Create a chord progression that combines Pitch-Class Set (PCS) harmonies with a Riemannian Transformation (RT) triadic progression. The RT progression includes chromatic mediant pairs, the SLIDE transformation and the symmetric scale hexachordal triad pair. The PCS is based on the all-interval tetrachord 4-Z15 and its Z-related companion 4-Z29. The harmony uses various PCS properties such as the original, transposed and inverted form, common notes for different forms, voicings that focus on specific intervals or dissonance distribution. This technique is demonstrated with an example orchestral composition. There's a companion document with text, diagrams and score excerpts available in the webshop.
Contents:
00:00 What this video is about
00:37 Section 1 Introduction, combine Riemannian and Pitch-Class Set based harmony systems
01:16 Section 2 Riemannian Transformations and triadic chord progression
01:20 Section 2.1 The full chord progression in C minor
02:15 Section 2.2 Chromatic mediants
03:23 Section 2.3 SLIDE transformation
03:57 Section 2.4 Hexatonic triad pair and symmetric scale
04:34 Section 3 Pitch-Class Sets (PCS)
04:38 Section 3.1 Pitch-Classes, Sets, Cardinal Number, Primary Form, Interval Vector
05:38 Section 3.2 All-interval tetrachord, 4-Z15, original and inversion form
07:16 Section 3.3 Z-related PC-Set 4-Z29
08:19 Section 4 Combination of RT and PCS harmony using specific PCS properties
08:24 Section 4.1 Common interval major and minor 2nd for 4 PCS forms
10:21 Section 4.2 PC overlapping 3rd when combining transposed forms, hexachord voicing
13:11 Section 5 Example composition
13:16 Section 5.1 Form, time signature, tempo, sections, orchestration.
13:54 Section 5.2 Instrumental forms, riff, motif, (counter)melody, arpeggios
20:50 Section 5.3 Reduced score and audio
22:59 Summary and conclusion
#tetrachord #RiemannianTransformation #harmony
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