Thank you, @Chris Fitzgerald, and thank you, @elberon.
I respectfully ask that, even if you recognize the college being talked about, please don't name it here. I respect that their theory program is different than the one I participated in, and in no way do I wish to shame, find fault with, or otherwise put down how others teach. I'm just trying to understand better myself, both for myself and in order to help my son since he went to the same school I used to teach at and therefore has the same backgroun.
Chris, I agree wholeheartedly that one ought to try to explain things as simply and in as plain language is possible. After I taught at Mannes, I taught at the local community college here, and I learned that lesson very quickly. I digress, but at the community college, I used to make it a point, on the first day of every class that I taught, to explain what was needed to pass the course and to make sure everyone in the room knew there'd be no great mysteries to be explained on the midterm and final exams.
A subject for another conversation ...
@elberon, let's take one of the terms you mentioned, tetrachord - the only way I've ever heard it used (not that others couldn't use it another way, of course) is in reference to 1/2 of a major scale. G-A-B-C is the first tetrachord of a G major scale; D-E-F#-G is the second tetrachord. I mention the term, once, when explaining this to students, but I describe them as "two identical, in terms of the distance between the notes, halves of a major scale, with a whole step between them" or words to that effect, followed by "their official name is 'tetrachord'".
And @elberon, I just saw your second post - no apology necessary. In this instance, I quote the line the Denzel Washington character uttered in the movie, "Philadelphia":
I prefer to keep the name of my son's school out of the conversation as I don't wish to take the chance of offending anyone. Suffice it to say that my son's first college was Mannes (after I'd already stopped teaching there) and he had 4 years of theory in their Preparatory Division and 2 more years of theory in the College before he dropped out. After a brief try at a non-music school, he's changed his instrument and is returning to a different music program as a transfer student. He's been placed about mid-way through the theory courses that are required of him. Having inherited most of his father's perfect pitch, he's placed out of ear-training altogether. Note that referring to myself in the third person in the previous sentence is pretentious.
Which brings me to my point - I think tetrachord (again, based on my experience) has a specific meaning in the context of learning music theory. It's not just any group of 4 notes, it's half of a major scale. So _that_ is what I'm trying to figure out about how "hexachord" is being used. It seems to have some sort of specific meaning, at least at this music school, and that meaning is _not_ in reference to serial music, or at least it's not _only_ in reference to serial music. E.g., here's part of something my son was given:
Any transposition of the ascending C major hexachord contains the six usable modes in the order Ionian, Dorian, Phrygian, Lydian, Mixolydian, and Aeolian on each scale degree respectively, and their consequent major or minor triads (M, m, m, M, M, m) avoiding the “Locrian” 7 th that generates a diminished chord.
The retrograde form of the C major hexachord creates a descending scale which can be used to understand the relative minor of C, or A minor. The exception is the tone G which must also serve as G-sharp, the Aeolian leading tone.
This means that any transposition of a C major hexachord will have a flanking pair of relative modes at either end of the interval string, which we may now call major and minor.
If transpositions a P4 above and below any major hexachords are created, these new hexachords will each provide 2 new relative major/minor pairs, which in turn will provide major (Ionian) and minor (Aeolian) replacements for the original mode found on each scale degree of any major hexachord.
This is achieved by using two transposing accidentals, and three minor leading tone
accidentals.
Again, thanks in advance for everyone for their participation, and I also ask that everyone respect my request not to name the college here.
-S-
