Pythagoras
- 6th century B.C.
- Fable of the Blacksmith Hammers
Harmony of the Spheres
- Relation of the proportion of heavenly bodies
- Planet “hums” based on orbital rotation
Overtones
Fundamental – Base sounding tone
Overtone – sympathetic vibrations
Harmonics – overtones whose frequencies are whole number ratios with the fundamental
The presence or absence of certain overtones helps define the timbre (tone color) of certain instruments.
The Harmonic Series
The 4,5,6, & 7 partials form a dominant seventh chord
Intervals
Pythagorean Hotline: 854-3332
Dominant Seventh
- The original “standard” dissonance in common practice, western music.
- Combination of two triads to create a chord containing the tritone
Tritone Resolution
The two diatonic notes in the tritone are the most unstable melodic tones in a major scale and should resolve to their closest diatonic neighbors.
The root motion of V-I is also a very powerful force in the dominant seventh resolution.
Leading Tone Sevenths
- Combination of supertonic and leading tone triads
- Common substitution for V7 (though it doesn’t have the V-I root movement
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