Re: sense of no limitations

> Date: Sat, 02 Jul 2005 21:42:44 -0000
> From: "Joseph Pehrson" <jpehrson@...>
> Subject: sense of no limitations!

> I still have one complaint about the Blackjack tuning system. I know
> the inventors are going to jump all over me for this, but I say this
> as somebody who has had some experience (like 30 years) composing
> about every day and trying to do creative projects: Blackjack is not
> entirely an *aural* scale but is, to a certain degree, a
> *theoretical* one.

Hi, there, Joseph, and it's a pleasure to have dialogues here enriched by
your composerly perspective. Your remarks raise some interesting questions
which I'll try to pursue while keeping the accent, as you do, on practical
performance or composition.

> In other words, because the small steps are only 33 cents apart and
> there are frequently two that can be part of a consonant triad (one
> is a *wrong* one and the other one the "correct" just one) it's
> possible to make "mistakes" that later have to be corrected in a
> theoretical appraisal. That is not an entirely aural process. You
> can say what you will. It's not entirely aural in the way that some
> other scales are aural, including 12-tET. One *knows* when
> the "wrong" note is played immediately. They are distinct enough in
> terms of distance.

Maybe I should invite a clarification here: is the problem that it's hard
in Blackjack to find an aurally pleasing sound or progression, or that the
aural patterns of Blackjack are sometimes conceptually surprising? The
first might happen if you were composing on paper, wrote a triad that you
thought was 0-383-700 cents, and then tried it at the keyboard and found
that it was actually 0-417-700 cents or 0-433-700 cents (respectively near
4:5:6, 22:28:33, and 14:18:21).

The second situation might happen if you played a triad you really liked,
made it part of your composition, and then found out that the major third,
which you had supposed to be 383 cents, was actually 417 or 433.

A quick comment for now: Blackjack might seem "different" from the
viewpoint of a conventional European 12-note tuning (e.g. Pythagorean,
meantone, well-temperament, 12-equal) not only because it has more notes,
and smaller intervals, but because the 116-2/3 cent generator creates a
pattern quite distinct from a familiar chain of fifths.

At any rate, when I compare the kind of 24-note tuning I'm accustomed to
using (two 12-note chains of Pythagorean, meantone, Wilson/Pepper, etc.)
with the "Wonder Tuning" (generator of about 233.985 cents, or 1/3 of a
pure 3:2 fifth, about twice as large as the Blackjack generator) in my
"23-skidoo" arrangement with 23 generators and thus 24 notes, the "ease of
navigation" is indeed much greater with the former kind of system. It
isn't just that Wonder has some small intervals of around 30 cents -- the
more conventional 24-note systems do also -- but the less familiar
arrangement and logic.

> However, Blackjack has so many other attractive qualities, including
> the extreme notational ease, that I suppose this is just a quibble...
> but here I am quibbling... :)
>
> J. Pehrson

Personally, I'd place something like Blackjack or 23-Skidoo rather toward
the far side of a continuum of "conventional/unconventional" schemes --
it's a decidedly different structure as compared with many 7-note scales
(e.g. medieval European modes, Near Eastern maqamat), or with a regular
chain of fifths (e.g. 12 notes or more).

Nearer the other side, there are things like my modified meantone in 12
notes based on Zarlino's 2/7-comma from F to C#, with the other four
fifths equally wide (about 6.42 cents). In the nearer transpositions, it's
like a usual meantone, and in the most remote range there are some
septimal approximations. Major thirds are at around 383, 396, 408, 421,
and 433 cents (the smallest and largest very close to Blackjack), and
minor thirds at around 275, 287, 300, and 313 cents.

An important point is that what seems "conventional" can depend on what
one's used to: someone not used to the meantone convention that a
diminished fourth like G#-C is much larger than a regular major third like
A-C# might find either a regular meantone or my modified meantone
"strange," for example.

Anyway, an open question: if your remarks, about which I wasn't sure
above, mean that sometimes you find a pleasing interval that turns out to
be an unexpected size, might this be a kind of serendipity? Of course, if
your remarks instead mean that you find it hard to find an aurally
appealing interval, that's something else.

In 20-tET, for example, I found that the interval D-F on my keyboard
mapping made a pleasing minor third contracting to a unison on E -- and
then realized that D-F on my mapping was actually not 300 cents (the
obvious 20-tET minor third) but 240 cents, also a large major second. This
made me realize that the "minor third" category could at times be this
flexible, with intervals around 240 cents an enhanced resource not only in
this tuning but in 25-tET, for example, and various other schemes with
such intervals.

In peace and love,

Margo

> Maybe I should invite a clarification here: is the problem that
it's hard
> in Blackjack to find an aurally pleasing sound or progression, or
that the
> aural patterns of Blackjack are sometimes conceptually surprising?
The
> first might happen if you were composing on paper, wrote a triad
that you
> thought was 0-383-700 cents, and then tried it at the keyboard and
found
> that it was actually 0-417-700 cents or 0-433-700 cents
(respectively near
> 4:5:6, 22:28:33, and 14:18:21).
>

***Hello Margo!

So nice to hear from you after quite a long time!

Certainly it is not that the progressions in Blackjack are not
consonant or pleasing. There are *many* *many* in Blackjack that are
wonderful. It is, indeed, the second instance where there is more
than one possibility.

> The second situation might happen if you played a triad you really
liked,
> made it part of your composition, and then found out that the major
third,
> which you had supposed to be 383 cents, was actually 417 or 433.
>

***This is it exactly... And actually, I was *prefering* the 417 or
433... but then thinking, well I'm *supposed* to be using "simple
just intonation" so maybe I should change this to 383! :)

However, in many cases I quickly get *used* to the 383...

After all, in the compositional structure of the larger, global form,
these alterations are really more of a "coloristic" than "integral"
nature, I believe...

> A quick comment for now: Blackjack might seem "different" from the
> viewpoint of a conventional European 12-note tuning (e.g.
Pythagorean,
> meantone, well-temperament, 12-equal) not only because it has more
notes,
> and smaller intervals, but because the 116-2/3 cent generator
creates a
> pattern quite distinct from a familiar chain of fifths.
>

***Sure! It's a different "starting point" and process for the
scale, for certain...

> At any rate, when I compare the kind of 24-note tuning I'm
accustomed to
> using (two 12-note chains of Pythagorean, meantone, Wilson/Pepper,
etc.)
> with the "Wonder Tuning" (generator of about 233.985 cents, or 1/3
of a
> pure 3:2 fifth, about twice as large as the Blackjack generator) in
my
> "23-skidoo" arrangement with 23 generators and thus 24 notes,
the "ease of
> navigation" is indeed much greater with the former kind of system.
It
> isn't just that Wonder has some small intervals of around 30 cents -
- the
> more conventional 24-note systems do also -- but the less familiar
> arrangement and logic.
>
> > However, Blackjack has so many other attractive qualities,
including
> > the extreme notational ease, that I suppose this is just a
quibble...
> > but here I am quibbling... :)
> >
> > J. Pehrson
>
> Personally, I'd place something like Blackjack or 23-Skidoo rather
toward
> the far side of a continuum of "conventional/unconventional"
schemes --
> it's a decidedly different structure as compared with many 7-note
scales
> (e.g. medieval European modes, Near Eastern maqamat), or with a
regular
> chain of fifths (e.g. 12 notes or more).
>

***This is an interesting observation. I wasn't aware that Blackjack
could be considered so "experimental..." but I guess it is in
a "fifths-meantone" sense, which, of course, encompasses so many
different scales...

> Nearer the other side, there are things like my modified meantone
in 12
> notes based on Zarlino's 2/7-comma from F to C#, with the other four
> fifths equally wide (about 6.42 cents). In the nearer
transpositions, it's
> like a usual meantone, and in the most remote range there are some
> septimal approximations. Major thirds are at around 383, 396, 408,
421,
> and 433 cents (the smallest and largest very close to Blackjack),
and
> minor thirds at around 275, 287, 300, and 313 cents.
>
> An important point is that what seems "conventional" can depend on
what
> one's used to: someone not used to the meantone convention that a
> diminished fourth like G#-C is much larger than a regular major
third like
> A-C# might find either a regular meantone or my modified meantone
> "strange," for example.
>

***Got it. That makes a lot of sense...

> Anyway, an open question: if your remarks, about which I wasn't sure
> above, mean that sometimes you find a pleasing interval that turns
out to
> be an unexpected size, might this be a kind of serendipity? Of
course, if
> your remarks instead mean that you find it hard to find an aurally
> appealing interval, that's something else.
>

***As I mentioned, it's the former. You know, maybe I should just
forget about any desire to have "simple just chords" or whatever, and
celebrate whatever sonorities I come up with as themselves. I was
leaning in that direction anyway. Then I don't have to "correct"
anything, since there was really nothing to "correct" in the first
place!... I heard what I heard.

Your comments have been most helpful in this regard!!!

> In 20-tET, for example, I found that the interval D-F on my keyboard
> mapping made a pleasing minor third contracting to a unison on E --
and
> then realized that D-F on my mapping was actually not 300 cents (the
> obvious 20-tET minor third) but 240 cents, also a large major
second. This
> made me realize that the "minor third" category could at times be
this
> flexible, with intervals around 240 cents an enhanced resource not
only in
> this tuning but in 25-tET, for example, and various other schemes
with
> such intervals.
>
> In peace and love,
>
> Margo

***I know from that past that you have been an "inclusionist...",
welcoming many different intervals and sounds.

I should follow this example, rather than didactically "correcting"
things that I heard properly in the first place!

Thanks for the interesting and very helpful comments.

Joe

Hello, Joseph and everyone, and I can an amusing story on the topic of
interval size (mis)recognition (re "no sense of limitations" thread).

The last few days I've been considering how to write a quick note
about my "temperament extraordinaire" with eight fifths (F-C#) in
Zarlino's 2/7-comma meantone and the others equally wide (and impure a
tad more than the narrow meantone fifths -- about 6.42 cents wide, vs.
about 6.14 cents narrow). While a piece in a Renaissance style using
some of the colorful augmented and diminished intervals could
illustrate the advantages of a meantone, that left the question: why
bother "taming" the Wolf fifth (G#-Eb) when Ab-Eb (or G#-D#) doesn't,
if I'm correct, come into play in my sample piece.

A ready solution: do a second piece, maybe an improvisation, in a
remote modality like Eb Dorian or Ab Mixolydian (here I'm speaking of
the medieval/Renaissance European modes rather than ancient Greek
ones) where Ab-Eb does get used.

To simplify things a bit (however questionably), I decided to try
using a MIDI controller transposition feature to remap the keyboard so
that Ab Mixolydian would be mapped to the keyboard as it if were the
untranposed mode at G-G (but with the actual steps and intervals from
the Ab-Ab transposition). I had mixed feelings about this, since it
might be better to practice playing in remote transpositions as part
of the experience of doing this piece -- longer to make fluid, but
edifying and satisfying.

Anyway, I tried the "shortcut," and soon took pleasure at the
"near-septimal thirds" I was playing at what mapped to A-C-E and E-G-B
on the keyboard. I was getting into a kind of early 13th-century (or
very late 12th-century?) conductus style, where these sonorities could
move nicely to fifths a step or down.

After I had done my "shortcut" recording, I checked the transposition
feature again, and concluded that I might have actually transposed the
keyboard mapping so that I was playing in F# Mixolydian rather than Ab
Mixolydian. That meant that "A-C-E" would have been actual G#-B-D#, or
0-300-708 cents -- a reasonable approximation of a Pythagorean
0-294-702 cents (if one disregards the little matter of the fine
quality of that fifth!), but distinct from the 0-275-708 I had been
going for as pleasingly "septimal."

My visual "E-G-B" would have been D#-F#-A# (or Eb-Gb-Bb) at 0-287-708
cents, with a minor third about the distance from Pythagorean on the
other side, and a nice approximation of 13:11, as well as an upper
421-cent major third -- very pleasant to play (like "A-C-E"), and in
the right general neighborhood, but still distinct from the intended
F-Ab-C at 0-275-696 cents (well, at least the major third would have
been the right size for the intended sonority).

In this tuning, interval sizes within a category change by steps of
about 12.57 cents -- maybe not too different from the 16-2/3 cents of
Blackjack. If the scenario above is what happened, then I had no
problem playing a 300-cent or 287-cent minor third and taking it as a
"near-septimal" 275 cents.

Anyway, having told the story and confessed my less than assured
technique when it comes to basic keyboard transposition as well as
interval size recognition, I might as well share the improvisation
itself:

<http://www.bestii.com/~mschulter/MixolydianDiversionTE1.mp3>

Thanks again, Joseph and all, for the dialogue and camaraderie and
sustaining humor.

Peace and love,

Margo

Hello, everyone, and here is an improvised piece _For Erin_ in a
slendro scale from Zephyr 24, a just tuning which includes the 20
notes of the 1-3-7-9-11-13 eikosany plus the four simple factors of 1,
3, 7, and 9.

<http://www.bestii.com/~mschulter/ForErin.mp3>

The scale combines notes from two overlapping 3:2 pentachords, one
taken from each keyboard, with eikosany or simple factors shown in
parentheses for each note (with C4 as middle C):

E*3 F#*3 G#*3 B*3
192/143 216/143 7/4 288/143
510.109 714.019 968.826 1212.064
(3) (1.3.9) (7.11.13) (9)
-------------------------------------------------------------
B2 C#3 E3 F#3
1/1 9/8 189/143 3/2
0 203.910 482.845 701.955
(1.11.13) (9.11.13) (3.7.9) (3.11.13)

The outer notes form a wide octave at about 1212 cents, or larger than
a simple 2:1 by 144:143, while the overlapping notes facilitate
complex unisons of 144:143 or about 12 cents (F#-F#*), and 64:63 or
about 27 cents (E3-E*3) -- nuances of a kind typical in gamelan.

Of course, the art is in getting the music to flow, and here I'm only
a beginner.

Maybe I should add that one of the things that attracted me to this
pattern was the division of the upper 4:3 fourth on the second
keyboard (F#*-G#*-B*) at 864:1001:1152 or about 255-243 cents, a
division which somehow reminded me of a recording of gamelan music I
had heard around the early 1970's. I have a special weakness for
intervals in this region.

My special thanks to Erin and Kraig for their inspiration, example,
and encouragement -- and to the authors of some fine Javanese studies
on the art of gamelan intonation and counterpoint available in an
excellent translation as well as those responsible for the English
edition, and to Jacky Ligon for many discussions about gamelan.

I'll be leaving tomorrow for another visit with my Mom -- and am very
excited about this -- so it's a pleasure to celebrate by posting
this.

Peace and love,

Margo

Margo,

{you wrote...}
>Hello, everyone, and here is an improvised piece _For Erin_ in a slendro >scale from Zephyr 24, a just tuning which includes the 20 notes of the >1-3-7-9-11-13 eikosany plus the four simple factors of 1, 3, 7, and 9.

Lovely. I like the way you sit on those near-unisons a couple of times. So good to hear the results of your Margo Makes Music system up and running!! :) Best to mom in LA...

Cheers,
Jon