music-theory-verification

Music Theory Verification

Overview

Music theory code involves modular arithmetic (mod 12) and interval calculations. Small errors produce completely wrong notes that may not be obvious until heard.

Core principle: Verify calculations against known musical facts before trusting code.

When to Use

• Debugging incorrect note display
• Verifying new scale/chord implementations
• Troubleshooting Nashville number display
• Checking fretboard/keyboard generation
• Validating transposition logic

The Chromatic Scale

Index:  0   1    2   3    4   5   6    7   8    9   10   11
Sharp:  C   C#   D   D#   E   F   F#   G   G#   A   A#   B
Flat:   C   Db   D   Eb   E   F   Gb   G   Ab   A   Bb   B

Interval Math

Note Value Calculation

// Adding interval to root
noteValue = (rootValue + interval) % 12;

// Example: G major 3rd
// G = 7, major 3rd = 4
// (7 + 4) % 12 = 11 = B ✓

Fret Note Calculation

// Note at fret position
noteValue = (openStringValue + fretNumber) % 12;

// Example: 3rd fret on A string (A = 9)
// (9 + 3) % 12 = 0 = C ✓

Common Errors

// WRONG: Forgetting modulo
noteValue = rootValue + interval;  // Can exceed 11!

// WRONG: Wrong modulo base
noteValue = (root + interval) % 11;  // Should be 12

// WRONG: Negative intervals without handling
noteValue = (root - interval) % 12;  // Can be negative!

// CORRECT: Handle negative
noteValue = ((root - interval) % 12 + 12) % 12;

Quick Verification Tests

Major Scale Test

Starting from C (0), major scale intervals [0,2,4,5,7,9,11] should produce:

C(0) D(2) E(4) F(5) G(7) A(9) B(11)

Starting from G (7):

G(7) A(9) B(11) C(0) D(2) E(4) F#(6)

Minor Scale Test

Starting from A (9), natural minor [0,2,3,5,7,8,10]:

A(9) B(11) C(0) D(2) E(4) F(5) G(7)

Chord Test

C Major chord [0,4,7] from C(0):

C(0) E(4) G(7) ✓

G7 chord [0,4,7,10] from G(7):

G(7) B(11) D(2) F(5) ✓

Nashville Number Verification

Nashville numbers represent scale degrees 1-7.

Calculation

// Find position of note in current scale
nashvilleNumber = scaleIntervals.indexOf(
  (noteValue - rootValue + 12) % 12
) + 1;  // +1 because Nashville is 1-indexed

// If not in scale, nashvilleNumber = 0 or null

Test Cases

C Major scale, notes C-D-E-F-G-A-B:

C → 1 (root)
D → 2
E → 3
F → 4
G → 5
A → 6
B → 7
C# → null (not in scale)

Mode Derivation Verification

Each mode starts on a different scale degree of the parent scale.

From C Major (Ionian)

Ionian (I):     C D E F G A B  [0,2,4,5,7,9,11]
Dorian (II):    D E F G A B C  [0,2,3,5,7,9,10]
Phrygian (III): E F G A B C D  [0,1,3,5,7,8,10]
Lydian (IV):    F G A B C D E  [0,2,4,6,7,9,11]
Mixolydian (V): G A B C D E F  [0,2,4,5,7,9,10]
Aeolian (VI):   A B C D E F G  [0,2,3,5,7,8,10]
Locrian (VII):  B C D E F G A  [0,1,3,5,6,8,10]

Verify Mode Intervals

If implementing a mode, verify against this transformation:

// Mode intervals from parent major scale
function getModeIntervals(modeNumber: number): number[] {
  const major = [0, 2, 4, 5, 7, 9, 11];
  const startIndex = modeNumber - 1;

  return major.map((_, i) => {
    const sourceIndex = (startIndex + i) % 7;
    const interval = (major[sourceIndex] - major[startIndex] + 12) % 12;
    return interval;
  }).sort((a, b) => a - b);
}

Fretboard Verification

Open String Notes (Standard Guitar Tuning E-A-D-G-B-E)

String 6 (low E): E = 4
String 5: A = 9
String 4: D = 2
String 3: G = 7
String 2: B = 11
String 1 (high E): E = 4

Fret Verification Points

Fret 5 on low E string: A (9) ✓
Fret 7 on A string: E (4) ✓
Fret 12 on any string: Same note as open (octave) ✓

Octave Calculation

// Standard MIDI octave calculation
// Middle C (C4) = MIDI 60
// C0 = 12, C1 = 24, ... C4 = 60

octave = Math.floor(midiNote / 12) - 1;
noteValue = midiNote % 12;

// For fretboard display
baseOctave = getStringBaseOctave(stringIndex);
octave = baseOctave + Math.floor((openNote + fret) / 12);

Piano Keyboard Verification

Key Position to Note

// White keys in octave: C D E F G A B (indices 0,2,4,5,7,9,11)
// Black keys: C# D# F# G# A# (indices 1,3,6,8,10)

function isBlackKey(noteValue: number): boolean {
  return [1, 3, 6, 8, 10].includes(noteValue);
}

61-Key Keyboard (Standard)

• Starts at C2 (MIDI 36)
• Ends at C7 (MIDI 96)
• Middle C (C4) is key 25

Debugging Checklist

When notes display incorrectly:

1. Verify root note value is correct (C=0, C#=1, etc.)
2. Check interval array is correct for scale/chord
3. Verify modulo 12 is applied consistently
4. Check for off-by-one in array indexing
5. Verify preferSharps is being respected
6. Test with C root (simplest case) first
7. Test with F# root (catches many edge cases)
8. Play the notes - does it sound right?

Console Debugging Helpers

// Add to MusicTheoryService for debugging
debugNote(noteValue: number, preferSharps: boolean = true): string {
  const sharps = ['C', 'C#', 'D', 'D#', 'E', 'F', 'F#', 'G', 'G#', 'A', 'A#', 'B'];
  const flats = ['C', 'Db', 'D', 'Eb', 'E', 'F', 'Gb', 'G', 'Ab', 'A', 'Bb', 'B'];
  return (preferSharps ? sharps : flats)[noteValue % 12];
}

debugScale(rootValue: number, intervals: number[]): void {
  console.log('Scale notes:', intervals.map(i =>
    this.debugNote((rootValue + i) % 12)
  ).join(' '));
}

debugChord(rootValue: number, intervals: number[]): void {
  console.log('Chord notes:', intervals.map(i =>
    this.debugNote((rootValue + i) % 12)
  ).join(' '));
}

Reference Tables

Circle of Fifths (Clockwise)

C(0) → G(7) → D(2) → A(9) → E(4) → B(11) →
F#(6) → C#(1) → G#(8) → D#(3) → A#(10) → F(5) → C

Interval Names to Semitones