Lesson 6
Breaking them on purpose
Five lessons establishing that these rules are agreements rather than laws. This one stops arguing and asks the question that was always underneath: if a convention is only an agreement, what is it for?
How much freedom is there
Start with something narrower. A dominant seventh is sounding. Where is the music allowed to go?
The rules answer this without being asked about cadences at all. The leading tone has to rise a semitone. The seventh has to fall a semitone. So whatever comes next has to contain both of those destinations, and that is a test you can run over every chord in the key.
Where the music is allowed to go
Two tendency tones, seven candidates, and not much of a choice.
The leading tone B must rise to C, and the seventh F must fall to E. Any chord that can follow has to contain both.
- Candidates
- 7
- The rules permit
- 2
- Selected
- I
- Legal resolutions
- 42
Two. The tonic, and the one other triad that happens to contain both notes the tendency tones are obliged to land on. That is why the deceptive cadence is a named thing rather than one of a dozen ways to avoid an ending: the rules leave exactly one alternative, so the tradition only ever needed a name for one. Play the forbidden ones and you can hear why the rules bother - and also that they are perfectly possible to play.
Two
Of the seven diatonic triads, exactly two contain both notes: the tonic, and the submediant. Everything else is unreachable without breaking one of the two resolution rules.
Which explains something about the vocabulary. The deceptive cadence is a named device, taught alongside the authentic one, and it can look arbitrary that this particular substitution got a name when so many others did not. It got a name because there are no others. The rules leave one alternative, so the tradition only ever needed a word for one.
One note decides whether it ended
Same dominant, same three upper voices. The bass chooses.
- upper three voices identical
- leading tone rises in both
- seventh falls in both
- breaks no rule either way
- vi contains every note of I
- roughness within 2.0%
- bass moves 3 semitones
- Roughness differs by
- 2.0%
- Roughness, I
- 0.474
- Roughness, vi
- 0.465
- Rules broken
- 0
Switch between them. Three of the four voices do not move at all between the two versions, both obey every rule in the course, and their roughness differs by two per cent. The deceptive chord is stranger than that, though: it contains every note the tonic chord had and adds one underneath. Nothing was taken away. One of these ends the music and the other does not, and the entire difference lives in what the dominant seventh had led you to expect. That is what a convention buys. Not a restriction on what may happen, but an expectation precise enough that moving one voice by three semitones is an event.
Nothing is broken
The pair in that figure was found by searching both sets of legal resolutions for one where the upper three voices could stay put. It exists. The same dominant seventh, the same soprano, alto and tenor, and the bass alone choosing between C and A.
Every measurement says these are the same event. Roughness differs by two per cent. The leading tone rises in both, the seventh falls in both, and neither breaks a single rule from lesson 3. The deceptive cadence is not a violation of anything. It is fully grammatical.
The relationship between the two chords is stranger than a substitution, as well. Because the resolution rules cost the tonic its fifth - which is lesson 3's finding arriving again - the tonic here is two notes, and the deceptive chord contains both of them and adds an A underneath. Nothing is removed. The music is denied its ending by a chord that has everything the ending had in it.
And it is unmistakable. Not subtle, not a matter of taste: everyone raised on this music hears the floor go missing. That effect is produced by three semitones in one voice, and none of it is in the second chord.
What the convention was for
This is the answer to the question the course has been circling. A convention is not a restriction on what may happen. It is a way of making an expectation precise enough that departing from it counts as an event.
Without the convention there is no deceptive cadence, because there is nothing being deceived. The chord is just a chord. The whole effect is borrowed from the strength of the expectation, and the expectation exists because a great many pieces did the ordinary thing first.
That is why the answer to can I break this rule is uninteresting and the answer to what does breaking it buy is not. Composers who broke these rules to real effect were not escaping the tradition; they were spending it. The effect is proportional to how firmly the rule was in force, which means it is a finite resource, and it is why the same device wears out.
The uncomfortable corollary, which this course should state rather than dodge. A listener who has not heard enough of the ordinary case does not get the effect. Not a diminished version of it: none of it. That is not a claim about musical sophistication - it is the same mechanism that makes a joke fail if you have not heard the setup, and it applies to everyone equally, including to any tradition whose conventions you have not spent time inside.
Where that leaves the rules
Lesson 1 measured one prohibition and found it took about a fifth of the options, with a real mechanism behind it. Lesson 3 ran six of them together and found they leave 42 arrangements out of 780, and force a chord the tradition separately calls defective. Lesson 5 found three repertoires that break the famous one on every chord change and one mode of seven that can even have the cadence.
None of that makes the rules worthless, and reading this course as debunking would be reading it backwards. Precise, learnable, widely-shared conventions are what make a shared expectation possible, and a shared expectation is the raw material of nearly every effect in the music. The rules are not true. They are agreed, and being agreed is what they needed to be.