Serve exact MIDI notes from GET /api/tunings (tuningMidis) (#829)

The tunings catalog is served as frequencies scaled to the reference pitch,
so every consumer that needs note identities (the v3 instrument badge's
TUNING_NOTE, plugins converging on the host profile model) reconstructs MIDI
numbers client-side via log2 — a rounding footgun at non-440 references, and
N copies of code the host can run once.

Add `tuningMidis` to the response: the same catalog keyed instrument-count →
name → absolute open-string MIDI notes (low → high). Built-ins come straight
from TUNING_PRESET_MIDIS (no float round-trip at all); provider-contributed
entries are inverted from their frequencies at the served reference via the
new freqs_to_midis() (the inverse of open_midis_to_freqs, garbage-guarded).
Purely additive — referencePitch/tunings are unchanged.

Tests: every built-in round-trips at 440; round-trip holds at 430/432/444/450
(the exact case client-side reconstruction drifts on); garbage rejected.


Claude-Session: https://claude.ai/code/session_01MS2YFb6UUSwJVV6CmEa25i

Signed-off-by: ChrisBeWithYou <christian.a.cowan@gmail.com>
Co-authored-by: Claude Fable 5 <noreply@anthropic.com>

tests/test_tunings.py

@@ -249,3 +249,30 @@ def test_flat_string_count_patch_resets_incompatible_named_tuning():
     patched = apply_flat_instrument_patch_to_profiles(settings, {"string_count": 7})
     assert patched["string_count"] == 7
     assert patched["tuning"] == "Standard"
+
+
+# ── freqs_to_midis (the /api/tunings tuningMidis inverse) ────────────────────
+
+def test_freqs_to_midis_round_trips_every_builtin_at_440():
+    from tunings import freqs_to_midis
+    for key, presets in TUNING_PRESET_MIDIS.items():
+        for name, midis in presets.items():
+            assert freqs_to_midis(open_midis_to_freqs(midis)) == midis, f"{key}/{name}"
+
+
+def test_freqs_to_midis_round_trips_at_nonstandard_reference():
+    # The consumer footgun this exists to kill: frequencies served at a 432/450
+    # reference must recover the SAME integer midis when inverted at that
+    # reference (client-side log2-at-440 reconstruction drifts here).
+    from tunings import freqs_to_midis
+    for ref in (430.0, 432.0, 444.0, 450.0):
+        for midis in (TUNING_PRESET_MIDIS["guitar-8"]["Standard"], TUNING_PRESET_MIDIS["bass-5"]["Standard"]):
+            freqs = open_midis_to_freqs(midis, ref)
+            assert freqs_to_midis(freqs, ref) == midis, f"ref={ref}"
+
+
+def test_freqs_to_midis_rejects_garbage():
+    from tunings import freqs_to_midis
+    assert freqs_to_midis([82.41, 0]) is None          # non-positive
+    assert freqs_to_midis([82.41, "x"]) is None        # non-numeric
+    assert freqs_to_midis([]) == []                    # vacuously fine