A chord cannot be rooted on the one degree whose fifth is a tritone

[Gamah]

Found from 8nj8bjys:0 — a pop song that sounds minor, spooky and out of key.

The chord

--score bar 14 against bar 13, in B lydian (B C# D# E# F# G# A#):

bar 13 [chord 0]  61 66 71 -> 63 66 71    C# F# B -> D# F# B    B sus2 -> B major   ok
bar 14 [chord 1]  65 66 72 -> 65 68 72    F  F# C -> F  G# C    ???    -> F minor

A chord rooted on the tritone, containing C natural — a semitone above the tonic and in no
reading of the key — for one bar in every four, all song. The lead's out-of-key note is that same
C: NearestSoundingTone correctly snaps the tune onto the chord that is actually sounding.

Why

PopProgressions row {0, 3, 5, 4} is commented I-IV-vi-V, which is true in major. Pop also
draws lydian, where degree 3 is the ♯4 and its triad has no perfect fifth. VoicedTone then
forces one — right for the shape a guitarist frets, and on that degree it imports a pitch from
outside the scale, so the chord comes out consonant, confident and in another key.

Every seven-note mode has exactly one such degree. It bites wherever a genre's progressions land
on it:

genre	mode	degree	rows affected
pop	lydian (1 in 4)	3	5 of 5
metal	aeolian (2 in 7)	1	3 of 6 — the ♭II rows, which are phrygian vocabulary
metal	harmonic minor (1 in 7)	1, 2, 6	6 of 6
ska	major (2 in 3)	6	2 of 6 — the ♭VII rows, which are mixolydian vocabulary
rock	dorian (2 in 5)	5	1 of 6 — the ♭VI row, which is an aeolian reading
punk, country	—	—	none

17 of 67 (genre, mode, progression) pairings.

The fix

Not a table per mode. Walk the root back two degrees until its fifth is perfect
(Harmony.PlayableProgressions, applied at the draw in Compose.cs). That lands on the triad
containing the original degree as a chord tone, in every scale this engine draws — lydian's ♯4
is II's third, dorian's ♮6 is the major IV's, phrygian's 5th is ♭III's, major's leading tone is V's.
That is not a coincidence to be tuned: a mode's characteristic note lives in a chord, and rooting a
chord on it is the mistake.

So a mode becomes a transformation of one progression table rather than a filter over it, and
variety goes up rather than down:

	before	after
clean (mode, progression) pairings	50	65
broken pairings	17	0

The seed above now draws [0 1 5 4] — I-II-vi-V, a real lydian pop loop — and bar 14 sounds
C# D# G# resolving to C# major, every note in the key.

Two rows do not survive the move and are dropped: ska's I-♭VII-V-I under major (collapses to
I-V-V-I) and rock's i-iv-♭VII-i under dorian (lands on the row above it). A row written as a
pedal keeps its repeats.

VoicedTone is untouched — with nothing ever rooted on the tritone degree it only ever sees
degrees where forcing the fifth is already correct, and it stays right for the power chord it was
written for.

Tests

Four new invariants in the harmony section, each with the vacuity check the file's style asks for:

• no drawn chord sits on a degree its mode cannot root (the guard)
• some written row really does name an unrootable degree (or the guard is vacuous)
• an unrootable degree's substitute contains it as a chord tone (the law itself — a scale added
  later that breaks it needs looking at, not accepting)
• substitution never turns a changing loop into a pedal

572 checks passed, node suite green, web/_framework re-staged from this engine
(bundle-stamp check clean). The render digests were unaffected — none of the 10 matrix seeds
draws one of the affected modes, which is worth knowing about that matrix rather than reassuring.

One judgement call left open

The written-table cap (no two genres share more than one progression) still holds and is still
asserted. But substitution can land two genres on the same realised changes — metal's ♭II rows
read as rock's ♭VII vamp under aeolian, because that is what those degrees are in aeolian. Six
such pairs. Arguably correct (they are genuinely the same aeolian vamp, separated by tempo, kit and
voicing) and arguably not, so the test prints the number rather than failing on it.

Not in this PR

8nj8bjys:0's other defect: the tune's consequent restates its antecedent verbatim, so the 8-bar
period is a 4-bar loop, and pop/punk get one 2-bar rhythm for the whole tune. Filed as PLAN.md
rank 38.

---

Second commit: the tune's period (was PLAN rank 38, now deleted)

Melody.Draw gives the consequent exactly one thing to vary — its own AnswerOp — and drawing it
freely lets it be the antecedent's. Over the same call that is the same phrase but for its last
note, so the four-phrase period collapses to the two-phrase tune it was written to be bigger than.
13 of 480 drawn periods did that, 8nj8bjys:0's chorus among them.

Two changes:

• The consequent's AnswerOp is drawn without replacement against the antecedent's, by zeroing
  a weight rather than by re-drawing — one draw either way, so the tune's stream does not shift. A
  genre that weights a single operator keeps it (an answer it would never write is worse than an
  answer heard twice).
• Melody.ShortShapeWeights — at MinPhraseBars only Contrasting puts a second rhythm into a
  tune, so Parallel and Varied hand the most exposed voice in the mix one two-bar rhythm to sing
  four times. Worst for pop and punk, whose single-bar four-chord cycle puts every phrase at the
  floor: the genres the period work was written for. {2, 3, 5} instead of {4, 3, 3} there — a
  lean, not a rule, since a parallel period is real at two bars too.

--stats, 100 songs × 6 genres, distinct phrase rhythms and contours within one tune:

	before	after
phrase rhythms	1.25 – 1.42	1.46 – 1.57
phrase contours	3.35 – 3.49	3.64 – 3.73

A period holds at most two rhythms, so the first figure reads the Contrasting rate almost
directly — half of tunes now, a quarter before.

New check: a parallel period never answers itself the same way twice. Verified non-vacuous — it
reports 13 of 480 with the without-replacement draw removed.

One thing from the original diagnosis was wrong and is not changed. I reported the chorus tune
as sparser than the verse and blamed a missing mechanism. The mechanism exists (move, 1 for the
chorus and 0.8 for the verse, leaning the length draw across the LongFrom split) and the engine
suite already asserts it over 60 tunes. 8nj8bjys:0 is one draw going the other way, which is what
a lean does. docs/composition.md now says so, so the row does not get re-filed off one song.

Digests re-blessed — this is meant to be audible. 573 checks passed, node suite green, bundle
re-staged.