 
Alright—here we go again, folks!
I’m still Seth Monahan, professor of music theory, and this is Video 9
in my series on the basics of classical harmony and counterpoint.
Now, it might be strange to say this—but there's nothing new in this video at all.
Instead, I wanna take some time to review—and hopefully clarify—the various uses of numbers we’ve encountered so far,
since this can be really confusing for new students.
Now I am sure you’ve noticed that music
theory relies heavily on numbers, and also
that small numbers—particularly the numbers
from 1 to 7—can be used in multiple ways.
We’re gonna talk about five such uses here: Roman numerals, scale degrees, chord degrees, Intervals, and
figured bass.
What these numbers have in common is that they all serve to describe some RELATIONSHIP.
But we need to be very, very clear on exactly what relationships those are.
Let’s lay them all out first, then look
at each in a bit more detail.
Roman numerals relate CHORDS to a major or minor KEYS.
Similarly, scale degrees relate NOTES to
KEYS.
Now chord degrees define the relationship of NOTES to CHORDS, independently of the key we're in.
Similarly, intervals relate NOTES to OTHER NOTES, again completely independently of key.
And finally, FIGURED BASS relates notes specifically to note that happens to be in the BASS VOICE.
Now to look really carefully at all these
relationships, we’re going to start with a short
choral phrase by Johann Sebastian Bach, from the Saint Matthew Passion, written in 1727.
And the text, “ich bins, ich sollte büßen,”
means “it is I…I who should atone or suffer.”
Here’s how it sounds.
Now that’s a particularly gorgeous chunk
of music, and it was sung marvelously. But to keep things manageable, we’re
gonna focus on only one chord: this V6/5 chord right before the end.
(And I’m showing the Db in parentheses here because it's held over from the previous chord.)
Let’s isolate this harmony and consider
it first in terms of its Roman numeral. What does that Roman numeral actually MEAN?
Earlier I said that Roman numerals relate
chords to keys.
This Roman numeral, “V,” relates this
chord to the key, Ab major, by way of its root.
Or, to be much more specific, the roman numeral
says “this is a chord that can be arranged
as a stack of thirds whose bottom note is
scale degree ^5 in Ab major…in other words, Eb."
But obviously, this V7 chord is made of four
notes, and they all have some specific identity
within the key of Ab major.
That’s where scale degrees come in.
As I explained earlier, scale degrees tell
us how individual notes relate back to the key they're in.
So while its convenient to refer to this
with one label (“V7”), we should also
be aware what notes of the scale it uses.
Stacking up in thirds from the root Eb (which is scale degree ^5, in green), we have G (which is ^7, in red),
Bb (^2, in blue) and Db (^4, in yellow).
And I'm going to use color throughout this presentation to make these things as clear as possible.
And if we look at Bach’s chord, all those
SDs are of course present—though they’re
arranged differently: the chord is inverted
and in open position.
Now ^7 (the red G) is in the bass, ^5 (the
green Eb) in the tenor, ^2 (the blue Bb)
in the alto, and ^4 (yellow Db) in the soprano voice.
So here's our Ab-major scale,
And we've taken these notes, ^2, ^4, ^5, and ^7,
And we've arranged them like this.
And of course Bach will resolve that...to that.
Now, it might be obvious at this point, but
Roman numerals and scale degrees, which we just discussed,
are alike in that they are key dependent.
This means that if we encounted this same
chord—in exactly the same voicing—in a
different key, the Roman numerals and the scale degrees would both
change.
Lets try this out.
Here, we’ll change the key marker to say
that we’re in Fm rather than Ab major.
That means the Roman numeral changes: now
the chord is VII6/5 rather than V6/5.
And to give you a sense of how this sounds, here we were in Ab major,
the chord resolved like that. In F minor, it might do something like this...
So different key, different Roman numeral, and
different scale degrees.
Now, from the bottom up, they’d be scale
degrees 2, 7, 4, and 6 in F minor—rather
than 7, 5, 2, and 4 in A-flat.
But let’s reset things back to A-flat major,
so we can take a moment to recall that there’s
another way to refer to the notes of this
V7 chord, and that’s with chord degrees,
which relate notes to chords—independently
of the surrounding key.
As it happens, we’ve already used one of
these degrees in our discussion, when we referred
to Eb as the chord’s ROOT.
And you know from Video 8 that each of a seventh
chord’s tones has a special name—the root,
the third, the fifth and the seventh—AND
that each of these names stick to these notes
wherever they appear.
So Bach’s harmony has the chordal third G in the bass, the chordal root Eb in
the tenor, the chordal fifth Bb in the
alto, and the chordal seventh Db way up on top.
So again: here's our chord as presented in the upper right: root, third, fifth, seventh,
and Bach has arranged it third, root, fifth, seventh.
You may also recall that chord degrees give
us one way to think about chord inversions.
For instance, when you see “V6/5,” you
may think, aha—that’s an arrangement of
V7 with the chordal third in the bass.
(And you’d be right.)
Now it’s also worth stressing out that,
unlike scale degrees and Roman numerals, these chord degrees DON’T
change when we change the key. They refer back to the chord, *not* to the key.
So if we went back to F minor again, notice
that Eb is still the chord root,
G is still the third, and so on—even though
the Roman numeral and scale degrees have changed.
So, moving on: yet another way of referring to
the notes of this chord are through the figured bass.
And as you remember, figured bass relates notes to the note that happens to be in the bass voice, via intervals.
Now I know that students often fall into the
habit of converting FB symbols directly into
chord inversions: you see “6/5” and you
think “OK—first inversion [seventh] chord." And you're right.
But it’s important to remember that “6/5”
is an abbreviation of “6/5/3” and that each
of those integers corresponds to one particular
note in this chord.
For this it might be helpful to think about
a closed-position 6/5 chord, where these intervals
are right there to see on the page, rather
than displaced by octaves.
Let’s compare this chord to the one Bach
wrote.
Both have a red G natural in the bass.
And the green Eb, which corresponds to the
“6” in the bass figures, appears as an
actual sixth above the bass in Bach’s chord.
But the yellow Db, which is indicated by the
integer “5,” is actually placed a fifth
*plus an octave* above the bass.
So here's the bass, there's the sixth above it, and there's the so-called "fifth" above it—even though it's a fifth plus an octave.
And finally, we see the same thing with the note that's a third above the bass.
Bach has placed this Bb not a third, per se, but a third *plus an octave* above the bass.
So if we take Bach's bass G, and go down 6...5...3 (that's how it sounds on the left),
then in the center of the screen you see...here's the bass...6...5...3 above the bass.
So that's how the chord on the left becomes the chord on the right.
Now, the last kind of relationship there is to talk about is intervals—which serve to relate
notes to other notes.
And by this, I mean we can relate any notes that happen to be near any other notes—like the alto voice to the
tenor voice, or one note in the soprano voice
to another in the same voice.
This won’t always come up in analysis—but
it might sometimes.
Indeed, in the chorale we’re looking at,
a keen observer might pay special attention
to the intervals between the soprano and alto
voices.
More specifically, he or she might notice
that they are always a third apart, with exactly
one exception—the downbeat of the second
bar, where they move out of phase for a moment,
giving us an accented minor second interval,
in what is surely the most expressive chord in the passage.
So those are the five relationships we’ve
learned so far.
And it’s a lot to keep track of.
But by going over them like this, my aim is to
persuade you of the importance of being as
specific as possible when you’re referring
to relationships in a musical passage.
Because the threat of confusion is pretty
much constant.
Just imagine: you’ve just gotten some homework
back from your teacher, there’s a big red
X and an explanation of what you did wrong.
And he or she writes: “on beat four, you’re
missing the fifth.”
"Missing the fifth?" That is the opposite of helpful,
and you’d have every
right to be frustrated at the vagueness of
this language: does your teacher mean scale
degree ^5?
Does he or she mean the *chordal* fifth?
Or perhaps he or she is referring to the fifth
above bass, as articulated by the bass figures.
For the same reason, I speak for all the music
theory teachers of the world when I ask that
you aspire to the same kind of precision
in your language.
And not just for the purpose of clear communication.
Vague language is often a sign of vague thinking.
And many common student errors come follow
from exactly the sort of fuzzy thought that
follows from this big pile-up of numbers. Just one very common example:
When we start learning about voice-leading—the
art of connecting chords in the classical
style—we’re going to learn that certain
notes must move in certain ways…particularly
in dominant seventh chords like the one we
see here.
When this chord moves to tonic—which it
almost always does—the chordal third will
need to move up, and the chordal seventh will
need to move down.
But notice also that the chordal third happens
to be scale degree 7.
And imagine the potential for confusion here:
in the same chord, you've got a chordal seventh that must
go down, but scale degree seven, which must go up.
You’re gonna need to be really clear on
which is which!
Students make this mistake all the time. They say "Oh, I thought the seventh goes up."
And you have to remind them: there are two sevenths here; you have to be specific.
Are you saying scale degree 7...or the chordal seventh? Precision of language leads to clear thought.
Now obviously, my hope is that this tour through
the numbers of music theory will be helpful
and not harmful.
I know that it’s easy to be overwhelmed.
But I can promise you that when you’re really
secure and really confident with these distinctions—and
the language we use to describe them—it’s
gonna give you a real leg up as things get
more complicated—which, alas, with music theory
they always do.
But it’s worth the effort—I promise you. So I’ll look
forward to seeing you soon for video no. 10.
