Overthink: Created page with a bit of theory

2025-10-02T22:58:33Z

Created page with a bit of theory

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In western music, the most important chords are the major and minor triads. The major chord is build with a root ([[1/1]])), a major third ([[5/4]]), and a fifth ([[3/2]]). The intervals between consecutive notes in this chord are 5/4, 6/5, and 4/3 in that order, with 4/3 being the interval between the fifth and a copy of the root an octave up. To obtain the minor chord, we invert the order of the intervals to 4/3-6/5-5/4, to get a chord of 1-4/3-8/5. At first this seems entirely different from our original major chord, but if we cycle the intervals to 6/5-5/4-4/3, we get the chord 1-6/5-3/2, which shares the perfect fifth 3/2 with the major chord. Note that this chord is just an inversion of 1-4/3-8/5. Also note that the major chord [[4:5:6]] is [[otonal]], and the minor chord [[10:12:15|1/(4:5:6)]] is [[utonal]]. In xenharmonic music, however, there are many more consonant chords than these.
== Major-Minor pairs ==
We then consider the fundamental otonal chord of the 7-limit, the harmonic seventh chord [[4:5:6:7]]. What is the corresponding minor chord? The intervals between consecutive notes in order are 5/4-6/5-7/6-8/7. Inverting the order of these intervals gives us a chord with intervals between consecutive notes 8/7-7/6-6/5-5/4, which can be inverted to 6/5-5/4-8/7-7/6. Above the root, the notes of this chord are 1-6/5-3/2-12/7, which just like the 5-limit minor chord, shares the 3/2 with the "major" 4:5:6:7 chord.

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Overthink: Created page with a bit of theory