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Dear Bruce, Murray, and Daniel,
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<div>I believe that we should distinguish between equal temperament, a tuning, and enharmonic equivalence, a relation. On the one hand, tones can be enharmonically equivalent in different temperaments, both equal and unequal. On the other hand, tones can also
be enharmonically non-equivalent in different tunings, both tempered and untempered.</div>
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<div>I was asking Severine Neff recently about enharmonicism and regions, because she analyzes flat 1^, not raised 7^, as a problematic scale degree and region in the first movement of Schoenberg's String Quartet No. 2 in F# minor (Norton Critical Score, p.
127), and she suggested to me that enharmonic regions are in fact distinct for him. I agree with her, and I would suggest that this distinction holds because regions for him are not points in an abstract space but places that actual pieces of music have gone
to along particular paths during "the tonal period" (Structural Functions of Harmony, p. 68). So there is indeed a difference between SMSM (the submediant major's submediant major) and bmM (the flat mediant minor's mediant major), because they represent different
paths. </div>
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<div><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: 'Lucida Grande'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; ">Matthew
Arndt<br>
Assistant Professor<br>
The University of Iowa School of Music<br>
2777 University Capitol Center<br>
Iowa City, IA 52240<br>
319-353-2181<br>
<a href="mailto:matthew-arndt@uiowa.edu">matthew-arndt@uiowa.edu</a><br>
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<div>On Feb 14, 2012, at 12:48 PM, Daniel Wolf wrote:</div>
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<div>Schoenberg clearly thought in terms of and preferred equal temperament (see his letter to Joseph Yasser, here:
<a href="http://www.jstor.org/pss/829999">http://www.jstor.org/pss/829999</a> , as well as the recordings of Schoenberg's works by the Kolisch Quartet; Kolisch famously tuned all four of his open strings to the (tempered) piano when playing the Phantasy Op.
47), but to the best of my knowledge he never explicitly mapped his regions onto a closed tempered tone space (a toroid space, for example, would have worked).<br>
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Daniel Wolf<br>
composer<br>
Frankfurt<br>
<a href="mailto:djwolf@snafu.de">djwolf@snafu.de</a><br>
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