (Spring 1998), pp. 41-56, at 50. Here the Musical
> Animal is comparing the 4:5:6 triad with the Bohlen-Pierce triad in
> its just version at 3:5:7.
>
> Most appreciatively,
>
> Margo Schulter
> mschulter@v...

Hello there, Margo, and everyone else interested in the secrets of intervals.

Thank you for your message, so friendly and thoughtful as always. We have
been studying it together, the Musical Animal and I, and the MA had some
interesting thoughts about those 11:7 and 14:11 intervals that you detected
in Secor's scale. On a piece of paper (the MA doesn't speak, as you well
know) it pointed them out to me. It sketched the frequency spectrum of an
octave, a fifth, a fourth, a major sixth and more intervals in the sequence
of descending consonance, including 11:7 and 14:11, all of them with their
lower harmonics and their combination tones up to about the third order. The
MA looked at me, and I knew what it was asking:

"Do you see how the great consonances, most of all the octave, the fifth and
the fourth, are inflicted by coincidences of their harmonics and by
combination tones that coincide with the very frequencies of the interval
tones and their harmonics, but only in just tuning? Try to tune a little, try
to temper, and you will get beats all over. Therefore the quest for
temperaments with as many as possible just fifths, and did you ever hear of
somebody trying to temper the octave? But those intervals like 11:7 and
14:11, they are practically carefree. They are perhaps no great consonances,
but they certainly lack dissonance. You don't need to fret over accuracy to
enjoy them. Their harmonics meet only where we can't hear them anymore, and
combination tones keep respectful distance from the base tones and their
harmonics. Don't you think that this contributes to their beauty decidingly?"

Well, who am I to argue with the MA about issues it is expert in. I just want
you to know about its ideas. With that, we wish to say good bye to you and to
the list for a few weeks. I will be on a trip to Europe, and the MA is going
to join me. That's fine with me, it's good to have a companion during those
long flights that shares one's thoughts.

Most appreciatively,

Heinz