Theory Fun

1.

In my Music Fundamentals class, we have been studying how to generate intervals above and below specific notes. I taught the students that for ascending intervals, they can use an ascending major scale as a starting point. For instance, if they need to determine a major third above G, all they need to do is consult the G major scale and note that the third note of the scale is B. All of the intervals from the tonic up to any other note in a major scale are major, except for scale degrees 4 and 5, which are perfect. Minor intervals are then generated by lowering the top notes of these major intervals a half step.

One of my students started asking questions about generating descending intervals and whether or not some sort of scale could be helpful. After thinking about this a little, we realized (something that is actually pretty obvious but I hadn't thought through before) all the intervals from the top tonic down to any other note in a major scale are minor, except for scale degrees 4 and 5, which are perfect! Thus, a descending major scale can be used as a template for determining descending intervals.

2.

I have one adult student outside the University. She plays for church services, and the focus of our lessons is for her to learn how to enhance her hymn accompaniments through improvisation.

An important skill to develop towards that end is the ability to quickly understand what chords and chord progressions are in the hymn at hand.

As we were analyzing chords in a hymn, we came upon a cadential six-four chord. As many of you know, the naming of that chord is controversial. Some call it "I six-four" since the pitches in the chord are those of a second inversion I chord. Some call it "V six-four" because it has a strong dominant feeling. The problem with calling it that, though, is that in the standard system for labeling chords with Roman and Arabic Numbers for roots and inversions, respectively, it is assumed that all the chords are stacks of thirds. Thus, the bass note of a cadential six-four chord couldn't really be the root of the chord since the distance from that pitch to the next chord member is a fourth and not a third. In addition to that problem, there is already a chord that is labeled "V six-four" without being inconsistent with labeling principles. The bass of that chord starts on scale degree 2, not 5. The phrase "Dominant six-four" is a little better, but it can still be a little confusing as "V" and "dominant" are synonymous when referring to scale degrees and chords (most of the time.) The phrase "cadential six-four" seems to be the clearest description of the chord's funtion and its inversion.

Now for the good part! I asked my student if the chord sounded like it had a tonic, dominant, or pre-dominant function. She accidentally but very accurately referred to it as "Tominant" - tonic pitches with rather dominant function.