About the Rainbow Fugue I started thinking about this piece in November 2001 when I was in bed with pneumonia, my wife Joan looking after me. In beween coughing fits I amused myself by trying to think up a fugue subject that would also be a Schoenberg-type tone-row, i.e. it would use each of the 12 notes of the chromatic scale exactly once. Afterwards I actually managed to compose a fugue using this subject, but it took 15 years, until May or June 2016, to finish. I called it the Rainbow Fugue because the rainbow contains all the colours, and this fugue uses all the chromatic notes, treated equally. The fugue subject comprises the first 12 notes in the 2nd violin part, starting on the note E. The next entry, in the viola part, is an exact transposition of the first entry, starting a tritone lower, on the note B flat. There are 12 subject entries in all, each one starting on a different note of the chromatic scale. The rest of the music is constructed from the 12 notes of the tone row formed from the subject E, C#, C, A# ( = B flat), F#, G#, A, F, D#, G, D, B, in accordance with the following transformation rule: each instrumental part falls into 12-note sections, each of which is formed from the tone row by applying one or more of the following operations (i) transposition (ii) reversing the order (iii) cyclic permutation (which means cutting the row into two segments and putting the second segment before the first instead of after). The first two rules are part of Arnold Schoenberg's method of serial music composition, but the third rule, which gives the composer more freedom, is not. For example, after playing the subject the first violin plays the same 12 notes that constitute the viola's first entry (Bflat, G, F#,...,G#, E#=F), but in reversed order (the so-called retrograde of the transposed row); so this 12-note section was obtained from the original row by using just two of the rules : transposition and reversal of order. And after playing the (transposed) subject the viola plays the 12 notes F, Bflat, G, F#,..., G#; these can be obtained from the transposed row in the viola's first entry (Bflat, G, F#,...,G#, E#=F) by a cyclic permutation, i.e. cutting it between the G# and the E#=F and putting the second segment (comprising, in this case, just the one note F) before the other segment, instead of after it. In the detailed analysis below, the word "retrograde" denotes the reversed row. Of course it is very difficult to write a musical set of parts under these restrictions. That is why it took so long. But I persevered because the method produced a lot of unexpected sounds, a small proportion of which could be fitted together, after a lot of work, to give something that made musical sense. Here is a list of the main melodic events in the fugue and how they are constructed from the original row Bar 1, v2 entry of fugue subject starting on E Bar 6, vla subject entry starts on Bflat Bar 14, cello subject entry starts on G Bar 19, v1 subject entry starts on Dflat Bar 24, v1 melody starts on Bflat which is note 2 (i.e. second note of the transposed row) Bar 27, v1 melody continues, repeating the previous (bar 24) version of the row in different rhythm bar 32, v2 melody starts on Eflat, at note 5 (i.e. 5th note of the transposed row) bar 33, vla melody starts on A, at note 5 (this is a canon with v2) bar 35, v1 melody starts on Bflat, at note 5. This repeats previous v1 melody a 5th higher. bar 36, v2 melody starts on E at note 5, repeating previous v2 part (and hence the entire canon) a 5th higher bar 38, cello entry starts on B bar 40, v1 entry starts on Eflat (this is a canon with cello) bar 45, v2 new melody starts on Fsharp, at note 10 bar 50, v1 same melody starting on A at 10th note bar 54, cello same melody starting on Eflat at 10th note _ bar 62, vla subject entry starts on A bar 64, v2 subject entry starts on D (a canon with vla) bar 66, v1 long slow melody starting on B (1st note of row) bar 71, v2 new melody using retrograde row, starting on C (6th note of retrograde 9 row) bar 73, vla this same melody starting on B (6th note of retrograde) bar 75, v1 same melody again starting on Gflat (6th note of retrograde) bar 77, cello, subject entry starting on F bar 78, vla subject entry starts on Aflat bar 82, cello long slow melody starting on E (9th note of retrograde) bat 87, v1 melodic fragment starting on Csharp (2nd note of row) bar 88, v2 a different fragment starting on D (2nd note of row) bar 90, vla plays v1's previous fragment, starting on Gflat (2nd note) bar 91, v1 plays v2's previous fragment, starting on G (2nd note) bar 99, v1 subject entry starts on C bar 99, v2 subject entry starts on Fsharp. The last and closest canon.