source file: mills3.txt Date: Sat, 13 Dec 1997 22:51:46 +0100 Subject: Tuning Artefacts From: Gregg Gibson In matters of temperament one must carefully distinguish between equal divisions of the octave that are temperaments, and those which are merely tuning artefacts. A temperament constitutes a system wherein every note can be obtained by a cycle of any one of the consonant intervals; in such systems every pitch can be introduced into music by a consonant disjunct interval, if desired, and not only by singing a conjunct dissonance, the exact pitch of which is difficult either to sing or to integrate into instrumental music. The prinicipal temperaments are 12- 19- 31- 43- 50- & 55-tone equal. A tuning artefact on the other hand has good representations of the consonances, but as in just intonation, these consonances are not reduced to a system wherein all consonances stand in a fixed proportion or equipartient ratio to one another, as for example in 19-tone equal the major third is always 6/11 as wide as the perfect fifth. In tuning artefacts on the contrary we find that these ratios are variable, which results in diminished or augmented fifths at divers places in the tonal fabric, or else similarly impure thirds. Moreover in such tuning artefacts, at least 1/2 of the tones form no part of the cycle of fifths - I mean those fifths that have consonant thirds - but lie forever outside it. Just intonation itself is far more tolerable than these inconsistent systems; examples are the 22-, 29- 41- & 53-tone equal systems. Very strangely, the last of these was lauded by Bosanquet (among others) as the ne plus ultra of intonational perfection! And so it is - in the same way that just intonation is mathematically perfect but perfectly unusable in practical music (of this or any other century), becuse of its undistributed, commatic errors. SMTPOriginator: tuning@eartha.mills.edu From: Gregg Gibson Subject: Just Intonation PostedDate: 14-12-97 01:47:51 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $MessageStorage: 0 $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: 14-12-97 01:45:52-14-12-97 01:45:52,14-12-97 01:45:34-14-12-97 01:45:35 DeliveredDate: 14-12-97 01:45:35 Categories: $Revisions: Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2 9-3-1997)) with SMTP id C125656D.000430E6; Sun, 14 Dec 1997 01:47:42 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA14763; Sun, 14 Dec 1997 01:47:51 +0100 Date: Sun, 14 Dec 1997 01:47:51 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA14762 Received: (qmail 27836 invoked from network); 13 Dec 1997 16:47:47 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 13 Dec 1997 16:47:47 -0800 Message-Id: <34938EA4.45F8@ww-interlink.net> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu