Music Theory
Acoustic Composition
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Quantifying a “good” melody – Note Repetition

Repetition of Notes

In music theory, notes refer to pitches that fall into our equal tempered (evenly spaced) system. We can quantify these pitches using Scientific Pitch Notation (SPN). This system uses the note name followed by a number to indicate the octave. For instance, middle C is notated as C4, while the lowest note on an 88 key piano is A0 and the highest note on an 88 key piano is C8. Let’s use SPN to quantify note repetition in the melody Happy Birthday.

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Out of the 25 total notes in this melody we can see there are only 8 different pitches ranging from G4-G5. Here’s a statistical breakdown of the occurrence of each pitch:

  • G4 – 8/25 = 32%
  • A4 – 2/25 = 8%
  • B4 – 2/25 = 8%
  • C5 – 6/25 = 24%
  • D5 – 2/25 = 8%
  • E5 – 2/25 = 8%
  • F5 – 2/25 = 8%
  • G5 – 1/25 = 4%

At this point you might be wondering how much of this is actually important. You have probably played and listened to music for years without considering note repetition. To further illuminate the importance of note repetition, let’s look at two other melodies. One with a high degree of repetition and one with zero repetition.

Nobody Knows the Trouble I’ve Seen – Traditional tune, first published in 1867

Once again we see an octave range, but this time it’s between E4 and E5. This melody has 31 notes and 6 distinct pitches.

  • E4 – 4/31 = 13%
  • F#4 – 4/31 = 13%
  • A4 – 6/31 = 19%
  • B4 – 3/31 = 10%
  • C#5 – 13/31 = 42%
  • E5 – 1/31 = 3%

Nobody Knows the Trouble I’ve Seen has been recorded countless times by artists such as Marian Anderson, Lena Horne, Louis Armstrong, Harry James, Paul Robeson, and Sam Cooke. Prior to being recorded, it was passed down through an aural tradition. Its survival in history at one point depended on its memorability and repetition!

In contrast, let’s look at a 31 note melody that has no repetition.

Note: It’s surprisingly difficult to write a 31 note melody that contains no repetition.

The range of the melody is much wider to accommodate 31 unique pitches. Our lowest note is an A3 and our highest note is a D#6 which gives us a 2.5 octave range. Since each note occurs only once there’s no need to provide a statistical breakdown of repetition, however you might notice that even without note repetition there’s still a sense of organization.

How is it possible that this still feels like a melody even though there’s zero repetition of notes?