I had so much fun writing my "New Divisions on an Old Italian Ground" that I want, like a cell, to keep dividing. I'm currently working on a piece for violin, viola, and piano that could easily benefit from this kind of thing (a ground round, perhaps?), so I decided to check out Christopher Simpson's The Division Viol, which is an actual method book for writing divisions from 1655. (Perhaps it might have, in retrospect, been a good idea to read this before writing my set of recorder divisions, huh?)
The text and illustrations are as interesting as the Divisions themselves. This lovely orb, for example, shows the relationship of music to the zodiac "The outmoft Circle reprefents the Zodiack, and the Aspects of the Planets, to which you fee the Diapason with its Interfections exactly agreeing . . ." The bottom drawing shows that "all the Sounds that can poffibly be joyned together in Mufical Concordance, are ftill but the reiterated Harmony of Three."
Here's taste of Simposon's prose: a passage that explains his concept of music in relation to the zodiac. This is the 13th section of the second part of this book, his "Reflections upon the Concords of Music" (I have modernized the spellings, but have retained the capitalization):
And here I cannot but wonder, even to amazement, that from no more than Three Concords, (with some intervening Discords) there should arise such an infinite variety, as all the Music that ever has been or ever shall be composed. And my wonder is increased by a consideration of the Seven Gradual Sounds or Tones, from whose various positions and Intermixtures those Concords and Discords do arise. These Gradual Sounds are distinguished in the Scale of Music by the same seven Letters which in the Calendar distinguish the seven days of the Week; to either of which, the adding of more is but a repetition of the former over again.
This Mysterious number of seven, leads me into a contemplation of the Universe, whose Creation is delivered unto our Capacity (not without some mystery) as begun and finished in seven days, which is thought to be figured long since by Orpheus his seven stringed Lyre. Within the Circumference of this great Universe, be seven Globes or Spherical Bodies in continual Motion, producing still new and various figures, according to their diverse positions one to another. When with these I compare my seven Gradual Sounds, I cannot but admire the Resemblance of their Harmonies, the Concords of the one so exactly answering to the Aspects of the other; as a Unison to a Conjunction, an Octave to an Opposition; the middle Consonants in a Diapason, to the middle Aspects in an Orb; as a Third, Fifth, Sixth, in Music, to a Trine, Quartile, Sextile in the Zodiac. And as these by moving into such and such Aspects transmit their Influences into Elementary Bodies; So those, by passing into such and such Concords, transmit into the Ear an Influence of Sound, which doth not only strike the sense, but even affect the very soul, stirring it up to a devout Contemplation of that Division PRINCIPLE from whence all Harmony proceeds; and therefore very fitly applying to sing and sound forth his Glory and Praise.