|
Determining Chord Roots |
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Series II lists the interval classes (in Hanson symbol terminology, PMNSDT) and the intervals within an octave (in semitones, 1-11) by relative stability (from left to right, most stable to least stable). The roots of each interval (according to Hindemith) are marked with an "R"—for example, the root of a perfect 5th (7 semitones) is its lower note, while the root of a perfect 4th (5 semitones) is its upper note. The tritone (T, or 6 semitones) is rootless. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
(all math mod 12)
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| According to Hindemith, the root of a chord is the root of its "best" interval, i.e., the most stable interval lowest in the chord's voicing. To find the best interval, begin by calculating the intervals from the upper voices to the bass, then continue by calculating the intervals from the upper voices to each successive chord member above the bass (doublings are ignored). The best interval is the most stable interval formed against the lowest chord member; its root is the root of the chord (refer to Series II). The process is illustrated in the table to the right. |
|
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
The interval, <2,7>, is the best interval (5 semitones); its upper note, 7, is its root. So, 7 is the root of the chord, 2-8-5-E-7.
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||