Western harmony gradually adopted higher-numbered harmonic intervals over history.

Evidence

The earliest polyphonic Western music, known as “organum,” made use of the octave, the perfect fifth, and its inversion, the perfect fourth. These are the intervals between the first and second, the second and third, and the third and fourth members of the natural harmonic series, respectively (see Figure 3.3). Later, the major and minor third began to be accepted, the intervals between the fourth and fifth and the fifth and sixth natural harmonics, with their inversions, the minor and major sixth respectively, which are the intervals between the fifth and eighth, and the third and fifth harmonics, respectively. The major triad, consisting of a major third and a minor third, and the minor triad, a minor third and a major third, became the building block of Western tonal harmony. The interval of the minor seventh started to be incorporated, and its inversion the major second, the intervals between the fourth and seventh and the seventh and eighth harmonics respectively. Twentieth-century composers have explored music composed using major and minor whole tones (the intervals between the eighth and ninth and between the ninth and tenth harmonics respectively), semitones (adjacent harmonics above the eleventh are spaced by intervals close to semitones) and microtones or intervals of less than a semitone (adjacent harmonics above the sixteenth are spaced by microtones.) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 933

Categorization

• DEFINE: Maps each historically accepted interval onto its harmonic-series position.
• SEED: Angle: the acceptance history of dissonance as a cultural evolution encoded in physics.
• CANDY: Great conversation fact: organum began with just octaves and fifths, microtones only entered in the 20th century.