I started reading it, and "couldn't put it down" (the laptop PC, that is). It got to be 2:00 am, so I added a link to it from one of my pages (http://www.pacificnet.net/~nowitzky/justint), so I wouldn't lose it among my thirteen gazillion bookmarks.
I did get as far as the name of your computer program, "Helm". I take it that stood for "Helmholtz" (My hero!).
Easley Blackwood's book, "The Structure of Recognizable Diatonic Tunings", is on my list of things to read too, but it ain't machine-readable, so it'll have to wait.
About your 30 Sep 1997 post to the TUNING list - As far as the idea that a lot of music relies on the "blurring provided by temperament" (courtesy James Kukula's phraseology), I'm still not convinced.
Here's my line of thought: What if you "blurred" the distinctions between pitches even more? Suppose, as an example, a melody, first played in major, then in minor. (It happens a lot in those "variations on a theme".) You could blur this melody into a "7tET" (7 equal intervals per octave), which would wipe away the distinction between major and minor. But you'd definitely lose something in the translation. In simplistic terms, you would no longer have that "happy the first time, sad the second" feel to it.
That's all for now (since it's now past 3:00 am). I look forward to reading the rest of your thesis.
--Mark Albin Nowitzky (MIT BS EECS '79) +------------------------------------------------------+ | Mark Nowitzky | | email: nowitzky@pacificnet.net | | www: http://www.pacificnet.net/~nowitzky | | "If you haven't visited Mark Nowitzky's home | | page recently, you haven't missed much..." | +------------------------------------------------------+
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>I was wondering why no one doing dynamic intonation seems to make use >of research in the area of automatic key recognition of music. There >is work done by Jamshed J. Barucha who uses a connectionist model
Interesting. I came up with "decent" key recognition algorithm nearly a year ago based upon ... well, oversimplifying it a bit ... tallying up a histogram of note frequency on a circle of fifths.
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> Interesting. I came up with "decent" key recognition algorithm nearly a > year ago based upon ... well, oversimplifying it a bit ... tallying up a > histogram of note frequency on a circle of fifths.
The advantage of a connectionist network model is that you only need a few input tones to get a reasonable response. The different activation levels of the key units is what indicates the key. So if C has the highest activation then F and G come next to that as in the circle of fifths. The network consists of layers with nodes for tones, major chords, minor chords and keys. The links have a weight and are symmetrical. An interesting conclusion of the article by Barucha is that even though the weight of the links between source chord C major and its parent keys F, C and G are equal, the parent keys are not activated to the same degree. It is in decreasing order: C, F, G which are the keys in which the chord is on the tonic, dominant and subdominant. This in accordance with the hierarchy of harmonic functions in music theory.
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 C125652C.0076E537; Fri, 10 Oct 1997 23:38:39 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA13555; Fri, 10 Oct 1997 23:39:15 +0200 Date: Fri, 10 Oct 1997 23:39:15 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA13551 Received: (qmail 28181 invoked from network); 10 Oct 1997 14:39:07 -0700 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 10 Oct 1997 14:39:07 -0700 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu