[Smt-talk] Discussion points re keyboard harmony

Raymond Buhr rjabuhr at gmail.com
Wed Jun 2 11:40:22 PDT 2010

	I have  been trying to bring my ideas about keyboard harmony to the attention of music theorists by recent announcements to the SMT-talk and SMT-announce mailing lists,  about a website that presents the ideas ("Picturing Keyboard Harmony, at www.pianotheoryman.com).  My hope was  to trigger some discussion,  but not much has happened yet. So, I decided to summarize the fundamentals in series of prose points, omitting  notation that may be a stumbling block in spite of its simplicity.   
	A short preamble may be helpful.  As a retired professor, I understand the reluctance of academics to pay attention to anyone from outside their field.  However,  I believe I have stumbled upon a theory of keyboard harmony that is worth looking at because it is  simple, general and deep. I say “keyboard harmony” but the theory seems perfectly general for any kind of music based on scales constructed from twelve nominally equal half tones.  That the theory seems to be unknown is amazing to me.  Perhaps I was able to stumble upon it because of the rather unique angle from which I approached keyboard harmony  as an adult beginner with no keyboard or sight reading skills: I “reverse engineered”  symbolic chord progressions of a wide variety of pieces of music in fakebooks, intrepreting the results in my own way with no encouragement and sometimes active discouragement from music teachers.   I had been taught some basic approaches to voicing chord progressions and was impatient to try them out on harmonically sophisticated pieces that I loved. I soon saw a cognitive disconnect between the complexity of the  chord progressions I was voicing and the simple keyboard patterns that resulted. The more complex the chord progression, the bigger the disconnect.  I begin to think that there must be a simpler way of representing chord progressions and, after several years of  experimenting, I found one.  The result amounts to a self-contained theory that views the same harmonic fundamentals as conventional music notation from a different angle.  It is completely independent of conventional music notation (key signatures, letter notes, sharps, flats, accidentals, chord symbols) while being easy to translate into it.  Conventional music notation is here to stay but there is no reason that it must be the basis for all harmonic thinking.. 

Discussion Points  
1. Scales are fundamental to all music.
2. A key signature offers two kinds of  7-note scales: major or natural minor.  In most actual pieces of music, more scales than these come into play, often many more, some with different numbers of notes than 7.  
3. Key signatures make this complex because they are complex to begin with and because they  identify scales not belonging to the written key signature only implicitly,  using accidentals.
4. The common practice of representing chord notes by degree numbers of chord scales is fundamentally flawed for several reasons.    It requires knowing  scales in advance. A proper numerical notation should self-identify scales.   It represents the notes of non-key signature scales by referring them to degree numbers of key-signature scales that are not actually in use. This sometimes forces thinking  in terms of different key signatures for different chords from the same non-key-signature scale,  and often results in ugly symbols such as “sharp 9th” and “flat 13th”. It assumes scales have 7 degrees, which forces an awkward way of thinking about scales with fewer or more degrees. 
5. A numeric scale notation that self-identifies scales of the home octave of a piece music makes everything simple. Such a notation requires exactly 12 symbols, no more, no less.  The home octave is the one starting on the tonic to which the piece eventually resolves. The same numeric notation applies to home octaves with different tonics.  The underlying letter notes are different but this is no problem because neither key signatures nor letter notes are  part of the picture.  This enables  the harmony of pieces of music with different main tonics to be seen in common terms. This is analogous to the use of Roman numeral chord symbols for the same purpose, without the complexity blowup for non-key-signature scales that that notation experiences.    
6. The number of fundamentally important forms of numeric tonic scales of any  home octave  can be counted on the fingers of two hands.  Chord scales are implicitly covered because a chord scale is the  tonic scale from which the chord originates, rotated to start on the root.   
7. Here is where  novelty comes in. I stumbled on the interesting fact that the number and positions of tritones in  tonic scales expressed in numeric notation can provide “tritone signatures” of the scales.  The major and natural minor scales (the scales of key signatures) have one tritone each, in different positions in the home octave. Scales from different key signatures than the written one that come into play through modulation bring in their tritones, which are in different positions again in the home octave.   The 6-note blues melody scale has one tritone that splits the scale octave in half.   The 6-note whole-tone scale is formed of three tritones a whole tone apart.  The 7-note melodic minor scale has two tritones a whole tone apart, leaving only three obvious notes to be filled in.   Several ornamental scales in common use also have two tritones a whole tone apart, making them effectively “clones” of the melodic-minor scale (same intervals starting from a non-tonic note).  The 7-note harmonic minor scale has two tritones a minor third apart. The 8-note diminished scale is formed of four tritones,  alternately a half tone and a whole tone apart.  The 10-note composite blues scale that combines the usual notes used for blues melody and harmony has four tritones a half tone apart.  Finally, of course, the  12-note chromatic scale is formed of six tritones  a half tone apart, all the independent tritones that exist (the other six are inversions of these).
8. Tritone signatures are like “seeds” from which  numeric scales can be “crystallized” in a very simple way. 
9. Tritone signatures of numeric scales used in a particular passage  can usually be recognized from tritones contained in the chords of the passage. Very simple tables summarize the tritones of scales and the tritones of chords. If the tritones of the chords of a passage include all the tritones of their home tonic scales, then a simple table lookup identifies both the tritones and the scales.   Otherwise, the melody line and the chords must be scanned for tritones that are spread horizontally instead of appearing vertically in chords. This is  not a table-lookup process but is not particularly difficult. Tritones will normally be found because almost all scales contain at least one (the only exceptions of which I am aware are major and minor pentatonic scales, the presence of which is very easy to recognize—they are major and natural minor scales with their tritones subtracted).
10. If scales are fundamental to all music, then tritone signatures of numeric scales are equally fundamental.  It may be said that such signatures reveal the deep structure of harmony in a very simple way. 
11. Getting scales into the fingers requires getting their intervals into the fingers. A numeric notation that self-identifies scales gives their intervals automatically, providing as good a starting point as any for learning scales. 
12. The complex chord progressions that sent me down this path tend to be tritone intensive, meaning more than half the chords contain tritones, often much more than half.  Because tritones are simple, this  makes for very simple, tritone-centered “backbones” of chord progressions. Turning such backbones into proper voicings of  chord progressions is very simple when you know the tonic scales.  The simplicity of tritone backbones is a beneficial side effect of the theory but not its main point. Tritone signatures of scales are its main point.  The theory applies to any kind of harmony involving  scales with one or more tritones.  It may even be said to include tritoneless  major and minor pentatonic scales because "zero tritones" is a kind of tritone signature.        

R.J.A. Buhr
1150 Lombard St. #21
San Francisco CA 94109
rjabuhr at gmail.com

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