Harmony - from 3th of Jan 2018 to 10th of Jan 2018

Lets talk about, maybe, the most important aspect of this piece - harmony.

At the beginning of this process, as I wrote on last 3rd of January 2018, I seated and played on the piano some chords related with the harmonic series in B flat and B natural and create three chords.

After this, I was thinking in how to transpose all my chords? I took the example of Colours (in circles) and identified these three chords in the circle of fifths (image 1)

Image 1 - chords were identified in the circle of 5th

The first stage was to create a journey between chords, as for example from chord 1 to chord 3 I could do B flat, F, C, G, D, A, E and B natural - and that could be, in a simple way, my journey between B flat which is chord 1 to B natural which is chord 3.

However, I realised that I could use other way of transposition, using just the human material I had so far. So, I decided, first of all, to create an opposite pole of each chord I have. For this, I needed to create the opposite pole of the harmonic series I’ve got. On the 5th of January 2018 - for the B flat harmonic series - I ended it up with a F natural harmonic series from the top to the bottom (opposite pole) (image 2)

Image 2 - B flat harmonic series opposite pole - F natural from the top to the bottom (22 partials no microtonality)

On the 9th of January 2018, I did the same for the harmonic series of chord 3 - B natural. Starting in F sharp from the top to the bottom (image 3)

Image 3 - B natural harmonic series opposite pole - F sharp natural from the top to the bottom (22 partials no microtonality)


After doing this opposite pole transformation, I took all the chords and inversions and create new transpositions using the number of the partials of the original chords - however in a opposite way. For chord 1 and its transpositions the result were (image 4)

Image 4 - opposite pole chord 1 and its transpositions


For chord 2 and its transpositions the result were (image 5)

Image 5 - opposite pole chord 2 and its transpositions


For chord 3 and its transpositions the result were (image 6)

Image 6 - opposite pole chord 3 and its transpositions



Maybe I should have stopped here, but I thought: “what if I transpose my chords and opposites to the range of the choir - split in two sections: Males and Females.”

Later on, with the harmonic series created from the range of the Males and Females sections from the ACJC Alumni choir I did some transpositions of the original poles. For chord 1 original pole, applied in mens spectrum (image 7); for chord 1 original pole, applied in ladies spectrum (image 8); for chord 2 original pole, applied in mens spectrum (image 9); for chord 2 original pole, applied in ladies spectrum (image 10); for chord 3 original pole, applied in mens spectrum (image 11) and for chord 3 original pole applied in ladies spectrum (image 12).

Image 7 - chord 1 original pole - applied in mens spectrum (Harmonic series in E)

Image 8 - chord 1 original pole - applied in ladies spectrum (Harmonic series in G)

Image 9 - chord 2 original pole - applied in mens spectrum (Harmonic series in E)

Image - 10 chord 2 original pole - applied in ladies spectrum (Harmonic series in G)


Image 11 - chord 3 original pole - applied in mens spectrum (Harmonic series in E)



Image 12 - chord 3 original pole - applied in ladies spectrum (Harmonic series in G)


After this, of course I needed to do the same transpositions to the opposite pole, thinking in each opposite harmonic series I explored before. For chord 1 opposite pole, applied in the mens spectrum (image 13); for chord 1 opposite pole, applied in the ladies spectrum (image 14); for chord 2 opposite pole, applied in mens spectrum (image 15); for chord 2 opposite pole, applied in ladies spectrum (image 16); for chord 3 opposite pole, applied in mens spectrum (image 17) and for chord 3 opposite pole, applied in ladies spectrum (image 18).

Image 13 - chord 1 opposite pole in mens opposite spectrum (opposite harmonic series in E which becomes in B natural from the top to the bottom)


Image 14 - chord 1 opposite pole in ladies opposite spectrum (opposite harmonic series in G which becomes in D natural from the tom to the bottom)

Image 15 - chord 2 opposite pole in mens opposite spectrum (opposite harmonic series in E which becomes in B natural from the top to the bottom)


Image 16 - chord 2 opposite pole in ladies opposite spectrum (opposite harmonic series in G which becomes in D natural from the top to the bottom)


Image 17 - chord 3 opposite pole in mens opposite spectrum (opposite harmonic series in E which becomes in B natural from the top to the bottom)


Image 18 - chord 3 opposite pole in ladies spectrum (opposite pole harmonic series in G which becomes in D natural from the top to the bottom)