Riemannian Transformations: Part 2 Five Paths to Domination

In this tutorial the elementary P, R and L Riemannian Transformations and the compound transformations PR, RP, PL and LP are applied to a dominant pedal point chord progression framework. Alternative triad transformation paths are shown in the Tonnetz diagram and interpreted in terms of Schillinger diatonic and symmetric system root cycle patterns. Five alternative paths are demonstrated with short orchestral composition and instrumental form examples.

Contents:
00:00 What this video is about
00:30 Introduction. Riemannian transformations, Schillinger root cycles, narrative value
03:19 Section 2. Application in a dominant pedal point chord progression framework
05:15 Path 1. Simple Riemannian transformations and negative diatonic root cycles
07:34 Path 2. Addition of compound Riemannian transformations
09:29 Path 3. Longer path with more compound transformations and positive root cycles
12:08 Path 4. Use the Tonnetz redundancy property, compound transformations only
13:56 Path 5. Modify Path 4 and obtain a compound positive closing cadence
16:12 More path options with the Tonnetz diagram redundancy property
16:53 Summary and conclusions

Companion booklet and blank Tonnetz diagram template for your chord progression at
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