Intervals

• lower tone = fundamental tone
• There are two groups that intervals can be classified into
  • Group I
    • major, minor, diminished, augmented intervals
      • seconds, thirds, sixths, sevenths
  • Group II
    • perfect, augmented, diminished intervals
      • unisons (primes), octaves, fifths, fourths
• This chart illustrates the different amounts of whole tones and semitones per interval (whole and half tones)

” = same word repeated downward

Naming Intervals

• From this information we are able to piece together the quality and quantity of intervals, as shown below

• quality – the type of interval
  • major, minor, augmented, diminished, perfect
• quantity – the distance of the interval
  • 1,2,3,4,5,6,7,8,9….

Inverting Intervals

Quantity

• When inverting intervals, the quality reverses and the quantity needs to add up to 9
  • 1+8=9
  • 2+7=9
  • 3+6=9
  • 4+5=9
  • 5+4=9
  • 6+3=9
  • 7+2=9
  • 8+1=9

Quality

• Perfect intervals remain perfect
  • P5 → P4
  • P4 → P5
• Augmented intervals become diminished intervals and visa versa
  • A3 → d6
• Major intervals become minor and visa versa
  • m7 → M2

Classifying Intervals

• Consonances
  • P1, P8, P5, M3, M6, m3, m6
  • Imperfect
    • M3, M6, m3, m6
  • Perfect
    • P1, P8, P5
• Dissonances
  • M2, M7, m2, m7, all diminished and augmented intervals
• P4
  • depends on usage in music
  • it is more inclined to be a dissonance

Harmony

• simultaneous concordance of musical tones