Integrated Music Theory 2023-24

Discussion 2e - The Overtone Series

Overtone Overview

Overtone Series

  • Notes in the overtone series in C: C, C, G, C, E, G, Bb, C, D, E, F#, G
  • The order of the overtone series in intervals - P8, P5, P4, M3, m3, m3, M2, M2, M2, M2, m2
  • Major scales are based on stacking perfect fifths (the first interval with two different pitches)
  • Intonation is based on how you divide the octave. If you divide it into 12 equal tones (equal temperament), it doesn’t perfectly line up the the overtone series. The tuning system that uses the overtone series is called “Just Intonation”.

Methods for memorizing how to write out an overtone series

  • 854-3332 + Lydian scale to the fifth
    • This method requires you to remember the quality of the intervals in the “phone number,” and also that the “scale” includes the last note of the phone number as Do
  • Can think of it in sections of tonic, subdominant, dominant
    • Working in C, the first 4 notes suggest C, the next 4 suggest the dominant of F (C’s subdominant), and the last 4 are Sol La Ti Do in G (C’s dominant)

“Why are certain intervals consonant verses dissonant?”

  • When the frequency of a tone lines up well with the frequency of another tone, we hear it as consonant.
  • The most simple ratio we can create is 2:1, where a tone vibrates at one half the frequency of another tone. We call this an octave. The next simplest ratio is 3:2. We call this a perfect fifth. As the ratios between two frequencies become more complex, the interval becomes more dissonant.

Equal Temperament vs. Just Temperament

  • Equal temperment means that every pitch is equally spaced apart in frequency.
  • Just temperment is when notes are tuned to the overtones of one fundamental pitch.

“How do we differentiate timbre?”

  • Every sound produces overtone, and our brain organizes all of the extra tones we hear into one sound. Different timbres occur becuase every sound source contains different levels of overtones.
  • A “big” sound (the kind we usually hear in professional musicians) just means that there’s a strong fundamental and a LOT of presence of the overtones within that person’s sound.

If the overtone series exists everywhere, how did non-twelve-tone music evolve?

  • In the case of gamelan and some types of Indian music, these systems were based off of the instruments constructed to play that music, not the voice.