Scope

General Remarks:

Beyond the intrinsic theoretical aspects of the instrument itself and the basics of diatonic solmisation there are many interesting subjects in music theory and music education which can be explored with the App in specific ways. This page provides some orientation for these possibilities and contains links to existing tutorials as well as suggestions for planned tutorials. There are two larger partly overlapping thematic areas. On the one hand, the concept of Mode itself is highly ramified with a diversity of utilizations in music theory, analysis and composition. On the other hand there are several subjects, where modes are not necessarily thematised, but where the combinatorics of the species of the octave comes into play.

The conceptual environment of mode involves the eight medieval modes of Gregorian chant, and the eight associated psalm tones. The family of the eight pseudo-classical modes form their theoretical counterparts: species of the octave with authentic and plagal divisions into species of the fifth and the fourth respectively. This family was eventually extended to 12 modes by Glarean and reordered by Zarlino to overcome the hybrid and therefore theoretically unsatisfactory ordering of the 8 church modes. There are several ways to familiarize oneself with the differences and tensions between the theoretical and the practical modes. The conceptual environment also involves the hexachordal covering of the medieval gamut (Musica recta) and the questions of hexachord mutation in the solmisation practice.

In order to comprehend controversies in the scholarly discourse about the role of modes and of hexachords the Renaissance polyphony it is insightful to reenact concrete arguments on the basis of the given examples. In particular the Midi-functionality of the App (from version 1.2 onwards) supports the inspection of prepared polyphonic examples. Instrumental music in the late Renaissance was catalytic for the combinatorial extension of the inventory of modes and their clustering and metamorphosis into the major and minor keys. The 84 configurations of the SolFa Mode-Go-Round provide a suitable meta-level in order to incorporate the practically relevant cases.

Species of the octave come implicitly into play, when issues in polyphony are studied on two levels: (1) on a generic level of scale degrees and (2) on a specific level with sensitivity to the location of semitones, and consequently of diminished fifths etc. A nice example is Athanasius Kircher's "Arca Musarithmica" from 1650. Another one is the study of Canon composition. Even for the study of diatonic sequences it is insightful to trace their instances through diatonic transpositions, acting on suitable species of the octave.

On the background of major/minor tonality the noun mode or the attribute modal is often used in order to highlight typical deviations from the unmarked case. The deviation occurs over the same tonic and in the same ambit. In other words, the marked modes are tropes (diatonic species of the same octave). There are four such cases, two in Major and two in Minor. Lydian and Mixolydian are minimal neighbors of the unmarked Ionian mode. Dorian, Phrygian are minimal neighbors of the unmarked Aeolian mode. Thus, in each case there is one scale degree where the marked case differs from the unmarked. And it is always either ti substituting for fa (sharpward alteration) or fa substituting for ti (flatward alteration). The Lydian fourth (syllable ti instead of fa), the Mixolydian seventh (syllable fa instead of ti), the Dorian sixth (syllable ti instead of fa) and the Phrygian second (syllable fa instead of ti).

Modes gained a renewed theoretical interest in post-tonal projects of composers such as Claude Debussy, Bela Bartok, Yannis Constantinidis and several others. A notable project in the tradition of minimal music engaging minimal modal transformations is Michael Torke's piece "The Yellow Pages".

The Lydian mode, still an outsider within Glarean's Dodecachordon, made a remarkable career in Jazz Theory under the influence of George Russel's "Lydian Chromatic Concept of Tonal Organization". The theoretical distinctiveness of this mode is the incidence of its origin (on the line of fifths) with the tonic. The chord-scale system, a further development of this approach, embeds chords into modes whose tonic coincides with the chord root.

Related Experiments:

• • Hexachordal Solmization

  • Hexachordal Games and Modes

  • Voice Leading Models and Modes

  • Diatonic Sequences

  • The Combinatorics of Canons

  • Iterated Alteration

  • Inversions of Triads and Seventh Chords as Modes

  • Neo-Riemannian Progressions