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
Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 10 Jun 1997 09:11 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA16443; Tue, 10 Jun 1997 09:11:17 +0200 Date: Tue, 10 Jun 1997 09:11:17 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA16316 Received: (qmail 25770 invoked from network); 10 Jun 1997 07:11:09 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 10 Jun 1997 07:11:09 -0000 Message-Id: <199706100308_MC2-182E-2351@compuserve.com> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu
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 with SMTP-OpenVMS via TCP/IP; Wed, 11 Jun 1997 06:54 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA05302; Wed, 11 Jun 1997 06:54:46 +0200 Date: Wed, 11 Jun 1997 06:54:46 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA05296 Received: (qmail 21418 invoked from network); 11 Jun 1997 04:54:36 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 11 Jun 1997 04:54:36 -0000 Message-Id: <339E318C.168@dnvr.uswest.net> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu
>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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