MusicArmonia

The Circle of Fifths

Visualizing Keys, Relative Modes, and Signatures

Harmonic Theory

The Circle of Fifths arranges the 12 chromatic pitches in a sequence of perfect fifths (7 semitones). Keys sharing adjacent positions are closely related: they share all but one accidental in their scales. This circular geometry shows how close major and minor keys are, and makes transpositions and modal modulation patterns visually evident.

In-App Implementation

MusicArmonia represents this theory through 4 concentric glassmorphic rings:

• Outer Ring: Shows the musical key signature (flats and sharps) rendered on a treble clef staff.
• Dynamic Ring: Focuses on diatonic functions, highlighting the Roman Numeral degrees (I, ii, iii, IV, etc.) for the selected key.
• Static Major Ring: Displays major key note names.
• Inner Ring: Displays relative minor key note names (e.g., A minor inside C major).

Interactive slices allow you to select keys, toggle scale families (Major, Harmonic/Melodic Minor, Pentatonic, Blues), and observe how diatonic functions shift color dynamically.

Neo-Riemannian Tonnetz

Mapping Triads, Transformations, and Voice Leading

Harmonic Theory

Pioneered by Leonhard Euler and popularized by Hugo Riemann, the Tonnetz (tone-network) is a slanted grid representing pitch space. Notes are connected along three geometric axes of consonant intervals:

• Horizontal Axis: Perfect Fifths (P5, +7 semitones).
• Upward Diagonal Axis: Major Thirds (M3, +4 semitones).
• Downward Diagonal Axis: Minor Thirds (m3, +3 semitones).

Triangular cells in this grid represent triads: triangles pointing upwards are Major triads, and triangles pointing downwards are Minor triads. Neo-Riemannian theory analyzes chord transformations based on note preservation (minimal voice leading distance), focusing on three primary operations:

• P (Parallel): Flips a major triad into its parallel minor (C major ↔ C minor) by changing the 3rd. It flips the triangle across its P5 edge.
• L (Leading-tone exchange): Relates a major triad to its minor partner a major third above (C major ↔ E minor) by moving the root a semitone. It flips the triangle across its minor third edge.
• R (Relative): Flips a major triad into its relative minor (C major ↔ A minor) by moving the fifth. It flips the triangle across its major third edge.

In-App Implementation

MusicArmonia models this hexagonal slanted grid dynamically. Hovering over a transformation (like L-P-R paths) displays the visual movement of the triad triangle flipping across its edges. Common notes glow, showing you how voices transition smoothly from one chord to another on the lattice.

Key Reference & Chord Builder

Nashville Numbers, Roman Numerals, and Chord Spelling

Harmonic Theory

The Nashville Number System and Roman Numeral Analysis abstract chord progressions from absolute pitches to relative scale degrees (e.g. I, IV, V, vi). This allows you to easily analyze harmonic relationships and transpose progressions instantly into any key.

In-App Implementation

The Key Reference view is a grid of 15 key columns and 12 scale degrees. It highlights diatonic intervals and notes. By tapping cells in this matrix, you can build custom chord spellings. The built-in Harmony Analyzer identifies the chord name (e.g. Cmaj7, Am9) and lets you save it to your sequence. You can then transpose your entire progression by clicking different key columns at the top, transposing your saved chords instantly.