Indexing the archive…
Your Universe of Digital Possibilities
Two tones, six semitones apart: does the pair go up, or down? The sound itself does not decide — the interval is exactly half an octave either way. Answer for pairs starting on all twelve pitch classes and the instrument finds the region your ear calls high, draws it on the chroma circle, and checks that it survives a change of envelope.
Partials an octave apart, weighted by a fixed bell-shaped envelope G over log frequency. Raising the pitch class c by twelve semitones gives back exactly the same set of partials — so the tone has a chroma but no definite height.
Pitch as two dimensions at once: the chroma c (which note) goes round the circle, the height (octave o) goes up, one turn per octave. Tones an octave apart stand directly above one another; a Shepard tone lights the same chroma at every turn.
The probability of one answer as the stimulus x changes: F a sigmoid (logistic or cumulative normal) centred on α, the point of subjective equality, with spread β; γ the guess rate, λ the lapse rate. Every Iris instrument fits it to the visitor’s own trials by maximum likelihood, with the PSE’s error from the profile likelihood.
The ninth percept hears a direction the sound does not contain. Pitch has two parts — how high, and which note — and a Shepard tone keeps the second while erasing the first, so the brain fills in the height from what it expects. What a spectrum is made of is The Spectrum; why a plucked string sings in octaves is The String; how many voices make one sound is The Chorus.