--- In tuning@yahoogroups.com, "Walter Lepore" <soundmaker@...> wrote:
>
> Hi Members,
>
> It's been awhile since I last posted a message. Hope all are well.
>
> I have a question please...
>
> What is in the mind of a "scale builder" when he/she creates a
scale?

Hi Walter,

Soooo glad you asked! 8-}

Over the course of many years, I have spent innumerable hours
addressing the (usually self-imposed) challenge to create both scales
(which are generally subsets of tunings) and tunings (which specify
exact pitches for scales) that are either "better" than, or in some
way different from whatever already exists.

My motivation for doing this is encapsulated in my response to an e-
mail from Paul Bailey earlier this year, part of which I've pasted
here. Paul also had some nice thoughts, so in the following you'll
be getting two for the price of one:

<< --- Paul Bailey wrote:
> ...
> (I thought I was the only one who fooled around with piano
> temperaments....)

I haven't done that with an acoustic piano for many years (since I
don't even own one any more).

FYI, my interest in alternate tunings started shortly after I learned
to tune a piano (because I wanted to keep my own piano in tune, just
so I would have an additional incentive to practice). I became
curious about why the fifths were tempered narrow, which in turn led
to investigation of other divisions of the octave and just
intonation. Ironically, after a short time I developed a greater
(more intense and longer-lasting) interest in alternate tunings than
in practicing the piano.

These days, fooling around with temperaments is something like a game
for me: to try to devise something better than what I've already
done -- like trying to beat my previous high score in a video game.
Nice thing about this game is, when it's over, I have something
useful to show for my time and effort. :-)

> ...
> The act of playing is a cyclic activity. The pianist's own response
to
> the sound should be, pretty much
> has to be, a link in the chain of events.

Yes, I agree.

> ... An incident illustrates the current condition. A
> Taubman pianist-teacher thinks that my interest
> in tunings is a form of Obsessive - Compulsive Disorder.

Hmmm, unfortunately at times that's not very far off the mark in
characterizing my build-a-better-tuning game :-( -- when I'm not
working with Dave Keenan on the microtonal notation to end all
microtonal notations (which, BTW, would never have happened if we
weren't prone to alternate-tuning addiction).

> I think he's
> missing the point that the tuning IS the music.

Thanks for reminding me that I should spend more less time theorizing
and more time composing in alternate tunings (which is what I really
had in mind when I first got into this).

> Nobody faults singers or instrumentalists for constantly working at
> intonation - it's virtually inseparable from tone production.
> Pianists should play the same way - except the piano has to be
tuned
> ahead of time -

Ahhh, well said! >> (End of quote)

> Its been my interest to discover why scales exist, why they are
> created and how to apply these new and old "collection of
> frequencies" to composition. This seemingly "basic" question can
> certainly have complicated answers.
>
> I do have adequate training in music theory and composition but
still
> learning the inner workings of tuning theory. Forgive me if this
> question ranks as an entry-level question.
>
> I'd like to know how my question relates to the following:
>
> 1) Designing a scale with Secundal, Tertian, Quartal, and
Quintal
> Harmonies in mind.

That may be a significant factor in the design, but if the scale is
other than heptatonic, those terms are apt to become blurred, or they
may need redefining. For example, building chords using every other
note of a pentatonic scale will result in "fourth-chords" (in
heptatonic terminology), where the "fourths" (of 2 pentatonic
degrees, or "thirds") may be in the neighborhood of any of the
following intervals: 5:7, 3:4, 9:7, or 4:5. By contrast, an interval
of 5:6 would fall into the 1-pentatonic-degree category.(i.e., a
pentatonic "second").

> 2) Designing specific tunings or scales for Composition

A composer may have a certain harmonic limit (e.g., 7-limit or 11-
llimit harmony) in mind or a certain combination of primes; one or
more intervals within that limit might then be used as a generator or
generators in an attempt to construct a scale with a reasonable
number of tones (and with reasonable melodic properties). Or a
composer may have certain melodic intervals in mind that might be
combined into a useful scale.

> 3) Scale builders who create/build scales without composition in
mind.

See tuning compulsion/addiction (above).

> 4) Why would a composer choose a specific tuning or scale over
> another.

I believe I need to clarify the distinction between a scale and a
tuning. I define a scale as a set of tones that may be used to write
a melody, in which the tones are related by (more or less) specific
interval-classes. A tuning is a set of tones for which specific
frequencies or frequency-ratios (either rational or irrational) are
given; tunings may be defined by one or more generating intervals, in
which case they may consist of an indefinite number of tones.

Examples of scales are: 1) a diatonic major scale (either just or
tempered), and 2) a pentatonic scale consisting of a single chain of
fifths (exact size unspecified). Examples of tunings are Pythagorean
tuning, 12-ET, 1/4-comma meantone temperament, 19-ET, 31-ET, 17-ET,
etc. A diatonic or pentatonic scale is contained in each of those
tunings, and those scales will sound somewhat different in each
tuning.

Some scales (such as the Blackjack scale) are organized in such a way
that they are capable of being played only in certain tunings, so the
choice of a tuning will determine which scales are available, and
vice versa -- or one's choice of tuning may be determined by how well
a particular scale sounds in that tuning.

Generally, one will choose a scale with a particular tuning (or
family of tunings) in mind, or one may devise (or choose) a tuning so
that (or because) it in some way optimizes a particular scale.

> I'm sure the question will come into better focus as responses
begin
> to filter in as it may be covering too broad an area initially.
>
> Any response relating to the initial question is appreciated.
>
> Thank you all for your time.
> Walter Lepore New Jersey USA

I hope I haven't raised more questions than I've answered. ;-)

--George