source file: mills2.txt Date: Fri, 16 May 1997 22:04:55 +0200 Subject: Re: Tuning ET vs. JI From: "Jo A. Hainline" On Thu, 15 May 1997 DFinnamore@aol.com wrote: > > >JI comes from the harmonic series, which is a > >quantization of linear frequency space. > > Lost ya there. Doesn't "quantization" denote equal divisions? E.g., in what > sense are the two spaces in 1:1, 9:8, 5:4 equal, or based on equal divisions > of linear frequeny space, whatever that means? Strange as it might seem, > after years of picturing frequency space logarithmically, I can't get myself > to visualize it linearally - it doesn't seem to make any sense that way. > > David, My limited understanding of the harmonic overtone series includes the idea that the pitches of the series develop from a "perfectly" vibrating body; a string or column of air, etc. The fundamental is the frequency of the full length of the body, the 2nd harmonic vibrates with 1 node and is twice the frequency, 2/1; the 3rd partial has 2 nodes and is 3 times the frequency, often expressed as 3/2, sounding 5th above the 2nd harmonic, etc. This "perfect" body vibrates in equal divisions, these divisions vibrating in frequencies which define the harmonic series. The intervals between the pitches gets gradually smaller and I suppose ultimately any and all intervals can be defined. Mathematically the relationship of the frequencies is logarithmic, but the pitches are very linear in their creation. It is interesting to me that 12tet has in many ways limited our understanding of musical expression. I play with several orchestras here in Reno with some very talented musicians and every time I play the 7th partial on my horn in warming up someone will look up wondering why I am playing out of tune! Bruce Kanzelmeyer Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 17 May 1997 03:01 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA04394; Sat, 17 May 1997 03:01:52 +0200 Date: Sat, 17 May 1997 03:01:52 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA04395 Received: (qmail 6226 invoked from network); 17 May 1997 01:01:48 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 17 May 1997 01:01:48 -0000 Message-Id: <970516205942_54573426@emout11.mail.aol.com> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu