<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div>Dear Jay(!)</div><div>Re-Reading my quick posting I realized, that in a moment of inattention I didn't insert your name into the salutation. Let me assure that I'm well aware about your valuable contributions to algebraic music theory since several years. Apologies for my inattention!</div><div>Sincerely</div><div>Thomas Noll</div><div><br class="Apple-interchange-newline"><blockquote type="cite"><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Dear John, <div>Many thanks for pointing to this very interesting article. </div><div>In this paper you seem to emphasize to a kind of "Hauptmannian" aspect in Curwen's Tonic SolFa, where the major scale appears as a triad of triads with the tonic triad in privileged the role of having singular overlaps with the other two triads which are mutually disjoint. </div><div><br></div><div>Your counter-factual 19-Tone illustration is very suggestive and thought-provoking. The ideas is, that the (maximally even) C-, F#-, and Gb- Major scales within the 19 tone scale have an analogous intersection behavior as the C-, F- and G- major triads in the (generic) diatonic scale; and that the relative voice-leading behavior between these scales is analogous to that between the triads. It is challenging to understand, what makes particularly these combinatorial properties "tonal". I mentioned Hauptmann, because your construction seems still to exemplify properties upon which one could project the process of a dialectical triad in Hauptmann's manner. </div><div><br></div><div>However, in the 19-Tone scale the extensions of three concepts fall apart, which have the same extension in the major scale: do, fa and so.</div><div>(1) The roots of the three "Curwen scales" are C, F# and Gb. </div><div>(2) The three "major thirds" in the role of the "sensitive intervals" are here C-E#, Gb-B, and G-B# . see section 4.4 in: <a href="http://www.mtosmt.org/issues/mto.11.17.1/mto.11.17.1.clampitt_and_noll.html">http://www.mtosmt.org/issues/mto.11.17.1/mto.11.17.1.clampitt_and_noll.html</a></div><div><div>(3) In the Ionian mode the Tones C, F, and G form a tetractys skeleton of the Ionian mode and the interval between F and G is the diazeuxis (i.e. the interval between the generator and its octave complement). This is still true for a fifth-generated 19-tone mode abaabaababa | abaabaab, (where a is an augmented prime and b a diminished second).</div><div>The species of the "fourth" abaabaab (wich here has 8 microsteps) is a prefix of the species of the "fifth" abaabaababa (wich here has 11 microsteps). And the remaining factor is the "diazeuxus" aba. It is not a step, though, in the 19-tone world. </div></div><div><br></div><div>The three triples of anchor notes are close but yet different (1) C-F#-Gb, (2) C-Gb-G, (3) C-F-G, </div><div>Sincerely</div><div>Thomas Noll</div><div></div><div><br class="Apple-interchange-newline"><blockquote type="cite"><table cellspacing="0" cellpadding="0" border="0"><tbody><tr><td valign="top" style="font: inherit;"><font class="Apple-style-span" face="arial">A study that relates Curwen's tonic sol-fa method to more recent formulations is accessible at:</font><div style="font-family: arial; "><br></div><div style="font-family: arial; "><a href="http://pi.library.yorku.ca/dspace/handle/10315/6610">http://pi.library.yorku.ca/dspace/handle/10315/6610</a></div><div style="font-family: arial; "><br></div><div><font class="Apple-style-span" face="arial">Jay Rahn, York University (Toronto)</font><br><br><font class="Apple-style-span" face="arial">--- On </font><b style="font-family: arial; ">Mon, 7/16/12, Eytan Agmon <i><<a href="mailto:agmonz@012.net.il">agmonz@012.net.il</a>></i></b><font class="Apple-style-span" face="arial"> wrote:</font><br><blockquote style="border-left-width: 2px; border-left-style: solid; border-left-color: rgb(16, 16, 255); margin-left: 5px; padding-left: 5px; "><br><font class="Apple-style-span" face="arial">From: Eytan Agmon
<<a href="mailto:agmonz@012.net.il">agmonz@012.net.il</a>></font><br><font class="Apple-style-span" face="arial">Subject: Re: [Smt-talk] Movable-Do subculture in the Romance tradition?</font><br><font class="Apple-style-span" face="arial">To: <a href="mailto:smt-talk@lists.societymusictheory.org">smt-talk@lists.societymusictheory.org</a></font><br><font class="Apple-style-span" face="arial">Date: Monday, July 16, 2012, 7:39 AM</font><br><br><div id="yiv1322517939"><style><!--
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--></style><div><div class="yiv1322517939WordSection1"><p class="yiv1322517939MsoNormal" style="font-family: arial; "><span style="font-size:11.0pt;font-family:"sans-serif";color:#1F497D;">“Moveable Do” syllables are (melodic) scale degrees, that is, intervals from the tonic (reduced modulo the octave). The “tonic Sol-Fa method” was codified and disseminated by John Curwen in the 19<sup>th</sup> century. However, the idea dates back to the “octave species” of medieval modal theory (and ultimately Greek theory). </span></p><div style="font-family: arial; "><span style="font-size:11.0pt;font-family:"sans-serif";color:#1F497D;"> </span><br class="webkit-block-placeholder"></div><p class="yiv1322517939MsoNormal" style="font-family: arial; "><span style="font-size:11.0pt;font-family:"sans-serif";color:#1F497D;">Eytan Agmon</span></p><p class="yiv1322517939MsoNormal" style="font-family: arial; "><span style="font-size:11.0pt;font-family:"sans-serif";color:#1F497D;">Bar-Ilan University </span></p><div style="font-family: arial; "><span style="font-size:11.0pt;font-family:"sans-serif";color:#1F497D;"> </span><br class="webkit-block-placeholder"></div><div><div style="border-right-style: none; border-bottom-style: none; border-left-style: none; border-width: initial; border-color: initial; border-top-style: solid; border-top-color: rgb(181, 196, 223); border-top-width: 1pt; padding-top: 3pt; padding-right: 0cm; padding-bottom: 0cm; padding-left: 0cm; "><p class="yiv1322517939MsoNormal"><font class="Apple-style-span" face="sans-serif"><b><br></b></font></p></div></div></div></div></div></blockquote></div></td></tr></tbody></table>_______________________________________________<br>Smt-talk mailing list<br><a href="mailto:Smt-talk@lists.societymusictheory.org">Smt-talk@lists.societymusictheory.org</a><br><a href="http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.org">http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.org</a><br></blockquote></div><br><div>
<span class="Apple-style-span" style="border-collapse: separate; font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; 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; "><span class="Apple-style-span" style="border-collapse: separate; font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; 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; "><span class="Apple-style-span" style="border-collapse: separate; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; 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; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; 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; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><div><br class="Apple-interchange-newline"><br><div><div>*********************************************************</div><div>Thomas Noll</div><div><a href="http://user.cs.tu-berlin.de/~noll">http://user.cs.tu-berlin.de/~noll</a></div><div><a href="mailto:noll@cs.tu-berlin.de">noll@cs.tu-berlin.de</a></div><div>Escola Superior de Musica de Catalunya, Barcelona </div><div>Departament de Teoria i Composició </div><div><br class="khtml-block-placeholder"></div><div>*********************************************************</div></div></div></div><div><br></div></div></span><br class="Apple-interchange-newline"></div></span><br class="Apple-interchange-newline"></span><br class="Apple-interchange-newline"></span>
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<span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: 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; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; 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; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; 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; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; 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; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><div><br class="Apple-interchange-newline"><br><div><div>*********************************************************</div><div>Thomas Noll</div><div><a href="http://user.cs.tu-berlin.de/~noll">http://user.cs.tu-berlin.de/~noll</a></div><div><a href="mailto:noll@cs.tu-berlin.de">noll@cs.tu-berlin.de</a></div><div>Escola Superior de Musica de Catalunya, Barcelona </div><div>Departament de Teoria i Composició </div><div><br class="khtml-block-placeholder"></div><div>*********************************************************</div></div></div></div><div><br></div></div></span><br class="Apple-interchange-newline"></div></span><br class="Apple-interchange-newline"></span><br class="Apple-interchange-newline"></span>
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