[Smt-talk] Movable-Do subculture in the Romance tradition?

[Thomas Noll]

Dear John, 
Many thanks for pointing to this very interesting article. 
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. 

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. 

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.
(1) The roots of the three "Curwen scales" are C, F# and Gb.  
(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: http://www.mtosmt.org/issues/mto.11.17.1/mto.11.17.1.clampitt_and_noll.html
(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).
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. 

The three triples of anchor notes are close but yet different  (1) C-F#-Gb, (2) C-Gb-G,  (3) C-F-G, 
Sincerely
Thomas Noll

> A study that relates Curwen's tonic sol-fa method to more recent formulations is accessible at:
> 
> http://pi.library.yorku.ca/dspace/handle/10315/6610
> 
> Jay Rahn, York University (Toronto)
> 
> --- On Mon, 7/16/12, Eytan Agmon <agmonz at 012.net.il> wrote:
> 
> From: Eytan Agmon <agmonz at 012.net.il>
> Subject: Re: [Smt-talk] Movable-Do subculture in the Romance tradition?
> To: smt-talk at lists.societymusictheory.org
> Date: Monday, July 16, 2012, 7:39 AM
> 
> “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 19th century. However, the idea dates back to the “octave species” of medieval modal theory (and ultimately Greek theory).
> 
>  
> Eytan Agmon
> 
> Bar-Ilan University
> 
>  
> 
> 
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Thomas Noll
http://user.cs.tu-berlin.de/~noll
noll at cs.tu-berlin.de
Escola Superior de Musica de Catalunya, Barcelona 
Departament de Teoria i Composició 

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