Sympathetic Vibratory Physics

Degree of Harmonicity is determined by chordal components (notes and intervals).

For each pair of notes in one octave, some intervals will create harmony (analogous to attraction), and others will create discord (analogous to repulsion). Here’s how this could be structured:

Perfect consonance (like constructive interference or in-phase vibrations):
Unison (C to C)
Perfect Fifth (C to G)
Octave (C to high C)

Moderate consonance:
Major Third (C to E)
Perfect Fourth (C to F)

Moderate dissonance (akin to mild out-of-phase vibrations):
Major Sixth (C to A)
Minor Third (C to Eb)

Strong dissonance (like destructive interference or out-of-phase vibrations):
Minor Second (C to Db)
Major Seventh (C to B)
Tritone (C to F#)

Each interval can be understood as producing varying degrees of harmony or discord, based on how closely related the frequencies are (just as in Bjerknes' experiments where vibrational phase alignment affects physical attraction or repulsion). This model aligns musical intervals with physical principles of phase alignment, offering a way to interpret harmony and dissonance through vibrational behavior.

If you switch from the diatonic to the chromatic scale, the number of intervals and potential relationships expands significantly, as the chromatic scale includes all twelve semitones in the octave. This change introduces more dissonant intervals due to the closer proximity of the notes.

Key differences include:

More dissonant intervals: The chromatic scale contains more minor seconds, tritones, and sevenths, which are more discordant.
Consonant intervals stay consistent: Perfect fifths, octaves, and major thirds will still be considered harmonic, though they appear less frequently.

The Bjerknes analogy would reflect a wider range of possible vibrational relationships, both in-phase (harmony) and out-of-phase (discord). The overall pattern holds, but the number of potential interval interactions increases dramatically.

Let’s create a concordance to discordance scale matching the most consonant intervals to the most dissonant, as per both standard musical theory and the Bjerknes Effect analogy.

Most Concordant:
Unison (Perfect phase alignment, maximum attraction)
Perfect Fifth
Octave

Moderate Concordance:
Major Third
Perfect Fourth
Major Sixth

Moderate Discordance:
Minor Third
Minor Sixth

Most Discordant:
Minor Second (Maximum out-of-phase, strongest repulsion)
Major Seventh
Tritone (Augmented Fourth/Diminished Fifth)

This reflects increasing discord as intervals become closer or involve more complex ratios, mirroring the interference effects in Bjerknes' experiments. [from Hurricane Set to Music]

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Degree of Harmonicity