The dissonant level of triadic chords

 Based on Sethares (2010) model to analyse the dissonant level between intervals, can also be expanded to measure the dissonant level of chords. In today's case, triadic chords, I calculated the common triads and 7th chords for comparison. Calculating the dissonant level of a chord is the sum of all the intervals in a chord (pic below). The same concept of calculating the dissonant of a note with harmonic partials.

Illustration of calculating a chord
Here is the calculation of the chords commonly used and sorted by the level of dissonance. The minor triad has a low dissonant level than the major. It is due to the note of the major 3rd interval is higher than the minor 3rd one. According to the equal-loudness contour, our ears are more sensitive to the higher pitch, thus, we perceive a louder tone and more dissonant. If we disregard the loudness factor of the pitch, the major and minor triad is composed with the same intervals, major 3rd, minor 3rd and perfect 5th, both of them should produce the same level of dissonance. 

ChordNotesDissonant
Minor triadC4Eb4G4C429.85773182
Major triadC4E4G4C431.97616471
Minor seventhC4Eb4G4Bb435.22296816
Major seventhC4E4G4B440.35804472
Dominant seventhC4E4G4Bb440.55303597
Augmented triadC4E4G#4C441.75415674
Half-diminished seventhC4Eb4Gb4Bb442.39034597
diminished triadC4Eb4Gb4C442.63317171
Augmented major seventhC4E4G#4B446.12333161
Diminished seventhC4Eb4Gb4Bbb46.34417635
Major seventh flat fiveC4E4Gb4B447.4465677
Minor major seventhC4Eb4G4B450.60406598
Augmented seventhC4E4G#4Bb451.01518015
Dominant seventh flat fiveC4E4Gb4Bb451.55220353
Diminished major seventhC4Eb4Gb4B453.86079921

This recalls the musical set theory, in the prime form, in its most compact form which sorts the interval from the narrowest of a type of chord. Major and minor are treated as the same. The calculation is very applicable to the set theory, linking the interval vector to the dissonant model. The interval class can be a scoreboard, each occurrence of an interval adds up the dissonant level, and different interval adds up to a different degree.

The next step, it will be more all-rounded if it is considered all types of inversion.

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