Lesson 5
Where traditions disagree
There is one test that separates a fact about hearing from an agreement about practice, and it is cheap to apply. A fact about hearing cannot be systematically contradicted by music that works. An agreement can, and regularly is.
The test
If a rule describes how ears work, then a repertoire built entirely on breaking it should fail. Not sound unusual: fail. Listeners should be unable to follow it, and it should not survive as a practice.
That is a strong prediction and an easy one to check, because the rules from lesson 1 are implemented. The checker does not know which century it is in. Point it at anything.
The examples in the next figure are constructed from definitions rather than quoted from transcriptions, which is what lets this lesson exist in a course that refuses corpus claims. Parallel organum at the fifth is a line doubled a fifth away; that is what the term means. A power chord is a root and a fifth. No assertion is being made about how any particular piece goes.
The rule, applied where it is not in force
Same checker as lesson 1. Different music.
A chant line doubled a fifth below, which is what the term means.
- Chord changes
- 8
- Breaking the rule
- 8
- Rate
- 100%
- Sounds broken
- no
Three of these score a hundred per cent against the most famous prohibition in Western music, and one of them is octave doubling, which the tradition that forbids parallel octaves uses constantly the moment it has an orchestra. A rule with a real mechanism behind it, breached completely and deliberately by centuries of music on either side of the period that invented it, is not a fact about hearing. It is a fact about what one repertoire decided it wanted its texture to do.
A hundred per cent, three times
Parallel organum breaks the rule on every chord change. So do power chords. So does octave doubling, and that one is the awkward case, because octave doubling is not a foreign practice at all: the same tradition that forbids parallel octaves between voices doubles melodies at the octave the moment it has an orchestra to do it with.
The rule was never a claim about sound. It is a claim about voices, in a texture where the number of independent parts is the thing being tracked. Lesson 1 got the mechanism right and the scope wrong, and the scope is where conventions live. Double a melody at the octave and you have not damaged anything, because nobody was counting those as two parts.
One rule, three repertoires on both sides of the period that invented it, all scoring maximally against it, none of them broken. Whatever the prohibition is, it is not a description of hearing.
The harder version
Parallel fifths are an easy target because the rule is explicitly a style marker. Here is a case where the tradition believes it has found something deeper.
Harmony lesson 4 derived why the authentic cadence works, and it was a genuine derivation. The dominant seventh contains the only tritone in the key, the tritone has a forced resolution, and the leading tone sits a semitone under the tonic. Two real mechanisms, neither invented.
So test whether they are available anywhere else. The seven modes are seven rotations of the same seven notes; if the cadence follows from something about hearing, it should not care much which rotation you start on.
Which modes can even have the cadence
Both conditions from Harmony lesson 4, checked on all seven.
Ionian: the seventh chord on its fifth degree is G B D F. It has both ingredients, so the authentic cadence is available.
- Modes checked
- 7
- With both ingredients
- 1
- Tritone only
- 1
- Leading tone only
- 1
One mode of seven. The cadence that most of Western theory is organised around requires two independent things to coincide, and they coincide in exactly one of the seven rotations of the same set of notes. Every other mode has music written in it, none of that music is missing an ending, and what those endings use instead is not a weaker version of this mechanism but a different arrangement entirely. A theory of closure built on the one case that has the tritone is a theory of that case.
One of seven
Only Ionian has both ingredients. The near misses matter more than the count: Phrygian has the tritone in its dominant seventh and no leading tone, Lydian has the leading tone and no tritone. So this is not one mode being richer than the others. It is two independent conditions that happen to coincide in exactly one of seven rotations.
Music exists in all seven. None of it is missing endings. What those endings use instead is not a degraded version of the authentic cadence but a different arrangement: a step down from the seventh, a modal final, a drone that never left. The mechanism Harmony lesson 4 derived is real, and it is available in one seventh of the cases, and a theory of closure built on it is a theory of that seventh.
Worth being careful about what this does not show. Common-practice music mostly is in Ionian or its minor, so a theory built for it is not wrong about its subject, and the modes are not equally common in any repertoire. The claim is narrower: the derivation explains why the cadence works where it is available, and cannot explain why closure works everywhere else, which it plainly does.
What the test actually buys
It does not show that the rules are arbitrary. Both of the ones examined here have real mechanisms and lesson 1 made the case for the first at full strength.
What it shows is a scope error that runs through most writing about musical rules. A mechanism is found, it is real, and the conclusion drawn is that the rule follows from how hearing works. The conclusion does not follow. What follows is that the rule is a good way to get a particular result, and the result was chosen.
The reliable signal is disagreement between traditions that were never in contact. Two groups can hold incompatible rules and both be producing music their listeners follow effortlessly. That is only possible if the rules are about the music and not about the ears, and it is the reason this course had to exist alongside the other four.