Re: For Dan Stearns -- stylistic consonance/dissonance

Hello, there, Dan Stearns and everyone.

Please forgive me for using this List to let you know, Dan, that
apparently there's some technical problem with mail delivery that's
affecting my e-mail replies to you in an offlist exchange: my messages are
getting returned with warning notices about failure to deliver within
three days, and in one instance with a notice of failed delivery due to
"permanent fatal errors" in the address. I'm not sure where the glitch
could be, or on whose end.

Anyway, moving back to "concordant/dual-purpose/discordant"
sonorities, I'd like to share your view that set rules or "universals"
tend to become questionable in various areas where things get
interesting. Like "universals" in the area of natural human languages,
such theories often get influenced by the specific cultural or
stylistic views of the theorists -- not so surprisingly.

For example, I would say that 9:8 is more _stylistically concordant_
than 7:5 or 10:7 in a setting like that of Western European organum of
the 9th-11th century era based largely on parallel fifths or fourths.
In this kind of setting, a 7:5 may have an effect somewhat analogous
to that of a "Wolf" as a "near-3:2" -- close, but not quite what was
expected.

The effect here might be a bit like that in rhymed poetry, where a
"near-rhyme" may sound quite "dissonant," a kind of "mistake," while
an occasional pair of lines in blank verse might seem less so.

Similarly, the Pythagorean major third at 81:64 is a commonplace in
13th-14th century style, where it serves as a "dual-purpose" sonority,
to borrow Ludmila Ulehla's 20th-century term: she uses this term for a
sonority neither fully concordant nor urgently discordant. However, if
we place such a third in a Renaissance texture where 5:4 or something
close is the norm, 81:64 may be perceived as an outright "dissonance,"
something jarringly "standing out" from the intonational norm.

Dan, your scale-building algorithms are to me a reminder that each
scale and style has its own "harmonic inertia," it own set (or
sometimes various alternative sets) of expectations which define their
own sense of musical congruence.

If searching for a "universal," I might propose the statement that
music is generally made under the influence of cultural and stylistic
norms, whether these be critically or uncritically borrowed from some
tradition, or possibly in part devised by the composer or performer.
To seek stylistically-independent definitions of "concord/discord"
would seem to me to be either an activity calling for rather cautious
circumscription, or else likely an exercise in mixing "universals"
with stylistically specific expectations.

One thing does stand out to me: whoever compares n-tET's, for example,
whether Ivor Darreg or Brian McLaren or Paul Erlich, is doing so under
the influence of certain stylistic assumptions -- although this can be
most obvious to someone with differing expectations, one might
humorously add.

Even if one rightly concludes that each equal temperament has its own
"flavor," the definition of that "flavor" depends on stylistic
expectations -- maybe it would be better to carry Darreg's assertion a
step further, and say that each equal temperament has a range of
"flavors," some of which may only be "discovered" (or "tasted") when
yet unknown styles are invented.

A largely style-focused approach, far from discouraging the analysis
of concordant/dual-purpose/discordant sonorities ("sonance" as the
Monz would have it), permits us to investigate in depth why a given
scale may or may not fit a given style -- and sometimes why it fits
both happily and surprisingly.

For example, Paul Erlich's famous charts of n-tET's say to me: "Here
is how I would describe these scales in terms of the n-limit music I'm
interested in making myself, where an n-limit paradigm fits my musical
intent more or less closely and consistency is an important
consideration."

For other styles, we would want other and often quite different sets
of tables.

An interesting example is 11-tET, radically unconventional from a
European perspective of composed music because it doesn't have
anything close to a usual fifth or fourth at 3:2 or 4:3. However, this
scale has several intervals which I would consider as relatively
"concordant," or as "dual-purpose" sonorities of a sort, for example
the following:

2/11 octave ~218.18 cents (~9:8 or ~8:7; M2 with some "concord")
3/11 octave ~327.27 cents (~6:5, maybe approaching the zone of 17:14)
4/11 octave ~436.36 cents (~9:7, about 1 cent wide)
5/11 octave ~545.45 cents (~11:8, about 6 cents narrow)
6/11 octave ~654.55 cents (~16:11, octave complement of ~11:8)
7/11 octave ~763.64 cents (~14:9, octave complement of ~9:7)
8/11 octave ~872.73 cents (~8:5, maybe approaching zone of ~28:17)
9/11 octave ~981.82 cents (~7:4, about 13 cents wide, or ~16:9)

This scale may cause acute "cognitive dissonance" for some of us
oriented to rules and patterns of European verticality in 9th-20th
century patterns which assume conventional fifths or fourths, but it
invites various new styles, or maybe styles drawing on precedents from
world musics where intervals other than fifths or fourths may take a
higher priority.

Personally, since I find that "consonance/dissonance" or
"concord/discord" are terms having strong stylistic associations, I
might prefer more neutral concepts such as "simplicity/complexity" for
theories of harmonic entropy and the like.

Anyway, Dan, your scale-generation methods are at once a wellspring of
diversity and a powerful tool either for devising captivating
variations on the familiar in a given tradition, or for moving to new
territory. Thank you for your skill and patience as a mathematician
and educator both on-List and off.

Most appreciatively,

Margo Schulter
mschulter@value.net

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

> For example, Paul Erlich's famous charts of n-tET's say to me: "Here
> is how I would describe these scales in terms of the n-limit music
I'm
> interested in making myself, where an n-limit paradigm fits my
musical
> intent more or less closely and consistency is an important
> consideration."

Of course these charts occur quite early in my paper, in order to help
narrow down the search for scale for the music I'm interested in
making myself, but could be dispensed with entirely as the criteria I
subsequently introduce in the paper are far more important than
anything in these charts . . . in fact if I were to rewrite the paper
from scratch today, I'd never mention any ETs until much later on the
paper, where I'd notice that the optimal decatonic tuning was very
close to 22-tET, a very happy accident for guitarists, keyboardists,
and composers used to the conveniences

--- In tuning@y..., PERLICH@A... wrote:

/tuning/topicId_18560.html#18587

> --- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
>
> > For example, Paul Erlich's famous charts of n-tET's say to me:
"Here is how I would describe these scales in terms of the n-limit
music I'm interested in making myself, where an n-limit paradigm
fits my musical intent more or less closely and consistency is an
importantconsideration."
>
> Of course these charts occur quite early in my paper, in order to
help narrow down the search for scale for the music I'm interested in
> making myself, but could be dispensed with entirely as the criteria
I subsequently introduce in the paper are far more important than
> anything in these charts . . . in fact if I were to rewrite the
paper from scratch today, I'd never mention any ETs until much later
on the paper, where I'd notice that the optimal decatonic tuning was
very close to 22-tET, a very happy accident for guitarists,
keyboardists, and composers used to the conveniences

Yeah... but those charts are great, and I don't believe that anybody
else has done them as clearly!

_______ ___ ___ ____
Joseph Pehrson