source file: mills2.txt Date: Fri, 6 Dec 1996 13:06:31 -0800 Subject: Crying "wolf": a response to Wolf From: kollos@cavehill.dnet.co.uk (Jonathan Walker) I suppose that given his surname, Daniel understandably felt an urge to contribute to an exchange on wolves; but I'll assume here that what he wrote wasn't just a pretext. Daniel Wolf wrote: > > Jonathan Walker has got his history right, but terminology often has a > life of its own, and now, following my Webster's Collegiate, the > _wolf_ for tuning is **a dissonance in some chords on organs, pianos, > or other instruments with fixed tones tuned by unequal temperament**, > or **an instance of such dissonance** (there is also a definition for > the faulty tones in certain stringed instruments, and the usual stuff > about _canus lupus_). I think we should accept the broader definition > of _wolf_that describes an effect or category of effects, rather than > specific intervals, and when we intend a specific interval it would be > best just to give the ratio itself. I don't want to take the matter any further than this reply to Daniel, before tedium sets in, but here, for what it's worth, is why I don't accept his appeal to what might seem, on the face of it, common sense. Regular dictionaries are not normally adequate for technical terms that require some theoretical background knowledge, and discussion in any field beyond the most rudimentary level would be rendered impossible if some participant were to insist that common dictionary definitions were the proper basis for the use of technical terms. Even specialist dictionaries such as Grove can't always be relied upon: anyone wanting basic information about just intonation from Mark Lindley's entry will gain a strange and most inadequate conception (the article is almost entirely about JI keyboards -- try it, if you haven't already). The second musical definition of wolf, concerning the acoustic properties of violin etc. bodies, is also well established and quite distinct -- it ought not to be taken as a sign of how hopelessly vague "wolf" under another definition has become, any more than it should be thought to render wolf qua *canis lupus* ambiguous. The account Webster's gives for the first definition is not only too vague by my reckoning, but is even misleading; here it is again: > "a dissonance in some chords on organs, pianos, > or other instruments with fixed tones tuned by unequal temperament" This fails badly: 1. Wolves are also formed in non-tempered tunings, both Pythagorean and just (I suspect the dictionary compiler thought all tunings are temperaments). 2. Worst of all, wolves are _not_ a feature of the entire range of well-tempered systems, which are all unequal -- in fact, as I said in the previous message, well-tempered systems were devised _for the very purpose of removing the wolf_. My point, in the previous message, was that the use of "wolf" for a 40/27 collapsed the two problems of a JI 5-limit keyboard into one. The diminished-sixth problem is shared with keyboards that use a Pythagorean, meantone or meantone related, or other non-well-tempered irregular system. The problem of the 40/27 (and other intervals that are a syntonic comma flat or sharp for the same reason) is unique to 5-limit keyboards. As a keyboard tuning for late 15th and 16th century music (as Zarlino intended it), it is of no use; the discovery of the reasons for this is perhaps the best route towards an appreciation of the virtues of meantone for keyboard instruments. In technical discussions, informed participants can only regulate themselves, collectively; general purpose dictionaries cannot be expected to serve as final arbiters. If we allow our terminology to become ambiguous, or hopelessly vague, we have only ourselves to blame. "Wolf" as in "wolf fifth" or "wolf fourth" is a useful term because it covers the same phenomenon over a range of different keyboard tunings/temperaments, and this means, as I said in the previous message that it covers quite different intervals, e.g. the 3-limit wolf fifth a Pythagorean comma flat of 3/2, and a 5-limit wolf of 192/125 41 cents flat, with meantone-related temperaments falling between these extremes. We even have the prospect of a wolf fifth which is closer to 3/2 than the regular fifths of one temperament, namely, the 1/10-comma temperament of the meantone family. The key to the concept, strictly defined, is to avoid thinking in terms of enharmonic equivalence, and to think of each note of the upper rank ("black" notes) as fulfilling one of two functions, but never both; the correct spelling of the interval, as G# to Eb etc., will always distinguish the wolf interval from the normal interval in a given tuning, whatever size the wolf interval happens to be. In the case of the 40/27 problem on a 5-limit keyboard, the spelling is correctly D to A: this is not a problem of letter names and sharp/flat chromas, but of plus/minus syntonic comma inflections. Fragmenting this phenomenon by stating precisely (by ratio) which intervals are concerned -- as Daniel suggests -- falls short of a complete solution: there are theoretical and historical contexts (in 15th to 18th century music) where a given piece could and would have been rendered according to different tunings, and "wolf" is needed in such contexts. Quite apart from being inappropriately precise in these contexts, how many people could tell, at a glance, what 192/125, 262144/177147 and 128/5^(11/4) all have in common? (Answer: The wolf fifths of the just, Pythagorean and 1/4-comma meantone systems respectively, which lie 41 cents sharp, 23.5 cents flat and 35 cents sharp of 3/2, but are each the diminished sixth within their respective systems.) -- 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; Sat, 7 Dec 1996 22:25 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA05249; Sat, 7 Dec 1996 22:27:17 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA09565 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id NAA22719; Sat, 7 Dec 1996 13:27:14 -0800 Date: Sat, 7 Dec 1996 13:27:14 -0800 Message-Id: <199612071625_MC1-CBE-2519@compuserve.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu