The foundational intervals of D地i music are traditionally derived by dividing a taut string into equal parts, then stopping the string at various locations along its length and plucking the two resulting segments to produce an interval. The intervals produced are classified as major and minor, depending on how the string is divided.
Early musicians divided their string into twenty-five equal parts. The major intervals were obtained by stopping the string at those positions which represented multiples of five, in a sense re-dividing the string into five equal parts. This resulted in two intervals: a Western double octave at the five and twenty stop (a ratio of 1:4), a Western perfect fifth at the ten and fifteen stop (a ratio of 2:3). See the right side of the diagram for an interactive demonstration of the major intervals.
The major intervals were highly valued by early musicians for a number of reasons. Collectively, they produced a pitch in three octaves plus a perfect fifth (and, by inversion, a perfect fourth); these simplest and most consonant intervals would be the building blocks of early compositional practice, and remain the most dominant sonorities of D地i music for millennia. Additionally, the reflexivity of the stops along the string痴 length -- the first stop divided it into five and twenty, the second into ten and fifteen; the third into fifteen and ten, the fourth into twenty and five -- was greatly admired and further reinforced the aesthetic weight accorded the major intervals.
The minor intervals were obtained through freer experimentation with stops, both in between the major multiples of five and absent any stops at all. The most important result of this experimentation was the discovery of the semitone. A free string without a stop produced a pitch a Western major third below the major octaves. Stopping the string at one twenty-fifth its length (a ratio of 1:24), however, produced a pitch a Western minor third below the major octaves -- a semitone above the unstopped string -- and a Western perfect fifth many octaves above it. (See the left side of the diagram for minor intervals.) With the semitone discovered, the twelve chromatic pitches we are familiar with were not long to follow.
Interestingly, the D地i method of dividing the string yields a just intonation tuning system, one which took the West a number of centuries to devise but was eventually supplanted by well and equal temperament as modulation between keys became compositionally important. Quite the opposite, early and later D地i music recovered thus far reveals no significant interest in modulation. This suggests that D地i retained just intonation.
Thus, the major intervals give us the basic architecture of D地i music -- octave, perfect fifth, perfect fourth -- and the minor intervals give us its interior -- semitones. Though not considered until later in D地i music history, if we take both major and minor intervals at the same time, we also get major and minor thirds. While they do not figure significantly into pre-Renaissance music, thirds and other intervals do become important in later stylistic developments.
