LOUD MATH
Music & Mathematics Curriculum — by Tribe of Abraham
Built
Planned
Future
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