relations among pitches

deriving a scale from nature

harmony: relations among pitches

• music is composed of rhythm, melody and harmony
• harmony is about the relations among the pitches of a set of simultaneously occuring pitched sounds
• these relations may be expressed as ratios of frequencies between two pitches
• the simpler the ratio, the less tension the sound creates in the listener

ratios of frequencies between two pitches

• the most consonant pitch ratio: 1:1
• next most consonant: 2:1
• next are 3:2 and 4:3
• applying these ratios to a base pitch results in a scale with 4 steps:
• for example, using a base pitch of 400 Hz:
  • 400 * 2 = 800 Hz
  • 400 * 3/2 = 600 Hz
  • 400 * 4/3 = 533 Hz
  • 400 * 1 = 400 Hz

imagining the beginnings of music

• imagine early man making a crude marimba by trimming sticks until the pitches they emit (when struck) sound good together
• he might easily have used sticks that emit pitches with the same ratios as shown above, since they are the least tense ratios
• he would naturally array these sticks in pitch order
  • low to high
• he has now made a simple scale
• a scale is a set of pitches, called scale steps
• he can now play simple melodies