Dynamic Tonality - Example: C2ShiningC

Example: C2ShiningC

An example of Dynamic Tonality can be heard in "C to Shining C" C2ShiningC (composed and recorded by William Sethares in April 2008). This sound example contains only one chord, Dmaj (the piece is, oddly enough, recorded or transposed in the recording to D major), played throughout, yet a sense of harmonic tension is imparted by a tuning progression and a timbre progression:

Cmaj 19-tet/harmonic -> Cmaj 5-tet/harmonic -> Cmaj 19-tet/consonant -> Cmaj 5-tet/consonant

  • The timbre progresses from a harmonic timbre (with partials following the harmonic series) to a 'pseudo-harmonic' timbre (with partials adjusted to align with the notes of the current tuning) and back again.
  • Twice as rapidly, the tuning progresses (via polyphonic tuning bends), within the syntonic temperament, from an initial tuning in which the tempered perfect fifth (P5) is 695 cents wide (19-tone equal temperament, 19-tet) to a second tuning in which the P5 is 720 cents wide (5-tet), and back again.

As the tuning changes, the pitches of all notes except the tonic change, and the widths of all intervals except the octave change; however, the relationships among the intervals, as defined by the temperament's comma sequence, remain constant throughout. This consistency among a temperament's interval relationships is what makes tuning invariance possible (Milne, 2007).

In the syntonic temperament, the tempered major third (M3) is as wide as four tempered perfect fifths (P5's) minus two octaves -- so the M3's width changes across the tuning progression

  • from 380 cents in 19-tet (P5 = 695), where the Cmaj triad's M3 is very close in width to its just width of 386.3 cents,
  • to 480 cents in 5-tet (P5 = 720), where the Cmaj triad's M3 is close in width to a slightly flat perfect fourth of 498 cents, making the Cmaj chord sound rather like a Csus4.

Thus, the tuning progression's widening of the Cmaj's M3 from a nearly-just major third in 19-tet to a slightly flat perfect fourth in 5-tet creates harmonic tension, which is relieved by the return to 19-tet.

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