source file: mills2.txt
Date: Thu, 19 Oct 1995 22:17:16 -0700

Subject: 88CET #22:  Wandering Tonics and #Parts

From: Gary Morrison <71670.2576@compuserve.com>

"Relativistic voice-leading" has an important consequence:  wandering tonics.
Here is a traditional-harmony chord progression in 88CET:
                
                                      B    B
                       A    A    A#
(2nd-line treble) G
                                 D         D
                                      C# 
                       B    B   
                  A
                                      F
                                           E
                            D    D    
(2nd-space Bass)  C    C

Func. Harmony:    I    IV64 ii  V7/V  V43  I6
  

   The equivalent progression in 12-tone notation is:
                
                                      G    G
                       F    F    F#
(1st-line treble) E
                                 C         C
                                      B 
                       A    A   
                  G
                                      F
                                           E
                            D    D    
(2nd-space Bass)  C    C

   ("IV64" is an attempt at an ASCII-text rendition of a roman-numeral IV with
the usual harmony-text 6-over-4 figured-bass notation for the chord inversion.
"64" denotes a second-inversion chord, "6" a first inversion, and "43" a third
inversion seventh chord.)

   Because 88CET has no octave, each inversion of what you convince your
audience is a tonic triad, places the tonic at a different pitch.  So the tonic
wanders over the course of this progression from (in the 88CET notation) the
second-space bass-clef C of the opening I chord, to the pitch-class of the D
(somewhat less than an octave above the C) of the final chord.  That even though
our ears "calculate" the tonics to be the same based upon how the parts move.  

   Wandering tonics have a very surprising effect if accomplished over a short
progression - short enough that the audience can remember the new and old tonic.
The harmony says that you've gone full-circle back to where you started, but you
mysteriously ended up somewhere else.  If the progression is too long,
especially if it has a lot of temporary tonicization, the audience will probably
not notice the effect at all.  

   Traditional harmony in 88CET poses another difficulty:  lack of octave
doubling makes it very difficult to sustain more than three-part traditional
harmony.  The possibilities for smooth voice-movement when voices can't move
through octave-doubles of other chord tones, dwindles rapidly.  Even in
three-part harmony, you end up having to use lots of chords with fifths below
their roots, or ninth chords (fifths above their fifths).  Secondary dominants
become more common than usual solely so to take advantage of the additional
chord tone!  


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