Diminished seventh chord in the context of "Irregular resolution"

In music, tonicization is the treatment of a pitch other than the overall tonic (the "home note" of a piece) as a temporary tonic in a composition. In Western music that is tonal, the piece is heard by the listener as being in a certain key. A tonic chord has a dominant chord; in the key of C major, the tonic chord is C major and the dominant chord is G major or G dominant seventh. The dominant chord, especially if it is a dominant seventh, is heard by Western composers and listeners familiar with music as resolving (or "leading") to the tonic, due to the use of the leading note in the dominant chord. A tonicized chord is a chord other than the tonic chord to which a dominant or dominant seventh chord progresses. When a dominant chord or dominant seventh chord is used before a chord other than the tonic, this dominant or dominant seventh chord is called a secondary dominant. When a chord is tonicized, this makes this non-tonic chord sound temporarily like a tonic chord.

In music, an interval cycle is a collection of pitch classes created from a sequence of the same interval class. In other words, a collection of pitches by starting with a certain note and going up by a certain interval until the original note is reached (e.g. starting from C, going up by 3 semitones repeatedly until eventually C is again reached - the cycle is the collection of all the notes met on the way). In other words, interval cycles "unfold a single recurrent interval in a series that closes with a return to the initial pitch class". See: wikt:cycle.

Interval cycles are notated by George Perle using the letter "C" (for cycle), with an interval class integer to distinguish the interval. Thus the diminished seventh chord would be C3 and the augmented triad would be C4. A superscript may be added to distinguish between transpositions, using 0–11 to indicate the lowest pitch class in the cycle. "These interval cycles play a fundamental role in the harmonic organization of post-diatonic music and can easily be identified by naming the cycle."

The half diminished scale is a seven-note musical scale. It is more commonly known as the Locrian ♮2 scale or the Aeolian ♭5 scale, names that avoid confusion with the diminished scale and the half-diminished seventh chord (minor seventh, diminished fifth). It is the sixth mode of the ascending melodic minor scale.

In the key of B♭, the half-diminished scale built on C is associated with Cm, which functions as a ii chord in minor (see chord-scale system).