Lecturenotes 2
  • scale quiz weds
    review key signatures, clef
    briefly go over modes
    introduce minor mode
    Some useful reference sites
  • Review concepts of interval quality/scale degree quality
    • intervals have qualities, just as scale degrees do
  • The perfect 5th and 4th
    • 5 or 4 letter names, never mix # and b. Both notes must have the same accidental except:
      • if a b and an f is involved, one of them, but not both, will be # or b (either b-f# or bflat-f)
    • There are 6 different 5ths/4ths in any major scale, more than any other interval
    • The first and the 5th degrees of the scale, tonic and dominant
  • Interval 'inversion'
  • Practice singing 5ths and 4ths, using familiar tunes
  • Brief history of the perfect 5th
    • In medieval music
      • As focal notes in chant
  • The Circle of 5ths/4ths (memorize this series)
    • Any 7 note segment is a major scale, bounded by the 7th and 4th degrees of that scale
    • This demonstrates the proximity of scales (number of intersecting notes).
    • Also demonstrates unique multiplicity of intervals in scale
    • brief description of pythagorean comma
      • 4/3 is frequency ratio of perfect 4th in overtone series
      • (4/3)^12 = 31.56929179344461567487 (complete circle of 4ths, c to b#)
      • but, stack of 12 4ths should span 6 octaves, 32 times frequency of first pitch, if enharmonic equivalence is to hold (c is some octave equivalent of b#). The difference between just and equal tempered ratios is called the Pythagorean comma, .2346 of a semitone, or about 24 cents, or about a quarter of a semitone (100 cents per semitone). (The difference between 32 and 31.569 etc is about .2346 of a semitone).
      • This is why it's so hard to tune a guitar
      • Some music using perfect intervals
      • The tempered tuning we use uses frequency ratios that are powers of 2, an interval x thus has the frequency ratio of 2 ^(x/12).
        • The difference between a tempered third (2^(4/12)) and a just third 5/4, e.g. is about 14 cents, or about 1/8th of a semitone.
        • The perfect 5th (just = 3/2, tempered = (2**(7/12)) differs by only 2 cents, or about 1/50th of a semitone.
        • The wider the distance in the circle of 5ths, the more out of tune it will be
        • examples of a few just intervals
          • Perfect 5th = 3/2
          • perfect 4th = 4/3
          • major 3rd = 5/4
          • minor 3rd = 6/5
          • major 2nd = 9/8
        • supercollider tuning demo
  • Tritones
    • only one tritone per scale.
    • To form a tritone(aug 4th/dim 5th
  • The fifth as a structural interval
    • Relation between structral significance of 5ths and tetrachord identity.
    • Importance of the 5th harmonically
      • Tonic and Dominant relations (much more on this later)