Import Harmonies
Harmony Layers
Frequency for 1/1. Default: C4 = 261.63 Hz
Tone label for 1/1. Default: D
Enter 6 ratios or vectors (one per line), e.g. 2, 3/2, 5/4 …
Width Assignments
Assign width to each basis generator. Click ± to set the slider range per row.
This app demonstrates the faithful keyboard construction from:
Planar Projections of Tone Systems and Faithful Keyboards
Marek Žabka, Komenský University Bratislava, 2026.
Pitch height (x-axis) is the standard cents value:
h = 1200·log₂(ratio).
Pitch width (y-axis) is determined by your width assignments to the basis generators of the chosen coordinate system.
A projection is pitch-faithful iff the pitch-height vector lies in the projection plane (Theorem 1). This guarantees distinct JI tones always map to distinct positions.
Multiple harmony layers can be shown simultaneously. Click or touch any key to hear it.
Send feedback or questions to:
marek.zabka@uniba.sk