the diatonic modes as inversions of each other, a little riff on George Rochberg's proposal that Western music has had cycles of favoring symmetrical and assymetrical paradigms for pitch organization in the last thousand years

It might be because I've been reading George Rochberg's A Dance of Polar Opposites this year, but I've been struck by a passage near the end where he wrote:

A Dance of Polar Opposites: The Continuing Transformation of Our Musical Language

George Rochberg, edited by Jeremy Gill

University of Rochester Press

Copyright © 2012 by Gene Rochberg

ISBN-13: 978-1-58046-413-0

ISBN: 1071-9989

The equalization of the modes via musica ficta into the major-minor standardization took centuries. The tendency to think symmetrically in the twentieth century was nurtured for approximately one hundred years in nineteenth-century tonal music. We can now see with absolute clarity that all the stages in the development of Western music are the end results of preoccupation--however unconscious--with either asymmetry or symmetry and their intermixtures. Seeing this will help to prepare for the next major step, which theoretically will play with juxtapositions of asymmetry and symmetry and their intermixtures (asymmetry enfolding symmetry; symmetry enfolding asymmetry); it is the next great turn of the spiral of morphological change and will make manifest heightened musical consciousness, itself a form of spiritual development. (page 145)

Now that might seem a bit more ... mystical ... than some might like and a bit residually Romantic but let me get to the key idea Rochberg built up to that he only got to in the Afterword.

The history of counterpoint precedes the history of harmony by about five hundred years. Harmony qua harmony grew slowly out of the rhythmic practices of contrapuntal music. Harmonic "concord" or "discord" had to be taken into account as the individual parts came together to form a total texture. A harmonic vocabulary was gradually established as the language of tonality.  .. (page 153)

Rochberg proposed that the history of Western music can be thought of as having centuries long pendulum swings from the medieval era chants through to the present day in which Western musicians gravitated toward music organized by pitch systems that favored symmetry or asymmetry as a general rule.  When you recognize how many plainchants were made in the dorian mode, a legendarily symmetrical mode, Rochberg's thesis seems, if not airtight, at least plausible. 

If we consider the ways in which the chromaticism of late late Romanticism was shifted into dodecaphonic techniques; or how the whole tone and octatonic scales emerged as prominent pitch systems; or the ways in which set-class theories began to emerge that emphasized hexachordal systems capable of omni-directional stasis, Rochberg's basic proposal has been that the twentieth century modernists introduced non-tonal (as in not-major and not-minor) pitch systems that were dominated by symmetrical rather than asymmetric pitch systems.  The mistake, in Rochberg's polemic, was that fans of the new high modernist stuff imagined this was new, even if someone like Webern could turn to Renaissance era canons for inspiration and that, those of us with a few years of choral singing with us, ,was an era full of dorian mode music.  Rochberg imagined that instead of merely having Western music theory and practice have constant pendulum swings between the symmetry of the dorian mode leading to the major key and minor key systems until elaborating chromatic extensions of tonality lead to a renewed non-tonal symmetrical age, we could begin to develop a musical language in which composers could shift back and forth between or juxtapose symmetrical and asymmetric pitch patterns as musical languages at will.  Thus the dance of polar opposites.

If that seems awfully abstract I am reminded of something my brother once pointed out to me years ago, that if you start at middle C and play the lydian mode you've got yourself the lydian mode, obviously, but if you start from middle C and play the same intervallic series going down you get the locrian mode.  Lydian and locrian can be thought of, therefore, as inversionally related modes.  Perhaps I can just show you what I mean by the observation my brother shared with me.

Famously the dorian mode is symmetrical, it's the same series going up or down, where as it is just as obvious that if you "invert" the lydian mode and descend by those intervals from a common starting point the descending lydian becomes the locrian mode; the descending aeolian mode becomes the mixolydian mode; and the descending ionian pattern becomes the phrygian mode.  By descent, as you can see, the idea is that the ratio relationships are retained but are sent moving downward, as distinct from the probably more normal understanding of climbing up the ladder or down the ladder where C ionian goes downward as CBAGFEDC.

Pertinent to Olivier Messiaen's observations about modes of limited transposition, once we get past the diatonic usual suspects a mode like the octatonic scale or the whole tone scale are modes of limited transposition because once you factor out any transpositions in which pitches are replicated significantly across the transpositions you find there are two modes of transposition for the whole-tone scale before all twelve tones of the chromatic equal tempered scale get used up.  The octatonic scale uses the twelve tones up by three transpositions, whereas the diatonic modes can appear along any of the twelve chromatic tones.

Now where this kind of thing moves beyond being purely theoretical to practical application would be in something like the following--I once long ago worked on a Kyrie setting where the Kyrie eleison was a gloomy locrian passage and my brother heard it and suggested that a simple and effective contrast would be to just take that locrian melody and invert it into lydian so that the corresponding christe eleison passage would have the warmth of Christ's divine mercy as a contrast to the supplication of the locrian mode Kyrie.  Ah, yes, that's a great, simple idea, so, of course, I took my brother's advice.

The older I get the more I think it would be nice if music theory books were written more by choral musicians and guitarists rather than pianists.  It's not that I don't love piano music, it's more that I read Ted Gioia's supposedly subversive history of music last year and it was conventional wisdom from start to finish and yet I also noticed that some of the writers he singled out for having to laugh at their attempts to muddy the waters on music history in some areas where he's committed to a clear narrative, those authors jumped out at me for including guitarists.  A guitarist is not necessarily going to look at blues and just default to saying "it didn't follow the rules of Western music".  Come on, we guitarists can attach a glass or metal slide to our little finger and do a full slide glissando across every conceivable pitch in an octave.  We can highlight the contrast between a C# natural harmonic off the A string against a C sharp played at the second fret of the B string to show the microtonal deviations in pitch that are possible.

This pianist's way of thinking about how blues doesn't follow the rules is mostly post-Romantic absurdity.  Anton Reicha mentioned in his treatise on melody how an opera singer used quarter tones to transition from phrase to phrase in an aria passage.  I've gotten very tired of canards foisted upon unsuspecting readers by keyboardists who have only ever worked with equal tempered instruments about how blues broke all the rules.  When Kyle Gann wrote long ago about how we should "make way for the guitar era" I think one of those ways we can make way for the guitar era could be to let guitarists who dig into music history, whether it's an Elijah Wald or a John W Troutman, do some work to demythologize some of the black and white myths about American popular music that maybe, hey, maybe we needed those mythologies in the twentieth century in order to give African diaspora music a chance to be heard and taken seriously as art but those tropes may be harmful to us in an era in which alt right nationalisms and essentialist race narratives about music, race and culture have been taken up as part of turf wars about academic music canons.

If I read Augustine's treatise on music and its rambling on poetic rhythm in poetry and I think about one of my friends talking about "flow" in rap then I'll just come out and say that Christian rappers who have never read Augustine's treatise on music might find it helpful.  If Augustine's treatise is almost entirely about the mechanics of the rhythm and pulse of language and how rhythm underlies meter and meter underlies verse then instead of people dismissing Augustine's reflections on the poetics of rhythm and meter in language as a prelude to musical thought as some idea of "rules" consider that in many an ancient society song and music were one and the same and therefore it's not mere pedantry for someone like Augustine to spend so much time on the metrical mechanics of poetry.  To upbraid him in such a way would be like telling a drummer there's no point in ever learning how to keep time by practicing to a metronome.  Augustine made a point of apologizing for how bonehead simple and baby-steps his treatise was because he wanted to lay foundations for more philosophical thought.

Unfortunately it seems many who read Augustine's treatise just skipped the baby steps stuff as boring when it's in those passages he drops more-than-just-hints that those who cannot use reason are unable to produce art and that music is the science of measuring well.  Music is something that must exist in our hands and bodies and minds; in our memory and that it is through the clarity of thought we can perceive music as music.  I'm eventually going to get to some of that . . . . but later.

Rochberg made no bones about being openly philosophical and about his concern that in a technocratic age such as ours music was often reduced to a kind of scientistic technocratic system rather than an art.  Or as Leonard B. Meyer put it back in 1974, critics and pedagogues were tempted to justify the humanities on the basis of tendentious comparisons to the sciences.

To put this all in a plain way, observing that if you invert this mode you get that mode doesn't have to be some way of thinking about music that reduces it to "numbers" as we understand it because for someone in the ancient world number was not just number.  Judging ancient writers on music who dealt with the ratios we have since, as Kyle Gann has put it in his fantastic book on the history of tuning systems, to be foundational to the intervals we use as the basic building blocks of music; we should regard those ratios as constants we can play with.  Meyer went so far as to say that there are two sets of "universals", the physical realm of sounds and the possibilities in overtones; and the cognitive capacities of humans; in the middle, however, Meyer declared there were no musical absolutes, and no musical universals, just the universals of the material world we can play with as musicians, and the universals of how human minds perceive and conceive of sound.  To formulate this in something akin to Christian theological arguments from history, the German Idealist may have given us a super-charged gnostic or neo-platonic conception of what a musical "universal" is that merely reified a set of options available in a specific time and place that have never been as universal as advertised.  There's plenty of beautiful music written in equal temperament but we are not bound to that.

So that's some stuff I've been thinking about since reading the aforementioned Rochberg book.