source file: mills2.txt Date: Tue, 10 Jun 1997 23:40:04 +0200 Subject: Re: Modulating tunings From: Daniel Wolf 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