The interval 1) the distance between two pitches 2) two notes combine to form an interval of an Augmented 6th is created when the sixth degree of the major scale a group of pitches arranged from high to low covering one octave is lowered a half step a semitone, the octave is divided into twelve half steps, and the fourth degree of the scale is raised a half step.
This Augmented 6th has the same sound and the same number of half steps as the minor 7th, ten half steps. Three slightly different chords are built around this interval.
The German 6th chord a group of three or more tones forming a harmony:
Root, M3, P5, Aug6 (Aug6 sounds like m7)
The French 6th chord:
Root, M3, Aug4, Aug6
The Italian 6th chord:
Root, M3, Aug6
The normal resolution music moving from greater to lesser tension, a dissonant chord or interval followed by a consonance of the Augmented 6th chord is:
The Augmented 6th expands to the octave an interval with the same note names but twelve half steps higher or lower and moves to the V chord.
Jazz musicians use this progression of a dominant 7 a Major chord with a m7th built on the fifth degree of the Major or minor scale, V7 chord moving down a half step to the chord below. It is called the tritone substitute. The secondary dominant is replaced with a dominant that is a tritone away from it. The result is a dominant 7 chord that is a half step above the chord it leads to.
see also: Staff Roman Numeral Chords, Roman Numeral Chords