How Frequency Ratios Unify Pitch, Rhythm & Timbre — Contemporary & Future Composition (Part II)

This final episode of Pythagoras and the Music of the Future explores how pitch, rhythm, and timbre can be unified through related frequency ratios originating in the natural harmonic series.

Building on Part I, which introduced ratio-based rhythmic structures, this programme shows how contemporary techniques—from additive to FM, and granular, synthesis — enable composers to create cohesive musical structures rooted in acoustical proportion.

Beginning where we left off in Part I, with the problem of extreme rhythmic complexity and the limits of human performance, we touch on the New Complexity movement and ask when digital realisation becomes necessary. From here, the programme examines how ratio-driven synthesis can result in logical and coherent articulation of the most complex rhythmic materials, impossible for human performance.

A series of examples from my Risonanze for Clarinet and Electronics demonstrates:

🔊 Additive / instrumental synthesis using captured clarinet tones

🔊 Pitch-shifting to blur the boundaries between harmony and timbre

🔊 Inharmonic spectral “washes” driven by complex rhythmic triggers

🔊 FM synthesis using interval-derived carrier/modulator ratios

🔊 Granular textures generated from ratio-derived rhythmic processes

The episode concludes with reflections on musical form, symmetry, retrograde structures, and the broader question of the “music of the future”— addressing the contrast between musical art and the prevalence of pastiche promulgated by the 'democracy of commercialism'.

This video is for composers, theorists, performers, and anyone curious about spectral music, acoustics, contemporary composition, and the evolution of musical language.

❓If you have questions or thoughts, please do leave a comment.

👓If you enjoy deep dives into acoustics, theory, or contemporary composition, please consider subscribing and exploring the earlier videos in this series and related materials;

🎬The Harmonic Series: What it is and How It Creates Timbre: Pythagoras & the Music of the Future - I    • The Harmonic Series: What it is and How It...  

🎬Musical Sounds Revealed as the Source of Melody & Harmony: Pythagoras & the Music of the Future - II    • Musical Sounds Revealed as the Source of M...  

🎬Twentieth-Century Music - Revolution or Evolution? Pythagoras & the Music of the Future - III    • Twentieth-Century Music - Revolution or Ev...  

🎬How Can Pitch and Rhythm be the Same Thing? Pythagoras & the Music of the Future - IV    • How Can Pitch and Rhythm be the Same Thing?  

🎬The Shared Source of Irregular Rhythms and Dissonant Intervals! Pythagoras & the Music of the Future - V    • The Shared Source of Irregular Rhythms and...  

🎬The Twelve Tone System in Context    • The Twelve Tone System in Context  

🎶New Music for Clarinet & Electronics: Risonanze by Robert Lennon    • New Music for Clarinet & Electronics: Riso...  

Chapters
00:00 - Introduction
00:38 - Compound & complex rhythms
01:16 - Playability of extreme rhythms
01:51 - The need for digital realisation
02:30 - Unifying complex rhythms and timbre
03:06 - Suitability of inharmonic timbres
03:19 - Introduction to examples unifying intervals & timbre
03:33 - Additive (instrumental) synthesis in 'Risonanze for Clarinet & Electronics'
04:09 - Inharmonic timbre created by layering clarinet pitches
05:22 - Second type of additive synthesis - use of pitch shifters
06:45 - Inharmonic timbres allied to complex rhythms
07:42 - Generating inharmonic timbres via FM synthesis
08:20 - Deriving carrier & modulator frequencies from interval ratios
08:35 - FM Basics - creation of timbres related to interval ratios
14:12 - Music of the past being written today!
09:59 - Additive synthesis with FM software
10:22 - Granular synthesis
11:40 - Form - relevance of retrograde structures
12:45 - What of the music of the future?
16:22 - Music as entertainment or as art
17:19 - Commercialism and the modern view of all music as entertainment
17:54 - Conclusion