<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Dear Dimitar, dear Colleagues<div><div><br class="Apple-interchange-newline"><blockquote type="cite"><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; ">I was also puzzled that Kostka and Payne consider IV a substitute for II. This is strange, given the fact that in classical and romantic music the typical subdominant bass is the 4th scale degree. II6 is a substitute for IV, not the other way around. In jazz, however, the II gets the upper hand, as II-V-I is the skeleton. Perhaps this is what confused the authors.</span></blockquote><br></div><div><div>your question goes at the heart of a joint investigation by Karst De Jong and myself. We approach this issue from a different angle, which considers the fundament progression as a quasi-modal phenomenon. I say "quasi" because these functional modes have only thee essential notes rather than seven. They form modes of the so called "tetractys scale" or structural scale (Carey/Clampitt).</div><div>The roots of IV V I and II V I exemplify the first and second mode, respectively. We label them S D T in either case. So far the basic idea.</div><div>But despite of the characterization of IV and II as the genuine subdominant scale degrees in the first and second functional modes, respectively, we also offer a concept of "functional chromaticism". The alteration interval in the world of functional modes, i.e. quasi the "augmented prime" in the internal language of the tetractys, is nothing but the usual minor third (in diatonic language).</div><div>In other words, within a first functional mode with the root of IV as the genuine subdominant scale degree there can still occur a fundament of II (or of V/V) which is then characterized as an "altered" IV rather than a genuine subdominant of a second functional mode. The analogous chromatic note in the second mode is the minor third below the tonic. That's typical for the turn around I VI II V I, where we regard the root of VI (or of V/II) as a functional alteration of the tonic degree. </div><div>For details see: </div><div>De Jong, Karst and Thomas Noll (2011): <a href="http://user.cs.tu-berlin.de/%7Enoll/FundamentalPassacaglia.pdf">"Fundamental Passacaglia: Harmonic Functions and the Modes of the Musical Tetractys"</a>, Agon, Carlos et. al. Mathematics and Computation in Music 2011, Berlin, Heidelberg: Springer: pp. 98 -114.</div><div><a href="http://user.cs.tu-berlin.de/~noll/FundamentalPassacaglia.pdf">http://user.cs.tu-berlin.de/~noll/FundamentalPassacaglia.pdf</a></div><div>Sincerely</div><div>Thomas Noll</div></div><br><div>
<div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; font-size: 12px; "><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><br class="Apple-interchange-newline"><br class="Apple-interchange-newline">
</div>
<br></div></body></html>