source file: mills2.txt Date: Mon, 5 May 1997 11:29:23 -0700 Subject: Post: RE: Why ET-x? From: PAULE >Excuse me if this question sounds a bit ignorant. I expected to find >discussions mostly of just tuning issues on this list, but there seems to be >as much discussion of various ET scales. This puzzles me. We've been stuck >with a handful of pitch "islands," to use Brian Eno's term, for a few hundred >years now. Finally, technology is giving us keyboards with virtually >continuous pitch possibilities, allowing us to produce music that is more >consistent with natural principles (acoustics, psycho-acoustics, etc.). Why >continue exploring various equal temperaments? What is the value in it? >Please understand, I'm not registering a complaint or leveling a criticism; >I just don't know what the heck's the dang big deal with ETs. Myself, I'm >glad to be rid of the dern varmints. But I'd be fascinated to see a good >apology (justification) in favor of them. >David J. Finnamore Psycho-acoustics has told us that our ears have limited pitch resolution, and that they develop short-term familiarity with a small set of specific pitches and specific melodic intervals. In my opinion, the greater the number of consonant harmonies you can make out of a small set of pitches and melodic intervals, the better. In this regard non-just tunings definitely win out over JI. Examples: 1. A 7-note diatonic scale in JI has three melodic intervals and five consonant triads. In meantone (or 12-, 19-, 31-, 50-tET), it has two melodic intervals and six consonant triads. 2. Another example eluded to already is tritone substitution. It is useful to have a half-octave, since it can represent 7:5 in some contexts and its own inversion, 10:7, in others. Using common tones in a changing context is an effective way to move to distant harmonies, but in JI, distant harmonies will have at most one common tone. JI of course has no half-octave. Another way of saying this is that Just Intonation has no "puns", or notes taken in two different senses, and typical JI theory does not admit punning. However, in creating intervals in JI, you will eventually come across some very complicated ratios that are so close to simple ones that they will function as consonances rather than dissonances. So the typical JI small-integersnsonance / large-integersssonance approach falls flat on its face. In ETs, as long as the ET is _consistent_ within the particular harmonic limit you are trying to represent, _accurate_ enough to represent it, and does not have notes too close to each other (34 is just barely OK in this last respect), the dichotomy between consonance and dissonance is unambiguous and you have all the benefits of extended harmony enjoyed by JI of that harmonic limit (I speak of odd-, not prime-number, limits here). Ultimately I have to agree that a continuous-pitch paradigm is most desirable. However, individual musical ideas within such a paradigm are likely to employ simple sets of fixed pitches, and some non-just tuning, perhaps even an ET, might be the best way to work out harmonizations and developments of a given idea. Combining all the ideas into a single composition, however, may require us to demand completely flexible pitch. Johnny Reinhard's compositions make this case even where simple-limit harmonic considerations are not often dominant. Here's my point of view: We have several hundred years of Western music in 12-tET, by, say, 100 great composers. Have the possibilities been exhausted? Somewhat. Does the existing repertoire have enough diversity to provide a lifetime of listening enjoyment of the most transcendent and sublime sort? Many seem to feel that it does. Therefore, even a single new tuning system should be enough for a composer to do a lifetime of work and, even if the composer is of the first rank, the composer will not exhaust 1% of the tuning's resources. Considering the range of expression contained in 12-tET music, any single microtonal tuning will, by increasing pitch resources, lead to an unimaginable new universe of moods and sensations. The technical difficulty of mastering a single new tuning, even a new ET, in the current educational environment, is plenty to expect of a composer whose main goal is to express himself/herself in a new way. David, Let's discuss more if you like this topic as much as I. -Paul E. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 6 May 1997 01:44 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA05404; Tue, 6 May 1997 01:44:26 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA05367 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id QAA09991; Mon, 5 May 1997 16:42:31 -0700 Date: Mon, 5 May 1997 16:42:31 -0700 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu