ELEMENTS: Harmony/Cadences

Worksheet

Find a piano (here in class, during the break, or in a dorm).
If you can't, then find a guitar.
If you absolutely can't find any instrument, play the dots on this page.

Play a diatonic or Ionian scale (see your handout on scales).
Number each note in your head as you play it:


1		2		3	4		5		6		7	8

	whole step		whole step		half step	whole step		whole step		whole step		half step

Pick out and play separately:

1,	5,	8


(if you are using the dots, take the time to test yourself by picking out 8, 5 and 1 out of the full scale above in No. 2)

Now play these three notes simultaneously in a chord:


8		again, to be sure you can hear the elements which create the simultaneity, play them individually in No.3
5
1

In this course, we will talk about pieces ending in "hollow" cadences: we mean that the very last chord or group of simultaneous notes is some version of the above sonority. The "hollowness" we refer to, is the fact that there are no notes between 1 and 5. When it is "hollow" like this, the interval is called an open fifth.

Now pick out the following notes and play them separately:

1,	3,	5,	8

And play them simultaneously in a four-note chord:


8		again, to be sure you can hear the elements which create the simultaneity, listen to them individually above
5
3
1

The use of 3 between 1 and 5 is considered to "fill" the fifth. This sonority is considered "filled" (not "hollow"), and is more familiar to our 21st-century ears as a final cadential chord.

What you need to make an effort to understand and internalize as a student of music history, is that before 1600 this sonority was perceived as "imperfect", (although from 1300 or so onward, it had been perceived as increasingly consonant and pleasing!) On the other hand, the first chord you played, 8-5-1, was heard as a perfect consonance, and thus the only suitable and fitting way to cadence or end a phrase or a piece.

Now let's talk about cadential formulae, or the way we approach the final sonority.

First, let's approach monophonically, one line at a time:

Play the following sequences, and listen to how they "resolve" to the tonic (1 or 8). (Reminder: the tonic or home-note was called the final in Gregorian chant.)


7...8	2...1

Again, the act of choosing the notes from the scale to create these musical "phonemes" is fundamental to developing an instinctive understanding of their meaning: if you are not doing this on a piano, guitar or another instrument, go back and pick out these notes out of the full scale in No. 2

Now try some many-voiced or polyphonic cadential formulae. Play the following.

(Listen to these "simultaneities" horizontally as well as vertically.)


	one at a time, horizontally	one at a time, vertically	all together
7...8
2...1
A possible cadential formula or resolution to a "hollow" 8-5-1 chord:
7...8
5...5
2...1
A possible cadential formula or resolution to a "filled" 8-5-3-1 chord:
7...8
5...5
4...3
2...1
Notice the dissonance of the 7-5-4-2 chord, which was created when you added 4, a tritone (the devil's interval) away from 7. Go back and play them individually in No. 2's scale so you can hear that perfect dissonance exposed.

You will not be expected to know exactly which pitches make up any of the cadential formulae we encounter in the music of study, but it is important that you recognize whether or not a cadence is occurring. All cadential formulae juxtapose a feeling of suspension with a feeling of resolution. In the cadential formulae immediately above, please note that this is accomplished harmonically: dissonance "resolves" to consonance. The cadential roles of these harmonic qualities, i. e. dissonance as a quality requiring resolution, and consonance as the resolver, will come to shape the story of Western harmony and the cultural empire of its tonal system.

One more thing. Play the following simultaneity:


5
3
1

This "filled" chord is specifically called a triad because of its very particular sound. The reiteration of 1 and 8 becomes understood and less important than it was in the antique 8-5-1. This does not mean that any one of 5, 3, or 1 may not be reiterated–they usually are. It just means that those three notes are all that's necessary for an ultimate sonority, after 1600.

You may hear of "inversions" of the triad:


1
5
3

This is often called a "first inversion" triad as opposed to the "root position" triad above. While the "root position" triad is preferred for cadential use, in any other harmonic function, the two inversions are virtually interchangeable.

However, this inversion is considered unstable because 5 is in the bottom. How do you hear it? Does it seem unstable to you?


3
1
5

If it doesn't, great! You are very open-minded and will have an easier time on our imminent journey into the music of the Middle Ages. If 3-1-5 does seem unstable to you, congratulations, you have been successfully brainwashed by the cadential formulae which permeate our culture: you expect a 5 in the bottom of the chord to resolve to a 1. Like this!


	one at a time, horizontally	one at a time, vertically	all together
7...8
5...5
4...3
2...1
5...1

Now you are probably hearing the most familiar cadential formula of all. ("Amen", anyone?) Notice how the bottom or "bass" notes moving from 5 to 1 helps to enhance and solidify the sense of resolution. This is a classic tonal system cadence.

Introduction to the Cadence

Worksheet