source file: mills3.txt Date: Sat, 16 Aug 1997 19:19:27 +0200 Subject: Re: S. Commas and Quartertones From: kollos@cavehill.dnet.co.uk (Jonathan Walker) Gary Morrison wrote: > Then again, I agree with you [Paul Rapoport] that "quartertone" > should be limited to specific pitch distance of 50 cents. This is not what Paul seemed to be saying: he left the size of the tone open, but required that the quarter tones be genuine fourth roots. As I've said before, I can't agree with either: the interval of a "quartertone" is sometimes correlated with a frequency ratio of 2^(1/24)/1, as in Vischnegradskij, but is more often left unspecified, as with "semitone" and "tone". Like the latter it is a term belonging to the phenomenal domain of pitch relations, rather than the acoustic domain of frequency ratios (which is where the syntonic comma belongs, as you appear to agree). There is no universal one-to-one mapping from the domain of pitch relations to the range of frequency ratios; sometimes such a mapping is specified (e.g. Ben Johnston) or implicit (Vishnegradskij), sometimes the mapping is one-to-two (as in the tunings c.1400 which incorporate both Pythagorean and quasi-just imperfect consonances), but by far most often, the mapping from pitch relations to frequency ratios is simply left open -- no single tuning system is required for the realisation of a given score. Quarter-tone notation is used freely and flexibly by many composers of non-keyboard based instrumental music today, and their notation shares the functional distinctions of semitone notation (i.e. signs for both 1/4-tone sharp and 3/4-tone flat are employed, and likewise 1/4-tone flat and 3/4-tone sharp). Are we to say that all string-quartet composers, from Barto'k to Ferneyhough, who have used quartertone notation were demanding a strict 12TET environment for their quartertones? Any case you construct for mapping quartertones to 50 cents will also map semitones to 100 cents and so on, but the term "semitone" has generally been used without any such specification in mind -- indeed it was used freely by many mediaeval theorists who explicitly discounted the bisection of the tone; for them, semitone, was an umbrella term for limmas and apotomes. Jonathan Walker SMTPOriginator: tuning@eartha.mills.edu From: non12@deltanet.com Subject: Info sought on recordings PostedDate: 16-08-97 21:13:12 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH RouteTimes: 16-08-97 21:13:18-16-08-97 21:13:19,16-08-97 21:11:25-16-08-97 21:11:25 DeliveredDate: 16-08-97 21:11:25 Categories: $Revisions: Received: from ns.ezh.nl by notesrv2.ezh.nl (Lotus SMTP MTA v1.1 (385.6 5-6-1997)) with SMTP id C12564F5.006992F6; Sat, 16 Aug 1997 21:13:09 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA31973; Sat, 16 Aug 1997 21:13:12 +0200 Date: Sat, 16 Aug 1997 21:13:12 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA31971 Received: (qmail 7150 invoked from network); 16 Aug 1997 19:04:50 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 16 Aug 1997 19:04:50 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu