Performing Adaptive and Reconstructed Tunings Live
Learning objectives
- 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
Capstone — one whole task that evidences the objectives
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.
Prerequisite modules
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
Supporting — enrichment, not gating