Thirteenth (interval)

In music, a thirteenth can refer to either an interval or a chord.

Interval

A thirteenth interval is between two notes that are thirteen scale degrees from the root of a chord and also the interval between the root and the thirteenth. The thirteenth is most commonly major or minor. For instance, the interval between C4 and A5 (in scientific pitch notation) is a major thirteenth, while the interval between C4 and A♭5 is a minor thirteenth.

Chord

A thirteenth chord is the stacking of six (major or minor) thirds, the last being above the 11th of an eleventh chord. Thus a thirteenth chord is a tertian (built from thirds) chord containing the interval of a thirteenth, and is an extended chord if it includes the ninth and/or the eleventh. "The jazzy thirteenth is a very versatile chord and is used in many genres." Since 13th chords tend to become unclear or confused with other chords when inverted, they are generally found in root position. For example, depending on voicing, a major triad with an added major sixth is usually called a sixth chord , because the sixth serves as a substitution for the major seventh, thus considered a chord tone in such context.

However, Walter Piston, writing in 1952, considered that, "a true thirteenth chord, arrived at by superposition of thirds, is a rare phenomenon even in 20th-century music." This may be due to four-part writing, instrument limitations, and voice leading and stylistic considerations. For example, "to make the chord more playable [on guitar], thirteenth chords often omit the fifth and the ninth."

Dominant thirteenth chord

Most commonly, 13th chords serve a dominant function (V13), whether they have the exact intervals of a dominant thirteenth or not.