source file: mills2.txt Date: Sat, 26 Oct 1996 20:09:37 -0700 Subject: Johnston's notation defended From: kollos@cavehill.dnet.co.uk (Jonathan Walker) Apologies for the length of the following message, but I thought I should say a few things in defence of Ben Johnston's notation. Daniel Wolf said (Sat, 26 Oct) > 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. Ben prefers a 5-limit syntonon diatonic default for two reasons, I think: he chose to explore the 5-limit thoroughly before moving on gradually to higher primes, so he devised his notation initially within a 5-limit environment, while perfectly aware that it was extendable. Since these 1960s "hyper-chromatic" works form the most "atonal" (faute de mieux) portion of his oeuvre, the syntonon diatonic itself is not of importance on the aural surface of the music, but it provided the 5-limit default he wanted. In later works, especially from the neo-classical phase of the last ten years, the syntonon diatonic is all the more clearly worth preserving as a default. I would imagine also that Ben believes, like Zarlino, that the syntonon diatonic is the ideal representation of the major scale/Ionian mode, towards which singers at least will aim if unhampered by intonational distractions from accompanying instruments (I would endorse this). Ben absolutizes his notation in two ways: A = 440 is observed, even though A+ = 440 would often remove the need for a great many plus and minus signs from his scores; secondly, if I understand correctly, C is fixed as an arbitrary 1/1 for notational purposes, regardless of the tonal centre of a passage (if any). Adam Silverman (or any other friends of Ben) is welcome to correct me if any of the above details sound dubious or plain incorrect. For my own theoretical purposes I remove these two anchors, and relativise the system completely; since I'm dealing with modal or tonal music, 1/1 is be identified with whichever letter-name is the modal final or tonal centre. I would use a syntonon diatonic default for pieces dating from the late Ars Nova or afterwards; earlier Ars Nova pieces have to be considered on their merits with regard to their suitability for just or Pythagorean intonation; Ars Antiqua I give a 3-limit default. In 5-limit Renaissance a capella music, a further licence is the gradual sinking of the 1/1 pitch (which need not happen quite so frequently as is usually maintained for JI performances). The notation can also be extended for the description of tempered systems which are derived from the 5-limit, such as the meantone family of tunings; other temperaments, such as certain 18th-century irregular temperaments (and of course 12-TET) are better suited to a 3-limit default. The choice depends on whether roots of the syntonic or the Pythagorean comma are employed in the construction of the temperament; some tunings, such as Kirnberger II, are ambiguous in this respect, and can be described in two ways. Furthermore, aurally near-identical tunings will receive different descriptions if their derivations are different: for instance 1/10-comma meantone and 12-TET are extremely close approximations of each other, but the former is properly describable in terms of (81/80)^(x/10) deviations from the syntonon diatonic, while the latter is most certainly not. Daniel Wolf again: > 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. Funny you should mention this, because one of the virtues of a 5-limit notational default is that pitch height _will_ correspond to notational height for much, much longer than a 3-limit default. This is a fairly big gain to offset your objection to the contextualisation of interval sizes in 5-limit default notation. Still, I'm not determined, as I said above, to defend a 5-limit default where it conflicts with the style of the music, or with the derivation of a tuning system. Which brings us on to your next point: > 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. Adam Silverman will no doubt defend himself capably here, but I could make a couple of comments. Ben's notation, like his music, quite deliberately works within, and extends the very tradition that Partch largely spurned. The staff notation used in that tradition was designed from the beginning for vocal performers who, of necessity, had to be able to conceptualise the sound in advance, in order to perform; instrumental performers were happy with tablatures for centuries until these systems faded away for various reasons in the 18th century. Since Partch concentrated heavily on fixed-pitch instruments, he was at liberty to use tablatures, or otherwise depart from the notational norm that he grew up with. The important use of voices and strings in Ben's works, together with his desire to work within that tradition renders his notation the best suited to his purposes. Does it suit Partch though? This is one corner of the "authentic Partch" debate, which I'd prefer not to enter (although I'll remind readers that if we had always followed artists wishes, the Canterbury Tales and much of Kafka's work would have been destroyed, to take two examples from a great many -- and is recording really consistent with corporeality?). Nevertheless, for those used to Ben's notation, the transcription of Partch's scores offers considerable analytical leverage; it's not in every case a plot to have performances on non-Partchian instruments. I can't see that a 5-limit default creates any great obstacle to our understanding of Partch, any more than a 3-limit default would -- if you're most familiar with the former, and you haven't a pair of 5-limit tinted spectacles glued to your face, what's the problem? Daniel, since I'm not entirely sure I understand "Johnston's notation ... goes against both the whole limit (factoring) idea of Partch, and Partch's decided invertibility", could you please expand on this, so that I can be certain of your objections? (And by the way, your apostrophes appear as asterisks -- have a look at your e-mail editing arrangement.) Johnny Reinhard said (Fri, 25 Oct): > My experience with Ben Johnston gives high marks for exactitude, but > loses too much due to the slowness with which it is read. Often > conflicting directions are used for a single note and so a mathematical > calculation is necessary. This process takes one out of real time. I doubt if Ben would ever have claimed that his notation allowed fluent prima vista performance, but what are these "conflicting directions"? Whatever some might say of Ben's notation, I can't see that inconsistency is a possible objection. Are you claiming there is an intrinsic flaw in the notational system, or just talking about an occasional slip of the pen? Perhaps an example would help. -- Jonathan Walker Queen's University Belfast mailto:kollos@cavehill.dnet.co.uk http://www.music.qub.ac.uk/~walker/ Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 28 Oct 1996 19:19 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA19446; Mon, 28 Oct 1996 19:19:24 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA19820 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id KAA22790; Mon, 28 Oct 1996 10:19:21 -0800 Date: Mon, 28 Oct 1996 10:19:21 -0800 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu