where do the 5ths go?

Here's something I've been thinking about lately...it's known that
the spiral of 5ths has been explored pretty well over the last few
thousand years, and by mathematically "bringing down" cycles of 5ths, we
obtain patterns of notes for an octave...no problem. But, there's
something wrong with that. Those 5ths that we mathematically alter...we
are not HEARING them in their proper place in the Universe. They are
actually sounding at some frequency well beyond our hearing. So, just
where are they, then? They must be doing something, somewhere...they do
exist, and are a part of the original fundamental sound that created
them. Scales built from these spirals are artificial, in a sense.
Understanding this endless spiral of harmonics is one thing on paper,
another in the world of Sound. If a "frequency" is out of the hearing of
human ears, is it perhaps affecting other parts of the being instead? Can
sound (and we know it can) have physiological effects that are
involuntary? How about spiritual effects? What if we heard a scale in the
actual pitch range of all the notes, instead of them being altered, moved
around, sort of? Are there beings somewhere who can hear a wider range
than we do? We know dogs, and I'm sure other animals as well, hear sounds
we do not...we also know stars, planets, etc, are all sending out
zillions of frequencies, well beyond our seeing or hearing. How, I
sometimes wonder, can we draw all of these different concepts together
and absorb them into a kind of music that could heal planets?

On a related note, Ben Johnson's comments about our society and harmful
music are well taken...of course, it's a big subject, and can make one
think of related topics. There are numerous societies with "out of tune"
musical systems, such as gamelan music...what's going on there, because
they seem rather peaceful as cultures, in general. Obviously, the INTENT
of the music is crucial...if you had just intonation music that promoted
satanism, I don't suppose that would do anyone any good, either. And,
what about the feeling that the performer/composer attempts to
communicate with this music in unnatural tunings? Does that help
balance the out of tuneness of the system? But, we are a screwed up
bunch, in a lot of ways, and I don't think the pop/rock scene is helping
much at all. And, the inharmonious vibrations of all that loud, out of
tune music: I can see how that phenomenon could be harmful to people. I
sure don't let my kid watch much TV, for the same reason. There is much
low level nonsense in our world today. As far as music and drugs, yes,
there's always been a lot of pot/alcohol/cocaine/heroin use in
music...but, I just read a couple of articles about Prozac and Ridilyn,
and an awful lot of non musicians are using these as well, including our
poor little kids, who are being drugged at school to help calm them down
and make them pay attention and be better students...scary stuff, a
nightmare to me. Our whole culture is drug ridden, not to mention all the
antibiotics we get in our system from cows milk. I truly believe that
music is one of the most powerful forces in the world...sounds like
Johnson does, too. That's why the math is fun and all, but the sound is
the real deal...and it sure does affect all beings that it
touches...Hstick

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The composer can expect the performer to perform intonation based on
the memory of different systems -- within reason. 2, maybe 3 different
systems is certainly doable. Individual distinctions from pitch to pitch
would seem unnecessary drudgery in the case of only 2 systems.

Rather than thinking of modulating between tunings, I prefer thinking in
terms of immigrating between tunings. Now there are imharmonic tones and
imharmonic chords in the theory.

My original music is self-described as polymicrotonal, specifically
because of the healthy use of different tunings in single compositions.
The recent premiere of my cello concerto Odysseus featured 60 musicians in
almost as many tunings, in all kinds of combinations. The sound was
new with unusual timbres in a new form of musical theater.

As those who were there have signalled, just about everyone enjoyed it,
were happy, uplifted, even amazed. It worked. Sure, I get some of the
credit. But it is because the sound space is so excitingly receptive to
still newer and fresher combinations of sounds in relationship that there
exists a new frontier in space.

It's said that in the sub-atomic world there exists _only_ intervals.
Everthing is built upon.

Johnny Reinhard
Director
American Festival of Microtonal Music - MicroMay '97 (May 16, 21-23)
318 East 70th Street, Suite 5FW
New York, New York 10021 USA
(212)517-3550/fax (212) 517-5495
reinhard@idt.net
http://www.echonyc.com/~jhhl/AFMM/

On Tue, 10 Jun 1997 UPB_MONIODIS@ONLINE.EMICH.EDU wrote:

> If one were composing a work in Just intonation and one wanted to
> modulate to Pythagorean intonation, would one reflect the comma
> change in a medial signature, or would one simply indicate
> "Pythagorean" above the staff, and let the staff lines assume
> the new diastemic values?
>
> --Polychronios
>

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One possibility: consider pythagorean to be a subset of just, and the
normal staff notation to be pythagorean extending by fifths/fourths
indefinitely in both directions with sharps and flats as usual but without
the 12tet equivalence classes. For each prime number higher than three
introduce two modifying symbol for raising or lowering a tone by an
interval (comma) where the new prime(2^n) is super- or subparticular to
3^n(2^n). E.g. a plus or minus sign to indicate raising or lowering by
81/80, rightsideup and upsidedown sevens for the septimal comma etc.. Allof the symbols can be combined freely. The advantage of this method is that
all intervals are notated invariably. Players can learn the music by
learning the intervals directly and the ''null position'' for pythagoreanintonation is relatively easy for string players.

One alternative is - a la Ben Johnston - to assume that a just diatonic
scale is the null position for the staff notation. In my opinion, the chief
disadvantage to this is that intervals are not invariably notated, but
vary in notation relative to the a given tonality.

Another notation is to use the 12tet pitches and to indicate cent
deviations in numbers. I find this a fine auxillary notation, but since Iconsider the rational relationships to be an essential part of a work's syntactic content, chose to limit this usage to an auxiallary role. (I
admit to one great exception: my second String Quartet uses cent-deviation
notation; the sixteen strings are tuned to octave multiples of the first
sixteen primes, and - aside from natural harmonics - are unstopped, a
pythagorean basis for the notation seemed to be beside the point. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
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>If one were composing a work in Just intonation and one wanted to
>modulate to Pythagorean intonation,

On a side note, Ivor Darreg proposed the word "transfer" for a change of
tuning system in the course of a composition.

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>>If one were composing a work in Just intonation and one wanted to
>>modulate to Pythagorean intonation,
> On a side note, Ivor Darreg proposed the word "transfer" for a change of
> tuning system in the course of a composition.

I should clarify that Ivor suggested that since "modulate" is already
reserved for a chance of tonal center.

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