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Scales, Modes and Symmetry
I find symmetry to be an important concept for the study of music. This relates to fundamental polarities that, intuitively, lie at the heart of a great many natural and philosophical systems. When we study 20th Century music, we'll see that symmetrical scales and symmetrical harmonies, and even symmetrical rhythms are all part of the contemporary musician's repertoire.
Ancient philosophies, going back to Bablyonian theory, notice the symmetry of what we today call the Dorian mode, and also posits a symmetry between what we today call the phrygian mode and the major, diatonic scale.
I cover this in detail in the first semester course, so navigate there if you would like to review the philosophical background to what will be a more practical manner on this page. You can login as a guest in that moodle course with the same enrollment key, 'harmony.'
To get at the notion of scales, modes and symmetry, I have a piano assignment, as laid out below and in the sidebar.
Dorian Mode
Note the symmetry -- the same order of tones and semi-tones regardless of the direction. Note also that our bass clef, one of the oldest clefs in our music, with roots back to the earliest Gregorian Chants notation, is fundamentally centered around D dorian -- indeed I copy this graphic from the intro class, in explaining the fundamental symmetry of the bass clef.
It is also useful to mention that many of our oldest instruments are centered around D, not C, reflecting the more ancient of our modal orientation. The entire string family is tuned to a Dorian/Aeolian tonality, with D and A as central strings. Guitars and bass guitars, of course, have as their lowest strings EADG and this also reflects a modal history. Is this one of the reasons that Rock music (and blues) is more modal in character? Certainly that's part of it, since most rock and blues composers compose at their instrument, rather than on manuscript paper.
Here is the pattern to play in all 12 keys in Dorian.
Major Scale and Phrygian Mode
As to the major scale and the phrygian, this is a concept that I find both useful and fascinating, as it points to possibilities for combining tonal and modal ways of thinking. Here is the basic musical result on the keyboard. Play this in all keys: a major scale ascending and a phrygian scale descending. Again, note the perfect symmetry here of half steps and whole steps.
This understanding is useful in contexts of jazz and modal writing. This arrangement was not used in a practical way during the period of common practice harmony, but if you look for it, this innate sense that downward motion is Phyrgian and upward motion is tonal or Ionian is everywhere. The Neopolitan 6th chord, is after all, a Phrygian phenomenon.
You should already know your major and minor scales, since you are required to pass your piano proficiency exam before taking or shortly after enrolling in this class. By way of observation and conceptual review:
Aeolian mode and the minor scales
The Aeolian in common practive usage became the natural minor scale. This remains the actual only scale in minor in the common practice system. The two scales that students are usually required to learn in all keys are artificial scales, based on common practice usage. Thus, since in minor keys the leading tone is rased when a dominant chord is to have a cadential function (i.e. V7 - i), the "harmonic minor scale" represents the aeolian mode with an artificially raised leading tone.
A B C D E F G# A
I've always found this scale a rather odd, if charming, construction, since we are taught traditionally to never create the melodic interval of an augmented second, and yet there it is in the scale. And when you read that the leap of the augemented second is "not used melodically," this is more a vocal prohibition, since there are plenty of instances of it in instrumental writing.
For this reason, I suppose, the melodic minor scale is constructed to suggest that in common practice, composers sometimes in certain circumstances raise both the sixth and seventh steps of a minor melody if the tune strongly leads to the tonic over a perfect cadence. By contrast there is a tendency to revert to the natural mode (with the seventh and sixth steps lowered) when the melody is descending.
A B C D E F# G# A A G F E D C B A
Intervals
I'm assuming that you know your intervals and that you can hear these easily. If not, there are plenty of ear training programs on the Web to help you in identifying them. "Practica Musica" is also availble on all our machines at Earlham, or you can buy a personal copy in the bookstore. You will, of course, need to know these for your ear training exam, and you'll be given information on the ear training practical exam soon.
Next is a discussion on Harmonic Polarity