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>

lib/tunings.py

@@ -98,6 +98,22 @@ def open_midis_to_freqs(midis: list[int], reference_pitch: float = DEFAULT_REFER
     return [round(midi_to_freq(m, reference_pitch), 2) for m in midis]
 
 
+def freqs_to_midis(freqs: list[float], reference_pitch: float = DEFAULT_REFERENCE_PITCH) -> list[int] | None:
+    """Return absolute open-string MIDI notes for frequencies at the supplied
+    A4 reference — the inverse of open_midis_to_freqs. None if any entry is
+    non-numeric or non-positive (a provider could hand us anything)."""
+    out: list[int] = []
+    for f in freqs:
+        try:
+            f = float(f)
+        except (TypeError, ValueError):
+            return None
+        if f <= 0:
+            return None
+        out.append(int(round(69 + 12 * math.log2(f / reference_pitch))))
+    return out
+
+
 def tuning_offsets_from_midis(instrument_key: str, midis: list[int]) -> list[int] | None:
     """Return semitone offsets from the instrument's standard open strings."""
     standard = STANDARD_OPEN_MIDIS.get(instrument_key)