Circular Variations on a Name

Revised

for solo piano

[4+ min.]

Revision Notes

Most critically new in this revision are the many adjustments of detail in both pitch and
attack time.  These are recalculations (not reconceptions), made possible by a more
dependable means - polar coordinates - of carrying out the axial rotation.

AntiVars I & II: These present Retrograde or Inversion - not the single function merging
them, but the two independently.  They are "Anti", as the rotation cycle never generates
them.  "I" includes the name parts only; "II" the counterpoint only in its perpendicular
rendition.

The detache articulation default has one generic exception: a slur's initial note. The slur
is specifically to connect, not all notes within it, but just two: start and end. Only the
former is to be elongated, with all intervening members matching default. The point is to
track rotational separation of the originally slurred pair, as accents track the theme's
original stresses. Overall, dynamics should be layered to delineate the intermixing name
parts as clearly as possible.

Per the usage style termed "forget", accidentals apply exactly once.

Original Notes

COMPOSITION
I am interested to explore the implications of generating retrograde inversion, not via the
immediate combination of two (horizontal + vertical) reflections, but through the gradual
integrated workings of one axial rotation.

To that end and with the characters of a friend's name, I notated a short melody as dots
on graph paper (X/Y=time/pitch), then marked separate transparent graph sheets each
with a tilt line at the next increment of 15 degrees.  Finally, viewing the original graph
through these at their respective tilts, I noted its new X/Y values at each step of rotation.

In the result, especially as the thematic identity of individual notes suffers some jumbling
at other than cardinal degrees, I have added several notations to aid listeners'/viewers'
tracking: colors for the theme's first, middle and last names; articulations--a pair each of
slurs and accents, one tenuto; and a between-staves vertical line marking the rotation's
timewise center.  (The pitch center is B3.)

The theme pitch classes were specified by mapping its name characters via an alphabet
loop around the scale of F-major:
                                         A Bb C D E F G
                                         ---------------------
                                         a          E F
                                         h  i   J    l
                                         o             t
                                                  y
PERFORMANCE
Articulation. The default throughout is detaché. This is not to say overly short, just that
the current note is to end perceptibly/clearly before the next begins.

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