In this page I have analysed one of Bach’s fugues from “The Well Tempered Piano” to see how he used the mechanisms of imitation, inversion, augmentation and diminution rhythms and phrases to build his composition.
The first phrase is completely transparent. It starts just off the first beat of the bar. Bach is just stating the original theme for all to hear the “subject” of the Fugue. The phrase is just 6 bars long. Within bar 2 we hear the phrase comes back in on the right hand as an imitation of the initial phrase. In bar 3 on beats 1 and 2, we hear an inversion of the original theme.
In the pick up of bar 2 Bach uses imitation and slightly develops the rhythm in bar 4 at beats 3 and 4. He also augments the phrase. The phrase is imitated again in bar 5. This time the phrase is an octave lower. The rhythm is imitated at the end of bar 6, only, this time, Bach has augmented the phrase. He also used the same mechanism at the start of bar 7. During Bar 8 Bach sustains a long D note in the bass line. It is my hypothesis that Bach sustained the dominant note in the bass to punctuate a diminished phrase. It also draws more attention to everything else happening in the left hand. In bar 9 the whole phrase is inverted.
In the right hand at beat 4 of bar 10, we hear a diminished rendition of the initial phrase. The original phrase then recapitulates in bar 12 where it is further developed with the addition of further notes and transposed in to the relevant major key of Bb. In bar 15 the subject of the fugue returns but transposed in to F major (the dominant major.) The overall phrase, from bar 12, ends on beat 2 of bar 17. In bar 13, however, we hear a similar rhythm that is augmented on beats 3 and 4 of bar 17.
At Bar 17, we hear 2 versions of the main theme being performed. One is at the start of the bar 17 and the other version ends at the end of the bar. In the bass line the rhythm is slightly developed at the end of beat 3 and in beat 4. This is overlapped with an inversion in the right hand. The phrase then returns back to the original in both bars 20 and 21.
The returning Rhythm inverts at bar 23 from where the rhythm is developed in to the inversions of scales at bar 25. These rolling scales run through until bar 29, where the bass hand announces the presence of the returning theme. Bar 30 is based on an inversion and the theme then re-occurs one last time at bar 31 this then takes us to the end of the piece.