source file: mills2.txt Date: Sat, 26 Oct 1996 00:32:32 -0700 Subject: Notation From: Daniel Wolf <106232.3266@compuserve.com> Adam Silverman mentioned the notation I prefer. I learned all of this from Erv Wilson. A good deal of my music tends to modulate over a wide harmonic lattice of several dimension. So for the players* sake, I like to have as little ambiguity as possible and would like all identical written intervals to have identical size. Johnston*s notation does not do this, as it is based upon a scale with a mixture of three and five intervals, and depends upon identification of a tonic. Thus, within the key of C, for example, Johnston*s fifths C/G and D/A are not both 3/2 intervals. Moreover, Johnston*s notation obviates the fact that the conventional staff notation is a perfectly natural vehicle for Pythagorean intervals. (And players of bowed stringed instruments do play fifths fairly well, but need to consciously correct to get thirds and other intervals in tune; outside of Anglo-Irish folksong - and there only inconsistantly - I have not encountered the syntonic diatonic as a _natural tendency_). So, I use the conventional notation (with potentially unlimited sharps or flats along the series of fifths) to describe a basic pythagorean series, modifications by the comma 81/80 and 80/81 are indicated by 45 degree slanted upward plus and downward minus sign. The septimal modifications of 64/63 and 63/64 are indicated by an inverted seven and an upright seven, respectively. The intervals of eleven 33/32 and 32/33 are indicated by arrows up or down. Additional symbols have been used for ratios of 13, 17, 19, 23, but I must admit to having been rather inconsistant with them. There are two pieces of self criticism that I may offer with my present answers: (1) Compound ratios do become a bit notation heavy, and are slower to read, but these relationships are more difficult to learn anyway, and this method seems to work. (2) In very microtonal passages, pitch height may not match notational height. I have decided to accept this point in lieu of going to a further step and using a notation with more than seven nominals, such as the twelve-nominal notation proposed by Wilson in Xenharmonikon. I am not particularly attached to my notation but I do find it curious that so many people have made transcriptions of Partch scores in Johnston*s notation which goes against both the whole limit (factoring) idea of Partch, and Partch*s decided invertibility. Moreover, the instances in Partch*s music which are based upon the syntonic diatonic scale are minimal. Daniel Wolf, Frankfurt Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 28 Oct 1996 15:17 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA03671; Sat, 26 Oct 1996 18:46:51 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA05479 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id JAA02749; Sat, 26 Oct 1996 09:46:48 -0700 Date: Sat, 26 Oct 1996 09:46:48 -0700 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu