source file: mills2.txt Date: Tue, 10 Jun 1997 09:11:17 +0200 Subject: where do the 5ths go? From: Daniel Wolf The answer to Neal's question might depend on your view of the fundamentals of mathematics. A strict finitist might very well not accept arbitrary transposition downward, while most will be satisfied that transposing thefundmental downward until octave multiples of all the desired tones fall within a given range is unobjectionable, even if the fundmental becomes so low as to be a completely theoretical entity. It is interesting to look at examples of systems where the octave is not the basic building block but rather the fifth or another interval. Classical harmonics used conjunct tetrachords and pentachords as well as the octave-filling disjunct tetrachords. Xenakis suggested reviving this technique. One way of hearing the three javanese slendro pathet is as conjunct pentatonic tetrachords (each with four tones encompassing an approximate acoustical fifth). A lot of melodies from very different repertoires might be usefully analysed in these terms, where formal unitsare defined by the range of a fifth. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 10 Jun 1997 20:07 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA21628; Tue, 10 Jun 1997 20:06:57 +0200 Date: Tue, 10 Jun 1997 20:06:57 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA21627 Received: (qmail 3254 invoked from network); 10 Jun 1997 17:34:54 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 10 Jun 1997 17:34:54 -0000 Message-Id: <01IJWP0IU9PE91WMQR@ONLINE.EMICH.EDU> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu