source file: mills2.txt
Date: Thu, 5 Oct 1995 22:40:25 -0700

Subject: 88CET #16:  Cadences?

From: Gary Morrison <71670.2576@compuserve.com>

Are there dissonant-to-consonant resolutions in nontraditional 88CET harmony
that can serve as cadences to reinforce phrasing or tonality? 

   Yes, although there is one caveat that I'll get into in greater detail later:
Many of them form dissonant-to-consonant resolutions at an overall higher level
of dissonance.  So if a typical authentic cadence were represented a drop in
harmonic tension of 3 to 1, on a hypothetical scale of 0 to 10, then some of
these may represent a reduction in harmonic tension from 5 to 3.  I like to call
this "raising the ante" - we're still reducing tension, but at higher overall
level.  

   But anyway, there certainly are interval resultions that can propel 88CET
nontraditional cadences somewhat analogously with how tritone resolution propels
some traditional cadences.  The 9:7 supramajor third can resolve outward to a
perfect fifth, or a minor sixth.  That latter case requires two voices to
resolve outward by whole-step.  Still, it is perhaps more powerful nevertheless
because it moves from a startling dissonance to a warm, poignant consonance,
rather than to a cold, bland interval like a perfect fifth.  Here is an example
of this sort of raised-ante resolution (recall my notation system presented
earlier):
                                        G
                                    F
                                    C     
                                        Bb

                                        G
                                    F
                                    C
                                        B

(This consists of two supramajor thirds separated by an off-fourth, resolving to
a perfect fifth below a minor sixth separated by a whole-step.  It has a
slightly deceptive-like taste.  

   The curious-sounding 15:7 minor ninth can resolve outward to the 19:8 minor
tenth, or 5:2 major tenth.  The 11:6 neutral seventh can resolve inward to a
major sixth.  This progression is probably a better example yet of this
raised-ante resolution:  
                  Bb                           Bb
                       A                            A
                                or similar     
                  E    E        yet subtly     E    
                                different:          Eb
                       Bb                           Bb
                  A                            A

All I can say about these two progressions is that you've got to hear them to
believe them!  They're really surprising, especially in a bright timbre like a
trumpet.  

   One might be tempted to try resolving a 14-step off-octave as a dissonance,
outward to major or minor tenths.  I've never managed to get this to work,
because those off intervals aren't dissonant; they're just wrong!  However,
resolving the 6-step off fourth outward to a minor or major sixth, or inward to
a subminor third, works a LITTLE bit better.  


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