Major sixth
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A major sixth is the larger of two commonly occurring musical intervals that span six diatonic scale degrees. The prefix 'major' identifies it as being the larger of the two (by one semitone); its smaller counterpart being, a minor sixth. The major 6th is abbreviated as M6, and its inversion is the minor third. Its most common occurrence is between the third and (upper) root of minor chords.
A major sixth in just intonation most often corresponds to a pitch ratio of 5:3 or 1.6666, or various other ratios, while in an equal tempered tuning, a major sixth is equal to nine semitones, a ratio of 1:29/12 (approximately 1.682), or 900 cents, 15.641 cents wider. The ratios of both major and minor sixths are the ratios of pairs of consecutive numbers of the Fibonacci sequence: 5 and 8 for a minor third and 3 and 5 for a major third, the golden ratio lying between the minor sixth and the major sixth.
The major sixth is one of the most consonant intervals after the unison, octave, perfect fifth, and perfect fourth. In the common practice period, sixths were considered interesting and dynamic consonances along with their inverses the thirds, but in medieval times they were considered dissonances unusable in a stable final sonority.