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.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01MS2YFb6UUSwJVV6CmEa25i
Signed-off-by: ChrisBeWithYou <christian.a.cowan@gmail.com>
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