Layered Hexachords: Combining PC-Set and Schillinger System Composition Techniques

This example composition is used for a YouTube tutorial on sketching with hexachords using techniques from set theory and the Schillinger System of Musical Composition. Two pitch-class sets, 6-Z12 with maximum dissonance and 6-Z49 with maximum consonance are the building blocks. Harmony is based on subsets, such as major and minor triads, the 4-25, 4-26 and 4-27 tetrachords, and continuities with the hexachords in original and inverted form.

The composition demonstrates voicing alternatives in variable density and strata harmony setting, pedal point, and progressions with chromatically moving middle parts. Melodic material is based on various expansions and melodic axes. Rhythm is partially based on a Euclidean rhythm rE(7,32).

The instrumentation uses many synthesizers and a limited set of orchestral instruments. The project was created in the Cubase DAW, then converted to a full score.

Contents:
00:00 Opening titles
00:27 Section 1 Introduction: what this video is about
01:17 Section 2 Source element, atonal music, Schillinger System
01:34 Section 2.1 Pitch-Class Sets 6-Z12 and 6-Z49, set forms and characteristics
04:12 Section 2.2 Example composition, form, sections
05:05 Section 3 Composition techniques, overview diagram, harmony, melody and rhythm
06:24 Section 3.1 Pedal point, single and double, primary axis
07:37 Section 3.2 Melodic 2-part phrases, interval-class vector element values
07:51 Section 3.2.1 Maximum consonance phrase
09:54 Section 3.2.2 Maximum dissonance phrase
11:10 Section 3.3 Major and minor triads, diatonic 3-part subsets, chord continuity
13:34 Section 3.4 Melody derived from triadic harmony, focus on consonance or dissonance
14:30 Section 3.5 Melodic form and scale expansion, triplet rhythm phrases
15:55 Section 3.6 Tetrachords and other subsets
16:07 Section 3.6.1 Major and minor third chord structures as layer in strata harmony
17:02 Section 3.6.2 Combination of trichord and moving bass part
17:49 Section 3.6.3 Tetrachord subsets, 4-25 to 4-27, chord continuity
20:44 Section 3.7 Hexachords in strata harmony
21:08 Section 3.7.1 Two 3-part layers for 6Z-12
23:35 Section 3.7.2 Three layers for 6-Z49, tetrachords and double pedal point
26:25 Section 3.8 Countermelody with divergent melody axis
27:11 Section 3.9 Variable density closing section with Euclidean rhythm
29:44 Section 4 Full composition, MIDI mockup, annotated reduced score
32:40 Summary and conclusion

#SchillingerSystem #PitchClassSet #CompositionTechniques

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