plagal cadence). Goldman concurs with Nattiez, who argues that "the chord on the fourth degree appears long before the chord on II, and the subsequent final I, in the progression I-IV-vii^o-iii-vi-ii-V-I", and is farther from the tonic there as well. (In this and related articles, upper-case Roman numerals indicate major triads while lower-case Roman numerals indicate minor triads.)

Circle closure in non-equal tuning systems

Using the exact 3:2 ratio of frequencies to define a

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