Harmony: Circle of Fifths, Flat Seventh Chords

You know that key signatures are generated by altering major scales by either raising the fourth degree or lowering the seventh degree. This corresponds to beginning a new major scale a fifth above or a fifth below, respectively. In C-major we suggest G-major by raising the F to F# and we suggest F-major by lowering the B-natural to B-flat. These rules apply to all keys. In harmony, raising the fourth transforms the ii chord to a major chord, which because of its function in relation to the V chord becomes the dominant of the dominant or V/V chord, otherwise it is just a new major chord on the second degree of a preexisting scale, a II chord. So, in C-major altering the F to F# changes a d-minor chord to D-major which can function as the dominant of G-major which in turn is the dominant of the original key of C-major. The D-major chord functions as V/V or "Five of Five" chord.

The modulation I IV is very pleasant, given the name of Plagel and is frequently used at the end of pieces to relax the listener with a gentle harmonic release. It is called the feminine cadence or half cadence and is often used even if the piece returns to the tonic via a V-I modulation as is often the case in Bach chorales and fugues for the organ, for example, but these cadential modulations are extremely common in popular mauic as well. Endings where the haronmy sways back and forth V-IV-I-IV etc. are common. One of the most fetching examples is at the end of Beethoven's "Heiliger dankesang" or the third movement from the String Quartet in A-minor #15 Op. 132.

Flattening the seventh degree of the I ( called tonic chord ) suggests a new chord that also modulates to IV. When constructed over the tonic triad it functions like an altered dominant chord of the new key in the sub-dominate. This chord is called the dominant-seventh chord and is extremely significant in the history of music. In C-major, we flatten the seventh degree, B to B-Flat, the resulting chord is a C-Major Flat Seventh chord that functions as a dominant to IV or V7/IV. We could write it as a I7 - IV, but V7/IV - IV better signifies its function. ( To be precise we should name these V flat 7 or I flat 7 or use the flat symbol from music notation. The above shortcut is understood to mean that.)