THE EXTRINSIC AND INTRINSIC TONICS OF THE INTERVAL
Intervals can certainly be considered the most archaic and elementary elements of music; they come before diatonic scales, perhaps even before overtones, and there would be much to say about the latter—and above all, much to disagree with, considering Hindemith's theory on them.
Music is also governed by an irrepressible gravitational force that interacts with the human perception of sound. This force acts particularly on intervals, but in a different manner depending on whether we consider the interval within the context of a diatonic scale—and thus playing a role within the scope of a tonality (the extrinsic tonic of the interval)—or as something in itself, i.e., detached from any concept of tonal character and therefore not falling within a diatonic concept (the intrinsic tonic of the interval).
EXTRINSIC TONIC OF THE INTERVAL:
Let us consider the C chromatic scale, that is, the scale that has C as its tonal center and proceeds by semitones up to the next C. After all, all altered and unaltered diatonic scales are extracted from the chromatic scale, so it makes no sense to consider them one by one.
The intervals C/C# - C/D – C/D# - C/E – C/F - C/F# - C/G – C/G# - C/A – C/A# - C/B have their tonic in C because they undergo the attraction of the tonal center, which is obviously C, and therefore tend to resolve in C.
INTRINSIC TONIC OF THE INTERVAL
Any interval, in addition to its attraction toward the tonal center, possesses its own "intrinsic tonic" toward which the other note of the interval tends to resolve. This concept is especially valid within the scope of intervallic harmony, in which diatonic scales are not considered.
I will analyze the various intervals:
Minor 2nd – upper tonic
Major 2nd – lower tonic
Minor 3rd - upper tonic
Major 3rd – lower tonic
Perfect 4th – upper tonic
Augmented 4th – lower tonic
Perfect 5th – lower tonic
Augmented 5th – upper tonic
Major 6th – lower tonic
Minor 7th – upper tonic
Major 7th – lower tonic
The utility of all this within the scope of composing an intervallic line lies in the fact that the note toward which the interval tends to resolve can become a tonal anchor, i.e., a provisional tonal center from which a diatonic scale departs, thus not excluding the presence of tonal or modal diatonic islands within intervallic composition.
Therefore, tonality is flexible and in continuous flux with temporary points of tonality. Tonality understood in this way no longer requires a diatonic tertiary order of harmonization; it is not necessarily centered on a single central tonic for the entire composition. This intervallic harmonic movement, with the creation of provisional tonal centers, has more tonal power than the insignificant assortments of notes that are heard routinely—these tonal centers can include all twelve notes in rotation and have no need to resolve.