Searching for New Sound - Music Composition ideas

 In the succession to the previous article on Blackwood's traditional formation the relationship of a diatonic scale can be written as 5w+2h=n-TET. w, h and n must be an integer and n>w>h>0,, as the diatonic behaviour. I calculated that from 5 to 60-TET by a Python program to see which number of equal temperaments satisfy or not the diatonic behaviour. The table below is the result. If it is labelled as False, it means it does satisfy the diatonic behaviour. If it satisfies, the chart will display number of microstep of a whole tone and half tone respectively. Based on the finding below, we can see that 12-TET is the smallest amount of steps the perform the diatonic behaviour. This is the reason 12 is the most used number. The 35-TET is the last one which does not perform in diatonicly, larger than that, the number are all satisfy diatonic behaviour. The 47-TET is the smallest n-TET can perform bi-diatonic behaviour, 7 microsteps for a whole step and 6 microsteps for a wh...

As a succession of the previous article of C. Vivier harmonized his melody by harmonic series, I was inspired and tried to do something similar, treating the harmonic series as a  scale and building triads. The example below is a  harmonic series on B-flat. I picked part of the series in the red box as an 8-note scale. (the digit on the notes show how many cents deviate from the equal temperament) A harmonic series on B-flat (the series is infinite, only the first 16 partials have shown) Now we stack chords with thirds, every 2 steps on the harmonic series scale (red box). The result is below. chords from the harmonic series I would like to borrow the idea of traditional functional harmony, the tonic, dominant and subdominant function, in order to give myself guidance on using these chords. Then, I rated the quality of the chords, 1 for the purest and 5 for the harshest. I did it by ear so it is subjective. (This is art.) Back to our traditional functional harmony. It is ...