01

Rhythm & Fractions

Grades 3–6

Math Concepts

Fractions as division
Numerator & denominator
Equivalent fractions
Comparing fractions
Adding fractions
Common denominators

Music Concepts

Beat subdivision
Time signatures
Quarter, eighth, sixteenth notes
Whole & half notes
Polyrhythm
Tempo

Apps

Fraction Drum Machine

Fraction Stack Visualizer

Polyrhythm Builder

Rhythm Notation Converter

02

Frequency & Number

Grades 4–7

Math Concepts

Multiplication & doubling
Ratios
Proportional reasoning
Powers of 2
Number patterns
Rate & cycles per second

Music Concepts

Pitch as frequency (Hz)
Octaves as doubling
The harmonic series
Consonance & dissonance
Tuning systems
String length & pitch

Apps

String Length & Frequency

Frequency Stacker

Harmonic Series Builder

Octave Explorer

03

Waves & Geometry

Grades 6–9

Math Concepts

Sine & cosine functions
Amplitude & period
Radians & degrees
Phase shift
Graphing functions
Superposition

Music Concepts

Sine waves as pure tone
Waveform shapes
Timbre & harmonic content
Phase relationships
Interference patterns
Beat frequencies

Apps

Wave Shape Explorer

Phase Relationship Visualizer

Beat Frequency Demo

Lissajous Figure Builder

04

Scale & Logarithms

Grades 7–10

Math Concepts

Geometric sequences
Logarithms
Exponential growth
The 12th root of 2
Equal temperament math
Irrational numbers

Music Concepts

Fret spacing on guitar
Equal vs just temperament
Semitones & cents
The chromatic scale
Why frets get closer
Decibels as log scale

Apps

Fret Position Calculator

Temperament Comparator

Decibel Scale Explorer

Just vs Equal Tuning Demo

05

Harmony & Ratio

Grades 6–9

Math Concepts

Rational numbers
Simple ratios
Greatest common divisor
Modular arithmetic
Circular geometry
Number theory

Music Concepts

Intervals as ratios
Perfect 5th (3:2)
Major 3rd (5:4)
Circle of fifths
Chord construction
Nashville Number System

Apps

Nashville Notation Wheel

Frequency Stacker / Keyboard

Interval Ratio Explorer

Circle of Fifths Navigator

06

Synthesis & Functions

Grades 8–12

Math Concepts

Functions & transformations
Piecewise functions
Rate of change
Multiplication of functions
Fourier series
Signal processing

Music Concepts

Additive synthesis
Envelope (ADSR)
LFO as rate of change
Ring modulation
Filters as subtraction
Timbre construction

Apps

Additive Synthesis Builder

ADSR Envelope Shaper

LFO Rate of Change Demo

Filter Frequency Subtractor

Ring Modulator Math

07

Pattern, Sequence & Structure

Grades 5–10

Math Concepts

Sequences & series
Fibonacci numbers
Golden ratio
Euclidean algorithm
Permutations
Symmetry & transformation

Music Concepts

Euclidean rhythms
Fibonacci in musical form
Twelve tone rows
Call & response
Canon & counterpoint
Groove sequencing

Apps

Groove Sequencer

Euclidean Rhythm Generator

Fibonacci Rhythm Explorer

Twelve Tone Row Builder

Canon Generator