What is in the mind of a "scale builder" when he/she creates a scale?

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?

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.

2) Designing specific tunings or scales for Composition

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

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

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

Hi Walter,

A few random thoughts in response to your question:

Some scales aren't designed, they evolve over time in a
musical culture. Later they may be described by theorists.

Musical instruments all have unique capabilities and
limitations in their production of sound. Aside from a
few indications unique for the violin, violin music is
notated with discrete notes. However if you look at a
violin melody with pitch detector software, you can see
it looks very little like a piano melody or even a flute
melody. So fixed scales are abstractions.

As for designed scales, the goals and methods of different
designers can be very different.

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

Different scales are suitable for different music. If one
wants smooth chords, one will have an easier time with a
scale of JI or near-JI values, and the converse.
Also one can choose the number of tones in the scale, which
is related to the size of the smallest intervals available
throughout the scale.
Not much is really known beyond this, but there is no shortage
of theories. At this stage, every composer must experiment
and find out for his/her self. If you want some ideas, have
a look at the Scala scale archive or say something here about
the kind of music you like (or the kind you want to write)
and people can give you suggestions.

-Carl

Walter Lepore 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?

I can only describe my own perspective, but there are various features of scales that you can look for: symmetry, variety of interval sizes, melodic and harmonic resources. One particular kind of scale that interests me is a scale with two sizes of steps, evenly distributed in the octave, and subsets of those kinds of scales. The size of the steps and the ratio of large to small step sizes is another thing to look for. If tonal harmony is important, the number of good approximations to small integer ratios of frequency, and where they fall in the scale, can also be an issue.

> 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.

The boundaries start to blur when you deal with "alternative" tunings. Take a perfect fourth divided into two equal intervals of 249 cents each: are those seconds or thirds? But in general if you're looking for a particular kind of harmony, check the symmetry of the scale. Scales that are good for quartal harmony will have patterns that repeat at the interval of a fourth, for instance. With tertian harmony you have to consider the various kinds of thirds in your scale -- besides major and minor, you can have intermediate sized neutral thirds, small "subminor" thirds or larger "supermajor" thirds.

> 2) Designing specific tunings or scales for Composition A couple of times I've had the experience of having a particular melody and chord progression in mind, but I had to set it aside until later when I was playing with a new tuning and realized that it would work with this old melody. If I were a little more systematic about such things, I might analyze the harmony and figure out which tunings would be appropriate. Some harmonic progressions benefit from certain small intervals (like 81/80 or 36/35) being "tempered out" or at least reduced in size; in other cases you might want to exaggerate these small intervals.

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

I suppose scales for improvisation would have a different set of criteria, if that's the sort of thing you're thinking of. (If you're not planning on making music with it, it's just a list of numbers...)

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

That's about as easy to answer as why a painter picks a particular shade of blue. Each scale has its own aesthetic quality; JI scales with exact integer ratios have a special kind of purity, while Indonesian gamelan scales have a more energetic quality. Scales with small intervals could be useful for portraying small things that move slowly. :-) Well, the reasons don't always have to make sense....

> 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.

Hi Walter,

Though many of my friends and relatives might say I am possessed by
demons, I think it's more something like The Muses playing in my
brain. (ok..so I'm divulging my panentheistic bent here) I would
like to say that all of my ideas are my own, but I can't deny that
there is some compelling force that keeps me interested in finding
new scales and exploring them compositionally. It all started many,
many years ago when I began to question the origins of the way the
keys on the piano were arranged the way they are. I have often
referred to myself as being self-taught because I have had very
little training, but I do feel that I have been guided by something
other than my own curiosity. Maybe there is just some major force
within the collective unconcious that wants to stay alive and finds
outlets where it can. It's not as scary as it might sound, except
for the blinding migraines, nausea, and propensity for walking in
front of busses when obsessed by a thought.

Music and math, as well as all of our art-sciences, want to be
sustained and we like to help keep the flame alive because we have a
mutually reinforcing realtionship with them. Some of us are more on
the edge and some of us want to preserve what has come before. It's
all in the same spirit, I think.

As for different types of scales.. I like to explore a new/old
scale musically and let it take me where it goes. I will then often
get an idea to start a song with what's unfolding. I normally don't
know where it's going to wind up. I will also sometimes get a
sketch of a melody going through my head when I read lyrics or
poetry.

Your questions are very good. I am looking forward to seeing the
variety of responses to your post.

Regards,

Robin

--- 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?
>
> 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.
>
> 2) Designing specific tunings or scales for Composition
>
> 3) Scale builders who create/build scales without composition in
mind.
>
> 4) Why would a composer choose a specific tuning or scale over
> another.
>
> 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
>

The fable of the old man, the boy, and the donkey, by Aesop.

--- 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