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Performing Adaptive and Reconstructed Tunings Live

  • learner can perform real-time adaptive retuning that slides toward consonance
  • learner can model retuning with the spring-tuning framework balancing just ratios, stability and tonal center
  • learner can reconstruct and apply a historical composer's likely tuning in performance

Perform a two-minute live-tuned piece: drive an adaptive-tuning engine (gradient-descent down the dissonance curve, spring-tuning constraints) so held chords retune toward consonance in real time, and open with a passage in a historically reconstructed tuning — narrating the tradeoffs the springs resolve.

This module builds toward a performance most audiences have never heard: a set where the tuning itself is a live instrument. In a live-coding or MIDI-keyboard rig — pitch-bend per voice, a slow-moving ambient or chorale-like texture where held chords give the ear time to notice intonation — you drive an engine that continuously nudges sounding pitches down the dissonance landscape toward consonance, and you open the set in a tuning reconstructed from a historical composer’s practice. The payoff is a performance with a story: why the thirds bloom, why the melody drifts, what the springs are fighting over.

The arc starts supported. First, run the adaptive engine offline on a fixed chord progression, watching how gradient descent on the dissonance curve pulls intervals into nearby minima — this is the core recurrent skill, drilled until reading and steering the retuning is automatic. Next, reframe the same behavior through the spring-tuning model: practice trading vertical springs (just ratios) against horizontal springs (melodic stability) and grounding springs (tonal center), because narrating those tradeoffs live is half the capstone. Then work the historical-reconstruction procedure on a short corpus, deriving and internalizing a well-temperament-style tuning you can open with. Finally, assemble the unsupported two-minute performance.

The three required atoms gate the capstone directly: you cannot drive the engine without the gradient-descent concept, cannot narrate tradeoffs without the spring model, and cannot open historically without the reconstruction procedure. The supporting atoms — sensory dissonance, dissonance curves, just intonation, and the related-spectrum-scale principle — are the psychoacoustic bedrock from the prerequisite module; revisit them just-in-time when the engine’s behavior surprises you.

Atoms in this module

Required — these gate the capstone

Adaptive tuning adjusts pitches in real time by sliding down the dissonance curve toward nearby consonant intervals
Concept L4 Performance AB
Spring tuning models adaptive retuning with vertical springs (just ratios), horizontal springs (pitch stability), and grounding springs (tonal center)
Concept L4 Performance A
Sensory dissonance analysis can help reconstruct the tuning a historical composer likely used
Procedure L4 Performance A

Supporting — enrichment, not gating

Sensory dissonance is the roughness caused by beating partials within the critical band
Concept L2 First instrument AB
A dissonance curve plots sensory dissonance vs. interval for a given spectrum, with minima at consonant intervals
Concept L3 Craft AB
Just intonation tunes intervals to small-integer frequency ratios to eliminate beats with harmonic timbres
Concept L2 First instrument A
A spectrum and a scale are 'related' when the spectrum's dissonance curve has minima at the scale's steps
Principle L3 Craft AB