<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Dear Colleagues,<div>I'm very grateful for your comments. I should confess, that the interest behind my inquiry is quite elementary. Together with the computer scientist Jörg Garbers I'm working on a combinatorial device – a kind of music-theoretical instrument –, which helps to easily grasp the concordances between note names, scale degrees and locations in the diatonic scale-step-pattern. The combinatorial scope is intended to embrace tone relations, which are relevant for several musical periods. Our first prototype is <span class="Apple-style-span" style="font-size: 12px; ">austerely diatonic and supports the 84 = 12 . 7 transposed species of the octave.</span> That makes it too rigid for the understanding of genuinely chromatic tone relations. As such our present "SolFa Mode-Go-Round" (working title) would perhaps have been a quite adequate contribution to the <span class="Apple-style-span" style="font-size: 12px; ">exhibits of the Museum Kircherianum in 1651. When Kircher worked on the "Arca Musarithmica" he proposed combination of generic polyphonic voice-leading patterns (musarithms) with</span><span class="Apple-style-span" style="font-size: 12px; "> text-driven</span><span class="Apple-style-span" style="font-size: 12px; "> </span><span class="Apple-style-span" style="font-size: 12px; ">modal specifications. More generally, with regard to the exploitation of transposed church modes, our instrument seems to convey combinatorial possibilities, which played a catalytic role for the development of the major/minor key system. </span></div><div><span class="Apple-style-span" style="font-size: 12px; ">But also the mechanics of the hexachord-mutation and the practical problems of hexachord-solmisation can also be nicely explored. If I understand Stefano Mengozzi correctly, he characterizes the hexachord-Solmiation as a mere meta-musical mnemotechnique, because of its limitations within a genuine diatonic world of tone relations. In other words, an earlier introduction of the 7th syllable "si" would have been useful, especially for the solmisation in the mi- and fa-modes, whose species of the fifth are not contained in the hexachord. [A discussion of the musical meaning of the hexachord is of course a separate subject].</span></div><div><span class="Apple-style-span" style="font-size: 12px; ">The most direct link to solmisation practice in harmonic tonality is provided through the Movable-Do with La-based minor (Thanks to Roberts Gierdingen for pointing at the ramifications within Movable-Do approaches). In our present design we decided to use solmisation syllables in the Guidonian tradition <span class="Apple-style-span" style="font-size: medium; ">to designate the </span><span class="Apple-style-span" style="font-size: medium; ">locations in the diatonic scale-step-pattern. In addition we use spacial and "choreographic" dimensions for the embodiment of the note names and</span> the scale degrees. Indirectly, we hope, our combinatorial instrument may nevertheless communicate a common neutral(!) basis for different solmisation techniques: Note-name solmisation, scale-degree solmisation, step-pattern-solmisation. Neutral as a guide to develop a mnenotechniques on the music-theoretical meta-level. A delicate obstacle to make this communication successful, seems to be the convoluted competition about the power of interpretation of the seven syllables: Do, re, mi, ... which are most attractive for singing, while Latin-inherited note names and scale degree numbers are less so. That is somewhat the practical background for my inquiry.</span><span class="Apple-style-span" style="font-size: 12px; "> </span><span class="Apple-style-span" style="font-size: 12px; "> </span></div><div><br></div><div>***********</div><div>There are fascinating theoretical issues involved, which implicitly motivate this hands-on approach. While it would have been possible around 1650 to build a purely mechanical version of the "SolFa Mode-Go-Round", there are some mathematical insights about the diatonic system, which have been discovered just in the last decades. </div><div>When I studied papers of John Clough, Jack Douthett, Eytan Agmon, Jay Hook and others about the diatonic scale I started to understand the algebraic nature of the concordance between note names, scale degrees and locations in the scale-step-pattern. During recent joint work with David Clampitt on a modal refinement of Jacques Handschin's concept of Tone Character we had many discussions about the role of the Guidonian solmization syllables as possible traces of the tone character in the music-theoretical meta-language. There are several interesting strands of ongoing theoretical discussion, which may be related to this. Steven Ring's interpretation of the Z7-coordinate in Eytan Agmon's diatonic model in terms of "qualia" is nicely exemplified in the ear-training task with Brahms's Symphony No. 4 (mentioned by Devin Chaloux).</div><div>The concept of tone character as a scale of tone-qualities, measured by the line of fifths (as Handschin puts it) relates to the well-formedness property of the diatonic scale in Norman Carey and David Clampitt's algebraic approach. The rule of the "si" and the rule of the "fa" (mentioned by Nicolas Meeùs) are in good accordance with that well-formedness property, which relates the mutation order of the syllables fa-do-so-re-la-mi-ti (~ si) to their scalar orderings.</div><div>Most inspiring for the mechanics behind the "Mode-Go-Round" is Jack Douthett's: "Filtered Point-Symmetry and Dynamical Voice-Leading", which may be interpreted as a novel and mathematically elegant variation on Ramon LLull's idea of mechanical combination.</div><div>Sincerely</div><div>Thomas Noll</div><div><br></div><div> </div><div> </div><div><br><div><div><br></div><br class="Apple-interchange-newline"><blockquote type="cite"><div bgcolor="#FFFFFF" text="#000000">
<font face="Calibri">The situation in 18th-century France was
slightly more complex because the solmisation then had seven
syllables (including *si*). <br>
<br>
The French had tricks to decide where to place the syllables.
There were basically two, the rule of the *si* – that the "last
sharp" (in the signature) and any accidental sharp was to be sung
*si* –; and the rule of the *fa* – that the "last flat" and any
accidental one was to be sung *fa*. Oddly enough, these rules
apply both in major and in minor: they place *ut* as the tonic in
major and *la* (or *re* if a flat is missing in the signature) as
the tonic in minor. The singer could begin singing straight away,
but did not know whether he sang in major or in minor, i.e.
whether *ut* or *la* (or *re*) was the tonic. Also, there was no
need to look at the clef, which singers disdained as a device for
instrumentalists.<br>
<br>
French theories of the time (e.g. Rameau's *Traité*) must be read
keeping this in mind. When Rameau says that it is difficult to
know the key of a piece, he means precisely that: one readily
knows its solmisation, but one does not know which syllable is the
tonic. He therefore suggests notating the key before the clef. And
the treatises about "transposition" usually are mere treatises of
solmisation, stating the rules of the *si* and of the *fa*, which
allow to sing "au naturel" independently of the key (i.e. the
"transposition") in which the piece is written. François Campion
describes the two forms of the minor as "layen" (tonic *la*) and
"réyen" (tonic *re*).<br>
<br>
The problem with this system, of which the consequences are still
dearly felt in our classes today, is that, as Campion explains,
any "diéze extraordinaire" (accidental sharp) brings about a
modulation – indeed, it displaces the *si*. Our students today
still tend to view modulations everywhere. And Schenker wrote (I
don't remember where) that the French are like the blinds: they
follow the wall with their hand and feel any asperity.<br>
<br>
I don't know when one changed from *ut* to *do*. It must have been
at some point in the second half of the 19th century. At any rate,
nobody would say *ut* today.<br>
<br>
</font>Nicolas Meeùs<br>
Université Paris-Sorbonne<br>
<font face="Calibri"><br>
<br>
</font>
<div class="moz-cite-prefix">Le 14/07/2012 03:46, Robert O
Gjerdingen a écrit :<br>
</div>
<blockquote cite="mid:17977BE0-DCC3-4CC9-851B-1FA96A646B0C@northwestern.edu" type="cite">
<br>
<div>
<div>On Jul 12, 2012, at 12:23 PM, Nicolas Meeùs wrote:</div>
<br class="Apple-interchange-newline">
<blockquote type="cite">
<div bgcolor="#FFFFFF" text="#000000"><font face="Calibri">The
solmisation syllables have long been used, in the French
tradition, as ...solmisation syllables. The conversion to
fixed-do solfège, in France, was not performed before the
middle or the second half of the 18th century. Movable-do
remained in (diminishing) usage at least until the
creation of the Paris Conservatoire around 1798.<br>
<br>
</font></div>
</blockquote>
<br>
</div>
<div>Nicolas is correct about the situation in France, but for
American readers there may be some confusion in his particular
use of the term "moveable do." In Anglo-American contexts, this
usually means the systems developed in Victorian England, where
"do" equals "tonic." Various earlier, continental systems going
back to Guido himself moved "Do" (or Ut), and note-names
reflected that fluidity until the middle of the nineteenth
century in many places within the "Romance tradition." But in
those systems "Do" did not equal "tonic." "Mi," for instance,
was not "3"; it meant a tone with a half-step above it and a
whole-step below it. So almost every sharped tone was a "Mi"
regardless of scale degree.</div>
<div><br>
</div>
<div>I assume that several subsequent messages will be triggered
by the lure of talking about solfège systems. It may be worth
mentioning that the flavor of a solfège system may matter less
than the age of the student to whom it is applied. College-age
students are "adult learners," which is why they may have
considerable difficulty learning any type of second language.
Adult learners of solfège (of any system) become about as
proficient in solfège as adult learners of beginning violin
become as violinists (which is to say, not very proficient). On
the other hand, almost any system taught to receptive children
over a period of many years will produce truly impressive
results.</div>
<div><br>
</div>
<div>Best wishes,</div>
<div>Bob Gjerdingen</div>
<div>Northwestern Univ.</div>
<div><br>
</div>
<div><br>
</div>
<br>
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_______________________________________________<br>Smt-talk mailing list<br><a href="mailto:Smt-talk@lists.societymusictheory.org">Smt-talk@lists.societymusictheory.org</a><br>http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.org<br></blockquote></div><br><div>
<div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; font-size: 12px; "><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><br class="Apple-interchange-newline"></div><br class="Apple-interchange-newline"><br class="Apple-interchange-newline">
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