Visualization and Scale-Model Methodology

Persian Music Scales uses a circular geometric representation to make interval relationships visible and transposable while preserving the numerical pitch model used by the application.

Octave and angular mapping

An octave is treated as 1200 cents and mapped to a full 360° circle:

angleDegrees = cents × 360 / 1200

Thus 100, 150, 200 and 250 cents correspond to 30°, 45°, 60° and 75° respectively.

Scale models

The seven Persian pitch-collection models documented here are read directly from the application's implemented scale data: Shur, Nava, Segah, Homayoun, Esfahan, Chahargah and Mahur / Rast Panjgah.

Transposition

Rotation changes note naming relative to the selected tonic while preserving the internal cent relationships of the selected model.

Microtonal labels

The app uses koron and sori labels when a modeled pitch falls 50 cents below or above a diatonic reference pitch. This is a computational convention of the app, not a claim that all Persian performance intonation is fixed to equal 50-cent offsets.

Model boundaries

A pitch collection alone cannot fully identify Persian modal practice. Finalis, shahed, melodic hierarchy, phrase grammar, variable tones, gusheh context, modulation and performer/tradition-specific intonation can all matter.

Reproducibility

The exact values are published in persian-scales.json.