# PitchDrops

> Free, open, adaptive relative pitch ear training progressive web application (PWA) with Bayesian mastery estimation, offline-first Web Audio synthesis, and microtonal Just Intonation tuning support.

PitchDrops (https://pitchdrops.com) is an open-access ear training platform engineered by Ed Boraas (Boraas Digital). It trains musicians, composers, producers, and vocalists to connect music theory with auditory recognition across intervals, chords, scales, modes, functional chord progressions, and absolute pitch.

The application operates offline-first using client-side Web Audio synthesis and high-resolution sampled acoustic instruments (piano, electric guitar, electric bass), driven by an adaptive spaced repetition engine based on Bayesian probability distributions and temporal memory decay.

## Core Training Modes
- [Interval Ear Training](https://pitchdrops.com/training/intervals/): Melodic (ascending/descending) and harmonic interval recognition from minor 2nds to compound intervals.
- [Chord Quality Recognition](https://pitchdrops.com/training/chords/): Major, minor, diminished, augmented triads, 7th chords (dominant, major, minor, half-diminished), and extended chords.
- [Scales & Church Modes](https://pitchdrops.com/training/scales/): Major and natural minor scales, pentatonics, church modes (Dorian, Phrygian, Lydian, Mixolydian, Locrian), and world scales (Hirajoshi).
- [Chord Progression Ear Training](https://pitchdrops.com/training/progressions/): Functional Roman numeral cadences and progressions (I-V-vi-IV, ii-V-I jazz turnarounds, secondary dominants, and modal mixture).
- [Note & Pitch Class Recognition](https://pitchdrops.com/training/notes/): Tonal pitch recognition within a C tonal center featuring voice-led cadential anchoring (I-IV-V-I), reference C anchors, continuous background drones, and unanchored solo listening.
- [Mixed Mode Daily Workout](https://pitchdrops.com/training/mixed/): Interleaved, multi-category ear training sessions targeted at the learner's skill frontier.

## Pedagogy & Architecture
- [The PitchDrops Method](https://pitchdrops.com/method/): Explains our Bayesian Mastery Estimation model (Beta distribution 4-AFC prior/posterior updates), 7-day half-life exponential memory decay, anti-frustration Zone of Proximal Development targeting (75%–80% sweet spot), and natural resurfacing through temporal decay.
- [Math Deep Dive](https://pitchdrops.com/math/): Rigorous mathematical derivation of the 4-AFC conjugate Beta prior, Bernoulli likelihood updates, 7-day memory decay asymptotic convergence, credible intervals, and active learning acquisition functions.
- [User Guide & FAQ](https://pitchdrops.com/guide/): Complete guide covering daily practice recommendations (5–10 mins/day), play styles (melodic, harmonic, random), tuning temperaments (12-TET, 5-Limit Just Intonation, 7-Limit Just Intonation), Web Audio synthesis vs sample playback, and PWA installation.
- [Progress & Statistics](https://pitchdrops.com/stats/): Deep breakdown of mastery tracking, historical accuracy, credible intervals, and practice streaks.
- [Application Settings](https://pitchdrops.com/settings/): Instrument voicing selections (piano, guitar, bass, sine, sawtooth, square, FM, AM synthesizers), tuning systems, and theme controls.
- [About PitchDrops](https://pitchdrops.com/about/): Background, mission, and developer contact information.

## Complete Curriculum & Theory Index
- [Full Documentation & Theory Reference (https://pitchdrops.com/llms-full.txt)](https://pitchdrops.com/llms-full.txt): Complete, concatenated curriculum documentation, formulas, interval semitone tables, chord interval structures, scale degrees, and progression catalogs.

## Optional
- [Privacy Policy](https://pitchdrops.com/privacy/): Local-first IndexedDB persistence, optional Firebase Google OAuth cloud backup, and clear analytics/advertising disclosures.
- [Terms of Service](https://pitchdrops.com/terms/): Application terms, acceptable use, and service guidelines.