source file: mills2.txt Date: Fri, 22 Nov 1996 23:52:22 -0800 Subject: Kopie von: Diatonic From: Daniel Wolf <106232.3266@compuserve.com> ---------- Weitergeleitete Nachricht ---------- Von: Daniel Wolf, 106232,3266 An: INTERNET:tuning@eartha.m, INTERNET:tuning@eartha.mills.edu Datum: 22.11.96 10:59 Betreff:Kopie von: Diatonic It is perhaps more useful to think of diatonic or pentatonic _environments_ instead of scales or modes. I think that this was an extreme problem for medieval music theory, applying Greek ideas - especially octave species - to a repertoire (chant) with a basis in Jewish cantillation. The practical instructions found in the treatises, particularly for singing with the aid of hexachords, are more useful. As Paul Hahn points out, the hexachord is the maximum Pythagorean structure without an augmented 4th/diminished 5th, and as such, can be used to control the placement of this interval while guiding decisions about ficta. Both chant and early polyphony are - for us - uncomfortably inconsistant when interpreted in terms of tonicity, so that the identification of a single octave species for a given piece is difficult, and probably tells us little about the structure of the piece. As scalar theorists, we too often forget that most music is vocal and unaccompanied, so that a fixed scale is an unnecessary precondition to composition or performance. That a melody composed from phrases lying with the compass of a pythagorean hexachord, and whose hexachords interlock at fourth and fifth intervals, will tend to produce a gamut with 7 tones is logical, but the appearance of particular 7-tone scales must be kept in the category of consequence and not cause. Moreover, the frequency of melodies in the repertoire with fewer than seven tones - and the existence of repertoire with more eight or more tones is a reminder that seven has no particular monopoly. What is, however, clear is that 5 or 7 or 12 (...) tones exhibit the _closing interval_ (in 7, the tritone, in 12 , the wolf) feature of MOS scales. What may be interesting is to devise hexachord-like solfegio systems for higher-number MOS*s, in which the closing interval is avoided through transposition of the solfege unit. I am curious to learn from Heinz Bohlen how his infill of the Major triad differs from that of Heinrich Schenker. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 23 Nov 1996 08:51 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA05015; Sat, 23 Nov 1996 08:53:07 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA04984 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id XAA10100; Fri, 22 Nov 1996 23:53:05 -0800 Date: Fri, 22 Nov 1996 23:53:05 -0800 Message-Id: <199611230250_MC1-C40-B944@compuserve.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu