Phigits: One-Part Takes on the Digits of Phifor autopiano solo[7:21]One number uniquely equals its inverse added to 1: the irrational 1.618..., embodied in Phidias's Parthenon statuary, Fibonacci's rabbit generations, and Luca Pacioli's "De divina proportione" - not to mention Le Corbusier. Music embodying Phi (as it is now named) has understandably tended to focus on the value's application as a ratio. I focus here instead on an exploration of its digits.
Wishing to map these as pitch values saturating 1 to 7 octaves, but with only 10 unique digits available in the customary representation, I opted to convert Phi (as much of it as needed per fill) to number bases matching those ranges: with octaves inclusive, 13 25 37 49 61 73 and 85. Each saturation series was ended when its last not-yet-occuring value appeared for the first time. At that point duration was assigned per pitch in inverse proportion to that pitch's frequency of occurrence within the series.
Depending on series range, there resulted from 4 to 8 such occurrence-frequency levels. I decided to use the first four of these (always present) to determine combinatorially which pitches in a given series would be realized instead as rests - i.e., silenced! There resulted 14 possible sound-vs-silence patterns per setting (omitting two that presented either all rests or no rests). I chose one for each setting - exclusively, so all-told presenting each pattern once. It is indicated in the score by "Tacet", with its selection of silent duration levels - from "1234", '1' being the longest - following.
The movements are arranged in two sets of seven. The first set presents octave ranges in ascending order, all member movements straddling the keyboard's center. The second set reverses this order, with members now ranging inwards from alternate keyboard extremes. Tempo progression exercises Phi as a ratio. Each set's min-vs-max metronome settings relate as 1-vs-Phi.1. Tacet 123_ 8. Tacet ___4
2. Tacet _23_ 9. Tacet 1__4
3. Tacet 1_3_ 10. Tacet _2_4
4. Tacet 12__ 11. Tacet __34
5. Tacet __3_ 12. Tacet 12_4
6. Tacet _2__ 13. Tacet 1_34
7. Tacet 1___ 14. Tacet _234
Clearly this piece is, for rhythmic reasons, not humanly playable. The score, then, is for listeners. It is laid out space-proportionally, with notehead sizes and colors varying to highlight the duration levels. Rests differ accordingly in color but not in image or size. Accidentals apply only to the immediate notehead, so exactly once. Alto clef is used exclusively (and the ottava never) in order to convey a spacial-proportional image of ranges.