Riemannian Transformations: Part 1 Schillinger Caught in the Tonnetz

An essential aspect of Neo-Riemannian Theory is chord transformation. This tutorial presents the 3 elementary Riemannian transformations (Parallel, Relative and Leading-tone exchange) and the compound transformations (PL, LP, PR, RP). Each of these is shown for major and minor triads in the Tonnetz diagram and staff notation. Transformations are interpreted in terms of the equivalent Schillinger Symmetric Harmony System Root Cycle, and demonstrated with a very short musical application example. Companion booklet and blank Tonnetz diagram template for your chord progression at
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Contents:
00:00 What this video is about
00:25 Section 1. Introduction, Neo-Riemannian Theory, Tonnetz, Schillinger Root Cycles
03:18 Section 2. Elementary Riemannian Transformations
04:16 Section 2.1. P-transformation, major triad- parallel minor
06:21 Section 2.2. R-transformation, major triad - relative minor
07:43 Section 2.3. L-transformation, major triad - mediant minor
08:52 Section 2.4. P', R' and L' inverse transformations, minor - major
10:41 Diatonic root cycles
11:16 Section 3. Compound Riemannian Transformations, chromatic mediants, film music narrative
13:48 Section 3.1. PL-transformation, C to Ab
15:06 Section 3.2. PR-transformation, C-Eb
16:09 Section 3.3. RP-transformation, C-A
17:20 Section 3.4. LP-transformation, C-E
18:20 Section 3.5. LP-trensformation, Cm-Abm
19:30 Section 3.6. RP-transformation, Cm-Ebm
20:53 Section 3.7. PR-transformation, Cm-Am
22:09 Section 3.8. PL-transformation, Cm-Em
23:20 Section 3.9. Triad combinations and symmetric scales
25:47 Summary and conclusion

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