The Spiral Form – Developing Variations

To pick up a previous thread, we first need a quick review:

Two years ago in Essays & Endnotes I began investigating a web of unlikely connections within and between seemingly unrelated areas. It began with "pure mathematics" inspired by a metaphor from nature –

The Form

This abstract pattern led to a connection to a poetic form invented by a 12th-century troubadour –

The Sestina

The same pattern was also noted in card shuffling techniques that probably track back to the first known playing cards in the 9th century –

Jeu de Cartes

Then the form crossed paths with computer science in the 20th century  –

Parallel Processing

The pattern was also uncovered by a 19th-century musicologist as one basis for diatonic theory in music –

Hauptmann Shuffle

Four further real-world appearances of the pattern –– (1) 3-card Monte, (2) tritina poetry, and (3) a string of triads in music generated by (4) a parallel processing routine from computer science –– all went into a single post to summarize and further illustrate the usefulness of the form in disparate contexts –

The Grifter, the Poet & the Composer

Earlier I spoke of two fairly recent applications of the spiral form in music. It's time now to take up this investigation once again to explore those applications and then close with potential compositional variations and strategies suggested by the spiral form. The summary question is: How far can we push the spiral form in compositional music theory?

Here is where the next post will eventually lead: