All the Pleiades series contain the same notes in different order

Using the Pleiades series we can find the possible ingredients of harmony (or voice parts) from any bass note. We do not need to use all the ingredients.


Just one bass note and 3 harmony notes are usually enough even for the most complex symphony or pop song.


For example A9 played:


A bass and C E B already sounds so full, mysterious and refined that nothing else might be needed. See for example the 3rd chord of Qui Tolis - Bach from Mass in B minor.


The A9 at the 3rd measure of Qui Tollis is possibly just these 3 notes but delegated to different instruments including human voices in different octaves etc. See full score or piano choir score.


In fact this same chord, A9, is the first chord of Just Hold Me - Maria Mena


Back to the Pleiades series.


They are easy, they are just 1 3 5 7 9 11 13.:


When bass is C the series is C E G B D F A


When bass is D the series is D F A C E G B


See how the second series can be derived from the 1st by beginning from the relevant note.


When bass is E the series is E G B D F A C


See how the same happens to the 3rd or all 7 series.


They all contain the same 7 notes in a different order.


How about the Bach's example?


On Qui Tollis, on the 3rd measure for example Bach has A on bass. The Pleiades series is A C E G B D F. Bach had chosen from all those notes just A bass and C E B. There is logic to the miracle of art. B was prepared for our brain all the time as B can be heard on the 1st and 2nd chord. C is the 3rd that makes the 9th (B) sound fabulous to listener's brain [Bach]. E is the 5th, another consonant interval. They all play their part in making the dissonant 9th interval sound miraculously euphonic.


For more on the Pleiades series see also:


http://euroelectron.blogspot.com/2018/08/the-pleiades-series.html


Reference:


Bach bass rules:


https://normanschmidt.net/scores/bachjs-general_bass_rules.pdf