Quantifying a “good” melody – Interval Repetition

Repetition of Invervals

In music theory, the term interval describes the distance between notes. We measure this distance in half steps or semitones. Interval names consist of a quality followed by a ordinal number (i.e. Minor 2nd, Major 3rd, Perfect 5th). The way in which intervals are named can be confusing at first so let’s focus on one thing at a time.

The ordinal numbers come from the letter names used in SPN. An interval of a 2nd always consists of two adjacent letters in our musical alphabet (C-D, A-B, and G-A) while a 5th is comprised of notes that are 5 letters apart (C-G, F-C, and D-A).

There are 5 types of interval qualities (major, minor, augmented, diminished, and perfect). The major scale serves as the template for naming these interval qualities

• C-C = Perfect Unison
  • 0 Semitones
• C-D = Major 2nd
  • 2 Semitones
• C-E = Major 3rd
  • 4 Semitones
• C-F = Perfect 4th
  • 5 Semitones
• C-G = Perfect 5th
  • 7 Semitones
• C-A = Major 6th
  • 9 Semitones
• C-B = Major 7th
  • 11 Semitones
• C-C = Perfect 8th (Octave)
  • 12 Semitones

We can understand the other qualities based on Major and Perfect intervals:

• Major – 1 semitone = Minor
• Major – 2 semitones = Diminished
• Major + 1 semitone = Augmented
• Perfect – 1 semitone = Diminished
• Perfect + 1 semitone = Augmented

Ok, now that all of that’s out of the way, let’s look at Happy Birthday again.

Here’s a sequential list of all of the intervals in Happy Birthday:

• G4-G4 = Perfect Unison
• G4-A4 = Major 2nd Ascending
• A4-G4 = Major 2nd Descending
• G4-C5 = Perfect 4th Ascending
• C5-B4 = Minor 2nd Descending
• B4-G4 = Major 3rd Descending
• G4-G4 = Perfect Unison
• G4-A4 = Major 2nd Ascending
• A4-G4 = Major 2nd Descending
• G4-D5 = Perfect 5th Ascending
• D5-C5 = Major 2nd Descending
• C5-G4 = Perfect 4th Descending
• G4-G4 = Perfect Unison
• G4-G5 = Perfect Octave Ascending
• G5-E5 = Minor 3rd Descending
• E5-C5 = Major 3rd Descending
• C5-C5 = Perfect Unison
• C5-B4 = Minor 2nd Descending
• B4-F5 = Diminished 5th Ascending
• F5-F5 = Perfect Unison
• F5-E5 = Minor 2nd Descending
• E5-C5 = Major 3rd Descending
• C5-D5 = Major 2nd Ascending
• D5-C5 = Major 2nd Descending

If we condense this list to eliminate repeating intervals we get the following:

• 5 Perfect Unisons
• 3 Minor 2nds
• 7 Major 2nds
• 1 Minor 3rd
• 3 Major 3rds
• 2 Perfect 4ths
• 1 Diminished 5th
• 1 Perfect 5th
• 1 Perfect Octave

Out of 24 total intervals here’s the statistical breakdown:

• 21% Perfect Unisons
• 12.5% are Minor 2nds
• 29% are Major 2nds
• 4% are Minor 3rds
• 12.5% are Major 3rds
• 8% are Perfect 4ths
• 4% Diminished 5ths
• 4% Perfect 5ths
• 4% Perfect Octave

It’s worth noting that vocal melodies, that is melodies meant to be sung, typically contain intervals smaller than a 7th and stay inside the range of an octave. This is especially true of songs meant to be sung by amateurs.