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Session 9B: Algebraic Combinatorics of Scales and Modes with Applications to Music Analysis

Saturday 20 September
Session Convenors: Thomas Noll/Marek Žabka

The timetable for this session has been slightly altered!

Subsession 1
Chair: Thomas Noll                               

10.00    David Clampitt
Analytical Applications of Singular Pairwise Well-formed Scale Structures


11.30    Jennifer Shafer
Unveiling the Invisible: An Examination of Structure through Wavelet Analysis

12.15    coffee break

Subsession 2
Chair: Marek Žabka                               

12.30    Norman Carey/Thomas Noll
Descending Diminished Seventh Chords: Integrating Perspectives of Chordal Structure, Fundament Progression, Diatonic and Chromatic Voice Leading

13.15    Jonathan Wild
Scale Theory in the 16th Century — the Case of Nicola Vicentino

14.00    lunch break                                          

Panel session
Chair: David Clampitt

The activity of exploring a certain mathematical territory with the goal of its application to music-theory is typically fraught with risks. The outcome is not clear until the work is accomplished. The panelists are encouraged to report on promising ongoing research projects and to share their initial motivations as well as intermediate results. The panel consists of statements by the contributors and subsequent discussions.Especially we intend to stimulate a dialogue with the participants from Session 6A on Tonality (organized by Christophe Guillotel-Nothmann). The planned contributions by Emmanuel Amiot, Jon Wild and Marek Žabka address the role of generatedness from different perspectives and levels of generality. The study of the phases in discrete Fourier Transforms of pitch class sets is brand-new and promising. By contrast, the distinction of the major third from the ditone dates back at least to Archytas. Nevertheless, in recent mathematical approaches by Žabka and Wild it affects issues of dimension and transformations and deserves to be reviewed in these recent contexts. Jessica Rudman’s contribution nicely complements Jon Wild’s presentation on Vicentino.

16.00    Marek Žabka
Well-Formedness, Myhill’s Property and Maximal Evenness – How to Generalize Them for Non-Pythagorean Scales?

16.45    Jonathan Wild/Marek Žabka
Panel 2: Fokker-Clough Chains of Generated Tone Systems; Theoretical and Computational Exploration

17.30    Jessica Rudman
Panel 3: Ugly Step-Sisters: A Scale-Theoretic Examination of the Greek Genera

18.15    All participants
General Discussion