Five-Course Series

The five-course series Harmonic and Tonality Fundamentals lays out the concepts and insights of Tonalibus in detail. This is in mostly images, graphs, and tables — so far without much text, if any. Along with the catalogue of anchored tonalities, the five-course series is the core of Tonalibus.

Five-course series contents

Each of the five courses begins with a module-specific introductory overview and ends with a concise review and module conclusion. For all but the last module there is also a preview built in. These previews gradually build up familiarity with the catalogue and its anchored tonalities. This is intended as opportunity for practical work with tonality applications. It may also trigger discussions, depending on the interests and focus of course participants.

1) The Harmonic Pivot and Anchor Tones, the first module of the five-course series or Basics A, demonstrates how two opposite spirals approach each other progressively or regressively, overlap, merge, and cross over through a harmonic pivot. Further, this module presents the so-called Quad Anchor Tone Circle or the four corners of the sound temple.

2) Harmonics Base and the Realization Shift, or Basics B, is the second module of the five-course series. It explores the patterns of prime, even, and odd harmonics in wave and circular forms. Further, this module features the harmonic realization shift reconciling linear fundamentals with curved actuality. This includes a concise proportional distribution of pitches within the octave.

3) Twelve-Step Scale and Tonality Fundamentals is the third module of the five-course series, or Basics C. Using circular, Möbius, and spiral views, it correlates harmonics and the twelve half-tones scale, arriving at the fundamental harmonic anchor. On that basis this module then explores and displays the basic step distribution pattern options in tonalities.

4) Quad Harmonic Anchors and the Quint Cycle, the fourth detailed module of the five-course series or Basics D, explores the harmonic anchor on spirals and then on circles. It presents the concept of the four quadrant harmonic anchors with four anchor tones or the four corners of the sound temple. Further, this module looks at multiple and partial anchors in tonalities, as well as the quint anchor cycle, a view of what is widely known as the circle of fifths.

5) Select Step Tonalities and Secondary Anchors, or Basics E, is the last module of the five-course series. It explores the circle of primary and secondary harmonic anchors, as well as the single pitch coloring of the individual twelve half-tone steps in the octave. Further, this module presents the tetrachord patterning of tonalities. In conclusion, there are the tonality tables, patterns, and lists that are the foundation of the catalogue of anchored tonalities.