note: land the programmed capture-signal model — division ladder, tempo resolution, anchored offsets, one record and one resolver

src/core/instrument/CMakeLists.txt

@@ -1,3 +1,4 @@
 add_subdirectory(engine)
 add_subdirectory(map)
+add_subdirectory(note)
 add_subdirectory(ui)

src/core/instrument/note/CLAUDE.md

@@ -0,0 +1,63 @@
+# src/core/instrument/note — the programmed capture signal
+
+## Scope
+
+The pure model of the note the sampler plays to itself when it resamples: how long it
+sounds, how hard, and how far around it the capture window opens. A fourth peer of
+`engine/` / `map/` / `ui/` under `core/instrument/`, and pure by the same rule — no REAPER
+types, no VST3 types, no host at all.
+
+It exists as its own directory because it is neither engine (it renders nothing), mapping
+(it resolves no capture and builds no `SampleData`), nor UI (it computes no geometry). It
+is a performance *description* plus its arithmetic, read by two consumers that must not
+diverge: the capture-signal popup that edits it and the bake that renders it.
+
+## Invariants
+
+- **One record, one resolver.** `NoteProgram` is the single source of truth and
+  `resolveNote` the single way to turn it into times. A preview that computes its own
+  window, or a bake that does, is the exact divergence this module exists to prevent — the
+  criterion is structural (one path), not "the numbers looked close."
+- **The tempo comes in as a parameter.** The BPM in effect at the project cursor is read by
+  the shell. Nothing here may reach for it, and no tempo is hardcoded anywhere in the
+  directory — `Tempo` has no default and cannot be constructed without one.
+- **Resolved times are rate-free seconds.** The standing ruling: no sample rate appears
+  here; the caller converts seconds to frames against the live rate.
+- **Note length is musical-division-only.** Offsets carry the ms/beats duality; the note
+  length does not. A free-duration note length would make two records describe the same
+  performance at one tempo and different performances at another.
+- **A division persists as its `{quarterExponent, modifier}` pair, never as its picker
+  index.** The index is presentation order and would silently re-map every saved record if
+  the ladder ever gained a rung or a modifier.
+- **An offset stores the denomination it was entered in.** The other view is derived on
+  demand. Storing resolved seconds instead would make a beats-denominated offset stop
+  following the tempo, which is the only reason to express one in beats.
+
+## Modules
+
+- `musical_division` — the note-length ladder: 1/64 through 64/1 (a rung is the base-2
+  exponent of its length in quarter notes, -4..8), each straight, dotted (x3/2), or triplet
+  (x2/3); the 39-entry picker order; and the `"1/8."` / `"1/4t"` label notation. Lengths in
+  beats only, so it links no tempo.
+- `tempo` — a validated project tempo plus every beats <-> seconds <-> ms conversion.
+  Construction (`Tempo::fromBpm`) is the only place a bad BPM is rejected, which is what
+  lets each conversion be total and every downstream resolver be failure-free.
+- `note_program` — `Velocity` (clamped 1..127), the denominated `OffsetAmount` and its unit
+  toggle, the anchored `StartOffset` / `EndOffset`, the `NoteProgram` record, and
+  `resolveNote`.
+
+## Gotchas
+
+- **A beat is a quarter note.** REAPER states project tempo in quarter notes per minute
+  regardless of time signature, so divisions resolve with no time signature in sight. A
+  beats *readout* that should track a compound meter's dotted-quarter pulse would need the
+  time signature threaded in — it is not, deliberately.
+- **`StartOffset` and `EndOffset` are distinct types on purpose.** They hold the same
+  payload and differ only in what they anchor to (note-on and note-off respectively);
+  collapsing them into one type with an anchor field makes the swap a runtime bug instead
+  of a compile error.
+- **Signs are uniform: positive is later in time.** So Daniel's "capture from 20 ms before
+  note-on" is a *negative* start offset, and a negative end offset truncates before release.
+  Both are legal; `resolveNote` only refuses to invert the window.
+- **ms <-> beats round-trips are lossless to double precision, not bit-identical.** The
+  conversion is a multiply/divide pair; compare with an epsilon.

src/core/instrument/note/CMakeLists.txt

@@ -0,0 +1,14 @@
+reasampler_pure_library(musical_division SOURCES musical_division.cpp)
+# Links only musical_division: the ladder is beats-only, so it must prove out with no tempo
+# in the link line at all.
+reasampler_test(musical_division LINK musical_division)
+
+reasampler_pure_library(tempo SOURCES tempo.cpp)
+reasampler_test(tempo LINK tempo)
+
+# The record composes the ladder and the tempo and nothing else — the programmed signal is
+# plain data, provable without the engine, the bank, or a host.
+reasampler_pure_library(note_program
+    SOURCES note_program.cpp
+    LINK PUBLIC musical_division tempo)
+reasampler_test(note_program LINK note_program)

src/core/instrument/note/musical_division.cpp

@@ -0,0 +1,68 @@
+// musical_division.cpp — see musical_division.h. Pure; standard library only.
+
+#include "core/instrument/note/musical_division.h"
+
+#include <algorithm>
+#include <cmath>
+
+namespace reasampler::instrument::note {
+namespace {
+
+double modifierFactor(DivisionModifier m) {
+    switch (m) {
+        case DivisionModifier::Dotted:  return 1.5;
+        case DivisionModifier::Triplet: return 2.0 / 3.0;
+        case DivisionModifier::Straight: break;
+    }
+    return 1.0;
+}
+
+int clampExponent(int quarterExponent) {
+    return (std::max)(kMinQuarterExponent, (std::min)(kMaxQuarterExponent, quarterExponent));
+}
+
+}  // namespace
+
+bool operator==(Division a, Division b) {
+    return a.quarterExponent == b.quarterExponent && a.modifier == b.modifier;
+}
+
+bool operator!=(Division a, Division b) { return !(a == b); }
+
+Division makeDivision(int quarterExponent, DivisionModifier modifier) {
+    Division d;
+    d.quarterExponent = static_cast<std::int8_t>(clampExponent(quarterExponent));
+    d.modifier = modifier;
+    return d;
+}
+
+double divisionBeats(Division d) {
+    const Division legal = makeDivision(d.quarterExponent, d.modifier);
+    return std::ldexp(1.0, legal.quarterExponent) * modifierFactor(legal.modifier);
+}
+
+Division divisionAt(int index) {
+    const int clamped = (std::max)(0, (std::min)(kDivisionCount - 1, index));
+    return makeDivision(kMinQuarterExponent + clamped / kModifierCount,
+                        static_cast<DivisionModifier>(clamped % kModifierCount));
+}
+
+int divisionIndex(Division d) {
+    const Division legal = makeDivision(d.quarterExponent, d.modifier);
+    return (legal.quarterExponent - kMinQuarterExponent) * kModifierCount
+           + static_cast<int>(legal.modifier);
+}
+
+std::string divisionLabel(Division d) {
+    const Division legal = makeDivision(d.quarterExponent, d.modifier);
+    const int e = legal.quarterExponent;
+    // Both branches meet at e == 2 ("1/1"): a division's written form is its length in
+    // whole notes, which is 2^(e-2).
+    std::string label = e <= 2 ? "1/" + std::to_string(1 << (2 - e))
+                               : std::to_string(1 << (e - 2)) + "/1";
+    if (legal.modifier == DivisionModifier::Dotted) label += '.';
+    else if (legal.modifier == DivisionModifier::Triplet) label += 't';
+    return label;
+}
+
+}  // namespace reasampler::instrument::note

src/core/instrument/note/musical_division.h

@@ -0,0 +1,50 @@
+// musical_division — the note-length ladder the capture signal is programmed from: 1/64
+// through 64/1, each straight, dotted, or triplet. Lengths are in BEATS only; the tempo
+// resolution belongs to `tempo`, which keeps this ladder provable without one.
+
+#pragma once
+
+#include <cstdint>
+#include <string>
+
+namespace reasampler::instrument::note {
+
+enum class DivisionModifier : std::uint8_t {
+    Straight,
+    Dotted,   // x 3/2
+    Triplet,  // x 2/3
+};
+
+// A rung of the ladder is the base-2 exponent of its length in quarter notes: -4 is 1/64,
+// 0 is 1/4, 2 is 1/1, 8 is 64/1. Holding the exponent rather than a table of literal beat
+// counts keeps every straight and dotted length exactly representable in double.
+inline constexpr int kMinQuarterExponent = -4;
+inline constexpr int kMaxQuarterExponent = 8;
+inline constexpr int kRungCount = kMaxQuarterExponent - kMinQuarterExponent + 1;
+inline constexpr int kModifierCount = 3;
+inline constexpr int kDivisionCount = kRungCount * kModifierCount;
+
+struct Division {
+    std::int8_t quarterExponent = 0;  // 1/4
+    DivisionModifier modifier = DivisionModifier::Straight;
+};
+
+bool operator==(Division a, Division b);
+bool operator!=(Division a, Division b);
+
+// Off-ladder exponents clamp rather than reject: the only ways to reach one are a corrupt
+// persisted record or a picker bug, and the nearest legal length beats a nonsense duration.
+Division makeDivision(int quarterExponent, DivisionModifier modifier);
+
+// Length in beats (quarter notes). Always > 0.
+double divisionBeats(Division d);
+
+// Picker order: shortest rung first, straight/dotted/triplet within each rung. Index is
+// presentation order only — see this directory's CLAUDE.md before persisting one.
+Division divisionAt(int index);
+int divisionIndex(Division d);
+
+// The notation divisions are named in: "1/16", "1/8.", "1/4t", "4/1".
+std::string divisionLabel(Division d);
+
+}  // namespace reasampler::instrument::note

src/core/instrument/note/note_program.cpp

@@ -0,0 +1,68 @@
+// note_program.cpp — see note_program.h. Pure; standard library only.
+
+#include "core/instrument/note/note_program.h"
+
+#include <algorithm>
+
+namespace reasampler::instrument::note {
+
+Velocity Velocity::of(int value) {
+    Velocity v;
+    v.value_ = static_cast<std::uint8_t>((std::max)(kMin, (std::min)(kMax, value)));
+    return v;
+}
+
+bool operator==(Velocity a, Velocity b) { return a.value() == b.value(); }
+
+bool operator==(OffsetAmount a, OffsetAmount b) {
+    return a.magnitude == b.magnitude && a.denomination == b.denomination;
+}
+
+bool operator!=(OffsetAmount a, OffsetAmount b) { return !(a == b); }
+
+OffsetAmount offsetFromMs(double ms) { return {ms, Denomination::Milliseconds}; }
+
+OffsetAmount offsetFromBeats(double beats) { return {beats, Denomination::Beats}; }
+
+double offsetMs(OffsetAmount amount, Tempo tempo) {
+    return amount.denomination == Denomination::Milliseconds ? amount.magnitude
+                                                             : tempo.beatsToMs(amount.magnitude);
+}
+
+double offsetBeats(OffsetAmount amount, Tempo tempo) {
+    return amount.denomination == Denomination::Beats ? amount.magnitude
+                                                      : tempo.msToBeats(amount.magnitude);
+}
+
+double offsetSeconds(OffsetAmount amount, Tempo tempo) {
+    return amount.denomination == Denomination::Beats
+               ? tempo.beatsToSeconds(amount.magnitude)
+               : msToSeconds(amount.magnitude);
+}
+
+OffsetAmount redenominate(OffsetAmount amount, Denomination to, Tempo tempo) {
+    if (amount.denomination == to) return amount;
+    return to == Denomination::Beats ? offsetFromBeats(offsetBeats(amount, tempo))
+                                     : offsetFromMs(offsetMs(amount, tempo));
+}
+
+bool operator==(const NoteProgram& a, const NoteProgram& b) {
+    return a.length == b.length && a.start.amount() == b.start.amount()
+           && a.end.amount() == b.end.amount() && a.velocity == b.velocity;
+}
+
+bool operator!=(const NoteProgram& a, const NoteProgram& b) { return !(a == b); }
+
+ResolvedNote resolveNote(const NoteProgram& program, Tempo tempo) {
+    ResolvedNote out;
+    out.noteOffSeconds = tempo.beatsToSeconds(divisionBeats(program.length));
+    out.captureStartSeconds = offsetSeconds(program.start.amount(), tempo);
+    out.captureEndSeconds = out.noteOffSeconds + offsetSeconds(program.end.amount(), tempo);
+    // An inverted window has no meaning to a renderer, so a far-negative end offset yields a
+    // zero-length capture the caller can reject rather than a negative one it cannot.
+    out.captureEndSeconds = (std::max)(out.captureEndSeconds, out.captureStartSeconds);
+    out.velocity = program.velocity.value();
+    return out;
+}
+
+}  // namespace reasampler::instrument::note

src/core/instrument/note/note_program.h

@@ -0,0 +1,99 @@
+// note_program — the programmed capture signal: one note length, one velocity, two anchored
+// offsets, and the one resolver a preview and a bake must share.
+//
+// Resolved times are rate-free SECONDS relative to note-on; the caller converts against the
+// live sample rate.
+
+#pragma once
+
+#include <cstdint>
+
+#include "core/instrument/note/musical_division.h"
+#include "core/instrument/note/tempo.h"
+
+namespace reasampler::instrument::note {
+
+class Velocity {
+public:
+    static constexpr int kMin = 1;  // 0 is note-off in MIDI; a programmed note must sound
+    static constexpr int kMax = 127;
+
+    Velocity() = default;
+    static Velocity of(int value);  // clamped into [kMin, kMax]
+
+    std::uint8_t value() const { return value_; }
+
+private:
+    std::uint8_t value_ = 100;
+};
+
+bool operator==(Velocity a, Velocity b);
+
+enum class Denomination : std::uint8_t { Milliseconds, Beats };
+
+// One magnitude, in the denomination it was entered in; the other view is derived on demand
+// and never stored. Which one was entered is itself the intent: a beats offset must follow a
+// tempo change and a ms offset must hold still, and only a stored denomination says which.
+struct OffsetAmount {
+    double magnitude = 0.0;
+    Denomination denomination = Denomination::Milliseconds;
+};
+
+bool operator==(OffsetAmount a, OffsetAmount b);
+bool operator!=(OffsetAmount a, OffsetAmount b);
+
+OffsetAmount offsetFromMs(double ms);
+OffsetAmount offsetFromBeats(double beats);
+
+double offsetMs(OffsetAmount amount, Tempo tempo);
+double offsetBeats(OffsetAmount amount, Tempo tempo);
+double offsetSeconds(OffsetAmount amount, Tempo tempo);
+
+// The unit toggle: the same instant restated in the other denomination.
+OffsetAmount redenominate(OffsetAmount amount, Denomination to, Tempo tempo);
+
+// Two types rather than one carrying an anchor field: the anchor is then unswappable at
+// compile time. Sign is uniform — positive is later in time — so a capture that opens before
+// the note is a negative start offset, and a negative end offset truncates before release.
+class StartOffset {
+public:
+    StartOffset() = default;
+    explicit StartOffset(OffsetAmount amount) : amount_(amount) {}
+    OffsetAmount amount() const { return amount_; }
+
+private:
+    OffsetAmount amount_{};
+};
+
+class EndOffset {
+public:
+    EndOffset() = default;
+    explicit EndOffset(OffsetAmount amount) : amount_(amount) {}
+    OffsetAmount amount() const { return amount_; }
+
+private:
+    OffsetAmount amount_{};
+};
+
+struct NoteProgram {
+    Division length{};
+    StartOffset start{};
+    EndOffset end{};
+    Velocity velocity{};
+};
+
+bool operator==(const NoteProgram& a, const NoteProgram& b);
+bool operator!=(const NoteProgram& a, const NoteProgram& b);
+
+struct ResolvedNote {
+    double noteOffSeconds = 0.0;       // == the note's sounding length, note-on being 0
+    double captureStartSeconds = 0.0;  // negative when the capture opens before the note
+    double captureEndSeconds = 0.0;
+    std::uint8_t velocity = 1;
+
+    double captureLengthSeconds() const { return captureEndSeconds - captureStartSeconds; }
+};
+
+ResolvedNote resolveNote(const NoteProgram& program, Tempo tempo);
+
+}  // namespace reasampler::instrument::note

src/core/instrument/note/tempo.cpp

@@ -0,0 +1,27 @@
+// tempo.cpp — see tempo.h. Pure; standard library only.
+
+#include "core/instrument/note/tempo.h"
+
+#include <cmath>
+
+namespace reasampler::instrument::note {
+namespace {
+constexpr double kSecondsPerMinute = 60.0;
+}  // namespace
+
+std::optional<Tempo> Tempo::fromBpm(double beatsPerMinute) {
+    if (!std::isfinite(beatsPerMinute) || beatsPerMinute <= 0.0) return std::nullopt;
+    return Tempo(beatsPerMinute);
+}
+
+double Tempo::secondsPerBeat() const { return kSecondsPerMinute / bpm_; }
+
+double Tempo::beatsToSeconds(double beats) const { return beats * secondsPerBeat(); }
+
+double Tempo::secondsToBeats(double seconds) const { return seconds / secondsPerBeat(); }
+
+double Tempo::beatsToMs(double beats) const { return secondsToMs(beatsToSeconds(beats)); }
+
+double Tempo::msToBeats(double ms) const { return secondsToBeats(msToSeconds(ms)); }
+
+}  // namespace reasampler::instrument::note

src/core/instrument/note/tempo.h

@@ -0,0 +1,37 @@
+// tempo — a validated project tempo and every beats <-> seconds <-> ms conversion a
+// beat-denominated capture value resolves through.
+//
+// A BEAT IS A QUARTER NOTE — REAPER states project tempo in quarter notes per minute
+// regardless of time signature, so a division resolves without one.
+
+#pragma once
+
+#include <optional>
+
+namespace reasampler::instrument::note {
+
+inline constexpr double kMsPerSecond = 1000.0;
+
+constexpr double msToSeconds(double ms) { return ms / kMsPerSecond; }
+constexpr double secondsToMs(double seconds) { return seconds * kMsPerSecond; }
+
+class Tempo {
+public:
+    // The only place a bad BPM is rejected, which is what lets every conversion below be
+    // total — no resolver downstream needs a failure path.
+    static std::optional<Tempo> fromBpm(double beatsPerMinute);
+
+    double bpm() const { return bpm_; }
+    double secondsPerBeat() const;
+
+    double beatsToSeconds(double beats) const;
+    double secondsToBeats(double seconds) const;
+    double beatsToMs(double beats) const;
+    double msToBeats(double ms) const;
+
+private:
+    explicit Tempo(double beatsPerMinute) : bpm_(beatsPerMinute) {}
+    double bpm_;
+};
+
+}  // namespace reasampler::instrument::note

tests/test_musical_division.cpp

@@ -0,0 +1,177 @@
+// Standalone tests for reasampler::instrument::note::musical_division — no VST3, no REAPER,
+// no framework. Same fast assert loop as the sibling pure tests.
+//
+// Covers: the beat length of all 39 divisions against a literal rung table (NOT the module's
+// own exponent formula); the 1/64 and 64/1 extremes; the four named example divisions; the
+// label notation; picker order and index round-trip; off-ladder clamping.
+
+#include "../src/core/instrument/note/musical_division.h"
+
+#include <cstdio>
+
+using namespace reasampler::instrument::note;
+
+static int g_fail = 0;
+#define CHECK(cond) do { if(!(cond)) { \
+    std::printf("FAIL line %d: %s\n", __LINE__, #cond); ++g_fail; } } while(0)
+
+static bool almostEqual(double a, double b) {
+    const double d = a - b;
+    return (d < 0 ? -d : d) < 1e-12;
+}
+
+// Length in beats (quarter notes) of each straight rung, written out rather than computed,
+// so a broken exponent formula cannot agree with its own mistake.
+static const double kStraightBeats[kRungCount] = {
+    0.0625,  // 1/64
+    0.125,   // 1/32
+    0.25,    // 1/16
+    0.5,     // 1/8
+    1.0,     // 1/4
+    2.0,     // 1/2
+    4.0,     // 1/1
+    8.0,     // 2/1
+    16.0,    // 4/1
+    32.0,    // 8/1
+    64.0,    // 16/1
+    128.0,   // 32/1
+    256.0,   // 64/1
+};
+
+static const char* const kStraightLabels[kRungCount] = {
+    "1/64", "1/32", "1/16", "1/8", "1/4", "1/2", "1/1",
+    "2/1", "4/1", "8/1", "16/1", "32/1", "64/1",
+};
+
+// --- The ladder ---------------------------------------------------------------
+
+static void testLadderSpansSixtyfourthToSixtyFourWhole() {
+    CHECK(kRungCount == 13);
+    CHECK(kDivisionCount == 39);
+    CHECK(divisionLabel(divisionAt(0)) == "1/64");
+    CHECK(divisionLabel(divisionAt(kDivisionCount - 1)) == "64/1t");
+}
+
+static void testEveryStraightRungHasItsWrittenBeatLength() {
+    for (int rung = 0; rung < kRungCount; ++rung) {
+        const Division d = makeDivision(kMinQuarterExponent + rung, DivisionModifier::Straight);
+        CHECK(almostEqual(divisionBeats(d), kStraightBeats[rung]));
+        CHECK(divisionLabel(d) == kStraightLabels[rung]);
+    }
+}
+
+static void testDottedIsHalfAgainAndTripletIsTwoThirds() {
+    for (int rung = 0; rung < kRungCount; ++rung) {
+        const int e = kMinQuarterExponent + rung;
+        CHECK(almostEqual(divisionBeats(makeDivision(e, DivisionModifier::Dotted)),
+                   kStraightBeats[rung] * 1.5));
+        CHECK(almostEqual(divisionBeats(makeDivision(e, DivisionModifier::Triplet)),
+                   kStraightBeats[rung] * 2.0 / 3.0));
+    }
+}
+
+static void testExtremes() {
+    // 1/64 straight is the shortest rung; 64/1 straight is the longest.
+    CHECK(almostEqual(divisionBeats(makeDivision(kMinQuarterExponent, DivisionModifier::Straight)),
+               0.0625));
+    CHECK(almostEqual(divisionBeats(makeDivision(kMaxQuarterExponent, DivisionModifier::Straight)),
+               256.0));
+    // The dotted 64/1 is the single longest programmable note.
+    CHECK(almostEqual(divisionBeats(makeDivision(kMaxQuarterExponent, DivisionModifier::Dotted)),
+               384.0));
+    // The 1/64 triplet is the shortest.
+    CHECK(almostEqual(divisionBeats(makeDivision(kMinQuarterExponent, DivisionModifier::Triplet)),
+               0.0625 * 2.0 / 3.0));
+}
+
+// --- The four named examples --------------------------------------------------
+
+static void testNamedExamples() {
+    // 1/8. — an eighth is half a beat, dotted is three quarters of one.
+    const Division dottedEighth = makeDivision(-1, DivisionModifier::Dotted);
+    CHECK(almostEqual(divisionBeats(dottedEighth), 0.75));
+    CHECK(divisionLabel(dottedEighth) == "1/8.");
+
+    // 1/4t — a quarter is one beat, the triplet is two thirds of one.
+    const Division quarterTriplet = makeDivision(0, DivisionModifier::Triplet);
+    CHECK(almostEqual(divisionBeats(quarterTriplet), 2.0 / 3.0));
+    CHECK(divisionLabel(quarterTriplet) == "1/4t");
+
+    // 1/16 — a quarter of a beat.
+    const Division sixteenth = makeDivision(-2, DivisionModifier::Straight);
+    CHECK(almostEqual(divisionBeats(sixteenth), 0.25));
+    CHECK(divisionLabel(sixteenth) == "1/16");
+
+    // 4/1 — four whole notes, sixteen beats.
+    const Division fourWhole = makeDivision(4, DivisionModifier::Straight);
+    CHECK(almostEqual(divisionBeats(fourWhole), 16.0));
+    CHECK(divisionLabel(fourWhole) == "4/1");
+}
+
+// --- Picker order -------------------------------------------------------------
+
+static void testPickerOrderIsShortestFirst() {
+    // Straight lengths ascend across rungs; within a rung the order is straight, dotted,
+    // triplet (so the index is not itself sorted by duration — only the rungs are).
+    for (int rung = 1; rung < kRungCount; ++rung) {
+        const double prev = divisionBeats(divisionAt((rung - 1) * kModifierCount));
+        const double here = divisionBeats(divisionAt(rung * kModifierCount));
+        CHECK(here > prev);
+    }
+    CHECK(divisionAt(0) == makeDivision(kMinQuarterExponent, DivisionModifier::Straight));
+    CHECK(divisionAt(1) == makeDivision(kMinQuarterExponent, DivisionModifier::Dotted));
+    CHECK(divisionAt(2) == makeDivision(kMinQuarterExponent, DivisionModifier::Triplet));
+}
+
+static void testIndexRoundTripsOverTheWholeSet() {
+    for (int i = 0; i < kDivisionCount; ++i) {
+        CHECK(divisionIndex(divisionAt(i)) == i);
+    }
+}
+
+static void testEverySetMemberIsDistinct() {
+    // No two indices name the same division, so the picker offers 39 real choices.
+    for (int i = 0; i < kDivisionCount; ++i) {
+        for (int j = i + 1; j < kDivisionCount; ++j) {
+            CHECK(divisionAt(i) != divisionAt(j));
+        }
+    }
+}
+
+// --- Clamping -----------------------------------------------------------------
+
+static void testOffLadderExponentClampsToTheNearestRung() {
+    CHECK(makeDivision(-99, DivisionModifier::Straight)
+          == makeDivision(kMinQuarterExponent, DivisionModifier::Straight));
+    CHECK(makeDivision(99, DivisionModifier::Triplet)
+          == makeDivision(kMaxQuarterExponent, DivisionModifier::Triplet));
+    // A record carrying an off-ladder exponent still resolves to a real length.
+    Division corrupt;
+    corrupt.quarterExponent = 120;
+    CHECK(almostEqual(divisionBeats(corrupt), 256.0));
+}
+
+static void testOutOfRangeIndexClampsIntoTheSet() {
+    CHECK(divisionAt(-1) == divisionAt(0));
+    CHECK(divisionAt(kDivisionCount) == divisionAt(kDivisionCount - 1));
+}
+
+int main() {
+    testLadderSpansSixtyfourthToSixtyFourWhole();
+    testEveryStraightRungHasItsWrittenBeatLength();
+    testDottedIsHalfAgainAndTripletIsTwoThirds();
+    testExtremes();
+
+    testNamedExamples();
+
+    testPickerOrderIsShortestFirst();
+    testIndexRoundTripsOverTheWholeSet();
+    testEverySetMemberIsDistinct();
+
+    testOffLadderExponentClampsToTheNearestRung();
+    testOutOfRangeIndexClampsIntoTheSet();
+
+    if (g_fail == 0) std::printf("musical_division: all tests passed\n");
+    else std::printf("musical_division: %d FAILED\n", g_fail);
+    return g_fail == 0 ? 0 : 1;
+}

tests/test_note_program.cpp

@@ -0,0 +1,359 @@
+// Standalone tests for reasampler::instrument::note::note_program — no VST3, no REAPER, no
+// framework. Same fast assert loop as the sibling pure tests.
+//
+// Covers: velocity clamping; the ms/beats denomination seam and its round-trip; anchoring
+// (start to note-on, end to note-off); the resolved window against hand-computed values;
+// every division resolving to its duration in seconds; proportionality across two tempos;
+// record equality and copy round-trip.
+
+#include "../src/core/instrument/note/note_program.h"
+
+#include <cmath>
+#include <cstdio>
+
+using namespace reasampler::instrument::note;
+
+static int g_fail = 0;
+#define CHECK(cond) do { if(!(cond)) { \
+    std::printf("FAIL line %d: %s\n", __LINE__, #cond); ++g_fail; } } while(0)
+
+static bool almostEqual(double a, double b, double eps = 1e-9) {
+    return std::fabs(a - b) < eps;
+}
+
+static Tempo at(double bpm) {
+    const std::optional<Tempo> t = Tempo::fromBpm(bpm);
+    if (!t) { std::printf("FAIL: fixture tempo %f rejected\n", bpm); ++g_fail; }
+    return t.value_or(Tempo::fromBpm(120.0).value());
+}
+
+// Beats per straight rung, written out rather than computed — see test_musical_division.
+static const double kStraightBeats[kRungCount] = {
+    0.0625, 0.125, 0.25, 0.5, 1.0, 2.0, 4.0, 8.0, 16.0, 32.0, 64.0, 128.0, 256.0,
+};
+
+static NoteProgram program(Division length, OffsetAmount start, OffsetAmount end, int velocity) {
+    NoteProgram p;
+    p.length = length;
+    p.start = StartOffset(start);
+    p.end = EndOffset(end);
+    p.velocity = Velocity::of(velocity);
+    return p;
+}
+
+// --- Velocity ------------------------------------------------------------------
+
+static void testVelocityCarriesInRange() {
+    CHECK(Velocity::of(1).value() == 1);
+    CHECK(Velocity::of(96).value() == 96);
+    CHECK(Velocity::of(127).value() == 127);
+}
+
+static void testVelocityClampsOutOfRange() {
+    // 0 is note-off in MIDI: a programmed note that does not sound is never the intent.
+    CHECK(Velocity::of(0).value() == 1);
+    CHECK(Velocity::of(-40).value() == 1);
+    CHECK(Velocity::of(128).value() == 127);
+    CHECK(Velocity::of(9000).value() == 127);
+}
+
+static void testResolvedNoteCarriesTheProgrammedVelocity() {
+    const Tempo t = at(120.0);
+    CHECK(resolveNote(program(makeDivision(0, DivisionModifier::Straight), offsetFromMs(0.0),
+                              offsetFromMs(0.0), 96),
+                      t)
+              .velocity
+          == 96);
+    CHECK(resolveNote(program(makeDivision(0, DivisionModifier::Straight), offsetFromMs(0.0),
+                              offsetFromMs(0.0), 0),
+                      t)
+              .velocity
+          == 1);
+}
+
+// --- The denomination seam -----------------------------------------------------
+
+static void testMsOffsetReadsBackInBothDenominations() {
+    // 120 BPM: one beat is 500 ms, so 250 ms is half a beat.
+    const Tempo t = at(120.0);
+    const OffsetAmount a = offsetFromMs(250.0);
+    CHECK(almostEqual(offsetMs(a, t), 250.0));
+    CHECK(almostEqual(offsetBeats(a, t), 0.5));
+    CHECK(almostEqual(offsetSeconds(a, t), 0.25));
+}
+
+static void testBeatsOffsetReadsBackInBothDenominations() {
+    // 80 BPM: one beat is 750 ms.
+    const Tempo t = at(80.0);
+    const OffsetAmount a = offsetFromBeats(2.0);
+    CHECK(almostEqual(offsetBeats(a, t), 2.0));
+    CHECK(almostEqual(offsetMs(a, t), 1500.0, 1e-6));
+    CHECK(almostEqual(offsetSeconds(a, t), 1.5));
+}
+
+static void testRedenominationRoundTripsLosslessly() {
+    const double bpms[] = {44.0, 91.7, 120.0, 200.0};
+    const double magnitudes[] = {-500.0, -20.0, 0.0, 0.25, 333.0};
+    for (double bpm : bpms) {
+        const Tempo t = at(bpm);
+        for (double ms : magnitudes) {
+            const OffsetAmount original = offsetFromMs(ms);
+            const OffsetAmount there = redenominate(original, Denomination::Beats, t);
+            const OffsetAmount back = redenominate(there, Denomination::Milliseconds, t);
+            CHECK(there.denomination == Denomination::Beats);
+            CHECK(back.denomination == Denomination::Milliseconds);
+            CHECK(almostEqual(back.magnitude, ms, 1e-9 + 1e-9 * std::fabs(ms)));
+            // Re-denominating never moves the instant it names.
+            CHECK(almostEqual(offsetSeconds(there, t), offsetSeconds(original, t)));
+        }
+        for (double beats : magnitudes) {
+            const OffsetAmount original = offsetFromBeats(beats);
+            const OffsetAmount back =
+                redenominate(redenominate(original, Denomination::Milliseconds, t),
+                             Denomination::Beats, t);
+            CHECK(almostEqual(back.magnitude, beats, 1e-9 + 1e-9 * std::fabs(beats)));
+        }
+    }
+}
+
+static void testRedenominatingToTheSameUnitIsIdentity() {
+    const Tempo t = at(120.0);
+    const OffsetAmount a = offsetFromMs(37.0);
+    CHECK(redenominate(a, Denomination::Milliseconds, t) == a);
+}
+
+static void testStoredDenominationDecidesWhetherAnOffsetFollowsTheTempo() {
+    // The whole reason the denomination is stored: at half the tempo the beats offset is
+    // twice as long in seconds, the ms offset unchanged.
+    const OffsetAmount inMs = offsetFromMs(500.0);
+    const OffsetAmount inBeats = offsetFromBeats(1.0);
+    const Tempo fast = at(120.0);
+    const Tempo slow = at(60.0);
+    CHECK(almostEqual(offsetSeconds(inMs, fast), offsetSeconds(inMs, slow)));
+    CHECK(almostEqual(offsetSeconds(inBeats, slow), 2.0 * offsetSeconds(inBeats, fast)));
+}
+
+// --- Note length in seconds ----------------------------------------------------
+
+static void testEveryDivisionResolvesToItsDuration() {
+    // 120 BPM: one beat is 0.5 s, so a division's length in seconds is half its beats.
+    const Tempo t = at(120.0);
+    const OffsetAmount none = offsetFromMs(0.0);
+    for (int rung = 0; rung < kRungCount; ++rung) {
+        const int e = kMinQuarterExponent + rung;
+        const double straight = kStraightBeats[rung] * 0.5;
+        CHECK(almostEqual(
+            resolveNote(program(makeDivision(e, DivisionModifier::Straight), none, none, 100), t)
+                .noteOffSeconds,
+            straight, 1e-9 + 1e-9 * straight));
+        CHECK(almostEqual(
+            resolveNote(program(makeDivision(e, DivisionModifier::Dotted), none, none, 100), t)
+                .noteOffSeconds,
+            straight * 1.5, 1e-9 + 1e-9 * straight));
+        CHECK(almostEqual(
+            resolveNote(program(makeDivision(e, DivisionModifier::Triplet), none, none, 100), t)
+                .noteOffSeconds,
+            straight * 2.0 / 3.0, 1e-9 + 1e-9 * straight));
+    }
+}
+
+static void testExtremeAndNamedDivisionsInSeconds() {
+    // 120 BPM: one beat is 0.5 s.
+    const Tempo t = at(120.0);
+    const OffsetAmount none = offsetFromMs(0.0);
+    struct Case { Division d; double seconds; };
+    const Case cases[] = {
+        {makeDivision(kMinQuarterExponent, DivisionModifier::Straight), 0.03125},  // 1/64
+        {makeDivision(kMaxQuarterExponent, DivisionModifier::Straight), 128.0},    // 64/1
+        {makeDivision(-1, DivisionModifier::Dotted), 0.375},                       // 1/8.
+        {makeDivision(0, DivisionModifier::Triplet), 1.0 / 3.0},                   // 1/4t
+        {makeDivision(-2, DivisionModifier::Straight), 0.125},                     // 1/16
+        {makeDivision(4, DivisionModifier::Straight), 8.0},                        // 4/1
+    };
+    for (const Case& c : cases) {
+        CHECK(almostEqual(resolveNote(program(c.d, none, none, 100), t).noteOffSeconds,
+                          c.seconds, 1e-9 + 1e-9 * c.seconds));
+    }
+}
+
+static void testNoteLengthIsProportionalToTempo() {
+    // Ratio only — no seconds value is asserted here, so the module's tempo-freedom is what
+    // is under test rather than any particular rate.
+    const OffsetAmount none = offsetFromMs(0.0);
+    const Tempo fast = at(160.0);
+    const Tempo slow = at(40.0);
+    for (int i = 0; i < kDivisionCount; ++i) {
+        const NoteProgram p = program(divisionAt(i), none, none, 100);
+        CHECK(almostEqual(resolveNote(p, slow).noteOffSeconds,
+                          4.0 * resolveNote(p, fast).noteOffSeconds, 1e-9));
+    }
+}
+
+// --- The resolved window -------------------------------------------------------
+
+static void testWindowAnchorsStartToNoteOnAndEndToNoteOff() {
+    // 120 BPM, 1/4 note = 0.5 s. Daniel's case: open 20 ms before note-on, close 500 ms
+    // after note-off.
+    const Tempo t = at(120.0);
+    const ResolvedNote r = resolveNote(program(makeDivision(0, DivisionModifier::Straight),
+                                               offsetFromMs(-20.0), offsetFromMs(500.0), 96),
+                                       t);
+    CHECK(almostEqual(r.noteOffSeconds, 0.5));
+    CHECK(almostEqual(r.captureStartSeconds, -0.020));  // note-on is 0, so the pre-roll is negative
+    CHECK(almostEqual(r.captureEndSeconds, 1.0));       // 0.5 note-off + 0.5 tail
+    CHECK(almostEqual(r.captureLengthSeconds(), 1.02));
+    CHECK(r.velocity == 96);
+}
+
+static void testEndOffsetMovesWithTheNoteLength() {
+    // The end offset anchors to note-off, so lengthening the note moves the window's end by
+    // the same amount and leaves its start alone.
+    const Tempo t = at(120.0);
+    const OffsetAmount start = offsetFromMs(-20.0);
+    const OffsetAmount end = offsetFromMs(500.0);
+    const ResolvedNote quarter =
+        resolveNote(program(makeDivision(0, DivisionModifier::Straight), start, end, 100), t);
+    const ResolvedNote half =
+        resolveNote(program(makeDivision(1, DivisionModifier::Straight), start, end, 100), t);
+    CHECK(almostEqual(half.captureStartSeconds, quarter.captureStartSeconds));
+    CHECK(almostEqual(half.captureEndSeconds - quarter.captureEndSeconds, 0.5));
+}
+
+static void testBeatsDenominatedOffsetsResolveAgainstTheSuppliedTempo() {
+    // 1/4 note, start -1/2 beat, end +1 beat. At 120 BPM (0.5 s/beat): note-off 0.5,
+    // window -0.25 .. 1.0. At 60 BPM every one of those doubles.
+    const NoteProgram p = program(makeDivision(0, DivisionModifier::Straight),
+                                  offsetFromBeats(-0.5), offsetFromBeats(1.0), 100);
+    const ResolvedNote fast = resolveNote(p, at(120.0));
+    CHECK(almostEqual(fast.captureStartSeconds, -0.25));
+    CHECK(almostEqual(fast.captureEndSeconds, 1.0));
+
+    const ResolvedNote slow = resolveNote(p, at(60.0));
+    CHECK(almostEqual(slow.captureStartSeconds, -0.5));
+    CHECK(almostEqual(slow.captureEndSeconds, 2.0));
+}
+
+static void testMixedDenominationsResolveIndependently() {
+    // A ms pre-roll and a beats tail on one record: halving the tempo moves the tail only.
+    const NoteProgram p = program(makeDivision(0, DivisionModifier::Straight),
+                                  offsetFromMs(-20.0), offsetFromBeats(1.0), 100);
+    const ResolvedNote fast = resolveNote(p, at(120.0));
+    const ResolvedNote slow = resolveNote(p, at(60.0));
+    CHECK(almostEqual(fast.captureStartSeconds, -0.020));
+    CHECK(almostEqual(slow.captureStartSeconds, -0.020));
+    CHECK(almostEqual(fast.captureEndSeconds, 1.0));
+    CHECK(almostEqual(slow.captureEndSeconds, 2.0));
+}
+
+static void testNegativeEndOffsetTruncatesBeforeRelease() {
+    // 1/2 note at 120 BPM is 1.0 s; closing 200 ms early ends the window at 0.8 s.
+    const Tempo t = at(120.0);
+    const ResolvedNote r = resolveNote(program(makeDivision(1, DivisionModifier::Straight),
+                                               offsetFromMs(0.0), offsetFromMs(-200.0), 100),
+                                       t);
+    CHECK(almostEqual(r.noteOffSeconds, 1.0));
+    CHECK(almostEqual(r.captureEndSeconds, 0.8));
+    CHECK(almostEqual(r.captureLengthSeconds(), 0.8));
+}
+
+static void testWindowNeverInverts() {
+    // An end offset past the window's own start collapses the window rather than inverting it.
+    const Tempo t = at(120.0);
+    const ResolvedNote r = resolveNote(program(makeDivision(0, DivisionModifier::Straight),
+                                               offsetFromMs(0.0), offsetFromMs(-5000.0), 100),
+                                       t);
+    CHECK(almostEqual(r.captureStartSeconds, 0.0));
+    CHECK(almostEqual(r.captureEndSeconds, 0.0));
+    CHECK(r.captureLengthSeconds() >= 0.0);
+}
+
+// --- The record ----------------------------------------------------------------
+
+static void testRecordRoundTripsAsAWhole() {
+    const NoteProgram original = program(makeDivision(-1, DivisionModifier::Dotted),
+                                         offsetFromMs(-20.0), offsetFromBeats(2.0), 96);
+    const NoteProgram copy = original;
+    CHECK(copy == original);
+    CHECK(copy.length == makeDivision(-1, DivisionModifier::Dotted));
+    CHECK(copy.start.amount() == offsetFromMs(-20.0));
+    CHECK(copy.end.amount() == offsetFromBeats(2.0));
+    CHECK(copy.velocity.value() == 96);
+
+    // Resolving reads the record and leaves it alone, so a preview cannot drift the state a
+    // later bake reads.
+    resolveNote(original, at(120.0));
+    CHECK(copy == original);
+}
+
+static void testRecordEqualityIsSensitiveToEveryField() {
+    const NoteProgram base = program(makeDivision(0, DivisionModifier::Straight),
+                                     offsetFromMs(-20.0), offsetFromMs(500.0), 96);
+    CHECK(base != program(makeDivision(0, DivisionModifier::Dotted), offsetFromMs(-20.0),
+                          offsetFromMs(500.0), 96));
+    CHECK(base != program(makeDivision(0, DivisionModifier::Straight), offsetFromMs(-21.0),
+                          offsetFromMs(500.0), 96));
+    CHECK(base != program(makeDivision(0, DivisionModifier::Straight), offsetFromMs(-20.0),
+                          offsetFromMs(501.0), 96));
+    CHECK(base != program(makeDivision(0, DivisionModifier::Straight), offsetFromMs(-20.0),
+                          offsetFromMs(500.0), 97));
+    // Same magnitude, different denomination is a different record even where one tempo
+    // makes them resolve alike.
+    CHECK(base != program(makeDivision(0, DivisionModifier::Straight), offsetFromBeats(-20.0),
+                          offsetFromMs(500.0), 96));
+}
+
+static void testRedenominatedRecordDescribesTheSameWindow() {
+    const Tempo t = at(133.0);
+    const NoteProgram original = program(makeDivision(-2, DivisionModifier::Triplet),
+                                         offsetFromMs(-35.0), offsetFromMs(420.0), 64);
+    NoteProgram restated = original;
+    restated.start = StartOffset(redenominate(original.start.amount(), Denomination::Beats, t));
+    restated.end = EndOffset(redenominate(original.end.amount(), Denomination::Beats, t));
+
+    const ResolvedNote a = resolveNote(original, t);
+    const ResolvedNote b = resolveNote(restated, t);
+    CHECK(restated != original);  // the record changed...
+    CHECK(almostEqual(a.captureStartSeconds, b.captureStartSeconds));  // ...the window did not
+    CHECK(almostEqual(a.captureEndSeconds, b.captureEndSeconds));
+}
+
+static void testDefaultRecordIsAQuarterNoteWithNoOffsets() {
+    const Tempo t = at(120.0);
+    const ResolvedNote r = resolveNote(NoteProgram{}, t);
+    CHECK(almostEqual(r.noteOffSeconds, 0.5));
+    CHECK(almostEqual(r.captureStartSeconds, 0.0));
+    CHECK(almostEqual(r.captureEndSeconds, 0.5));
+    CHECK(r.velocity >= Velocity::kMin && r.velocity <= Velocity::kMax);
+}
+
+int main() {
+    testVelocityCarriesInRange();
+    testVelocityClampsOutOfRange();
+    testResolvedNoteCarriesTheProgrammedVelocity();
+
+    testMsOffsetReadsBackInBothDenominations();
+    testBeatsOffsetReadsBackInBothDenominations();
+    testRedenominationRoundTripsLosslessly();
+    testRedenominatingToTheSameUnitIsIdentity();
+    testStoredDenominationDecidesWhetherAnOffsetFollowsTheTempo();
+
+    testEveryDivisionResolvesToItsDuration();
+    testExtremeAndNamedDivisionsInSeconds();
+    testNoteLengthIsProportionalToTempo();
+
+    testWindowAnchorsStartToNoteOnAndEndToNoteOff();
+    testEndOffsetMovesWithTheNoteLength();
+    testBeatsDenominatedOffsetsResolveAgainstTheSuppliedTempo();
+    testMixedDenominationsResolveIndependently();
+    testNegativeEndOffsetTruncatesBeforeRelease();
+    testWindowNeverInverts();
+
+    testRecordRoundTripsAsAWhole();
+    testRecordEqualityIsSensitiveToEveryField();
+    testRedenominatedRecordDescribesTheSameWindow();
+    testDefaultRecordIsAQuarterNoteWithNoOffsets();
+
+    if (g_fail == 0) std::printf("note_program: all tests passed\n");
+    else std::printf("note_program: %d FAILED\n", g_fail);
+    return g_fail == 0 ? 0 : 1;
+}

tests/test_tempo.cpp

@@ -0,0 +1,135 @@
+// Standalone tests for reasampler::instrument::note::tempo — no VST3, no REAPER, no
+// framework. Same fast assert loop as the sibling pure tests.
+//
+// Covers: BPM validation (the only rejection point, which is what makes the conversions
+// total); seconds-per-beat at several tempos; beats<->seconds and beats<->ms round-trips
+// across tempos and signs; the proportionality between two tempos, asserted as a ratio
+// rather than against any fixed seconds value.
+
+#include "../src/core/instrument/note/tempo.h"
+
+#include <cmath>
+#include <cstdio>
+#include <limits>
+
+using namespace reasampler::instrument::note;
+
+static int g_fail = 0;
+#define CHECK(cond) do { if(!(cond)) { \
+    std::printf("FAIL line %d: %s\n", __LINE__, #cond); ++g_fail; } } while(0)
+
+static bool almostEqual(double a, double b, double eps = 1e-9) {
+    return std::fabs(a - b) < eps;
+}
+
+static Tempo at(double bpm) {
+    const std::optional<Tempo> t = Tempo::fromBpm(bpm);
+    if (!t) { std::printf("FAIL: fixture tempo %f rejected\n", bpm); ++g_fail; }
+    return t.value_or(Tempo::fromBpm(120.0).value());
+}
+
+// --- Validation ---------------------------------------------------------------
+
+static void testUsableBpmIsAccepted() {
+    const std::optional<Tempo> t = Tempo::fromBpm(137.5);
+    CHECK(t.has_value());
+    CHECK(t && almostEqual(t->bpm(), 137.5));
+}
+
+static void testUnusableBpmIsRejected() {
+    CHECK(!Tempo::fromBpm(0.0).has_value());
+    CHECK(!Tempo::fromBpm(-120.0).has_value());
+    CHECK(!Tempo::fromBpm(std::numeric_limits<double>::quiet_NaN()).has_value());
+    CHECK(!Tempo::fromBpm(std::numeric_limits<double>::infinity()).has_value());
+}
+
+// --- Conversions ---------------------------------------------------------------
+
+static void testSecondsPerBeatFollowsBpm() {
+    CHECK(almostEqual(at(60.0).secondsPerBeat(), 1.0));
+    CHECK(almostEqual(at(120.0).secondsPerBeat(), 0.5));
+    CHECK(almostEqual(at(240.0).secondsPerBeat(), 0.25));
+}
+
+static void testBeatsToSecondsAtAKnownTempo() {
+    // 90 BPM: one beat is 2/3 s, so four beats are 8/3 s.
+    const Tempo t = at(90.0);
+    CHECK(almostEqual(t.beatsToSeconds(1.0), 2.0 / 3.0));
+    CHECK(almostEqual(t.beatsToSeconds(4.0), 8.0 / 3.0));
+    CHECK(almostEqual(t.secondsToBeats(8.0 / 3.0), 4.0));
+}
+
+static void testBeatsToMsAtAKnownTempo() {
+    // 150 BPM: one beat is 400 ms.
+    const Tempo t = at(150.0);
+    CHECK(almostEqual(t.beatsToMs(1.0), 400.0, 1e-6));
+    CHECK(almostEqual(t.msToBeats(400.0), 1.0));
+    CHECK(almostEqual(t.msToBeats(100.0), 0.25));
+}
+
+static void testMsAndBeatsRoundTripAcrossTemposAndSigns() {
+    const double bpms[] = {33.0, 77.3, 120.0, 174.6, 300.0};
+    const double values[] = {-500.0, -20.0, 0.0, 0.5, 250.0, 12345.678};
+    for (double bpm : bpms) {
+        const Tempo t = at(bpm);
+        for (double ms : values) {
+            CHECK(almostEqual(t.beatsToMs(t.msToBeats(ms)), ms, 1e-9 + 1e-9 * std::fabs(ms)));
+        }
+        for (double beats : values) {
+            CHECK(almostEqual(t.msToBeats(t.beatsToMs(beats)), beats,
+                              1e-9 + 1e-9 * std::fabs(beats)));
+        }
+    }
+}
+
+static void testSecondsRoundTrip() {
+    const Tempo t = at(101.7);
+    CHECK(almostEqual(t.secondsToBeats(t.beatsToSeconds(3.25)), 3.25));
+    CHECK(almostEqual(t.beatsToSeconds(t.secondsToBeats(-1.75)), -1.75));
+}
+
+// --- Proportionality -----------------------------------------------------------
+
+static void testHalvingTheTempoDoublesEveryBeatDuration() {
+    // The ratio is the claim; no seconds value is asserted, so the test cannot encode a
+    // fixed tempo of its own.
+    const Tempo fast = at(140.0);
+    const Tempo slow = at(70.0);
+    for (double beats : {0.0625, 0.75, 2.0 / 3.0, 16.0, 256.0}) {
+        CHECK(almostEqual(slow.beatsToSeconds(beats), 2.0 * fast.beatsToSeconds(beats), 1e-9));
+    }
+}
+
+static void testSecondsScaleInverselyWithBpm() {
+    const Tempo a = at(96.0);
+    const Tempo b = at(123.0);
+    const double beats = 3.5;
+    CHECK(almostEqual(a.beatsToSeconds(beats) / b.beatsToSeconds(beats), 123.0 / 96.0));
+}
+
+static void testMillisecondsAreTempoFree() {
+    // The ms<->seconds pair carries no tempo — that is what lets a ms-denominated offset
+    // hold still while a beats-denominated one moves.
+    CHECK(almostEqual(msToSeconds(250.0), 0.25));
+    CHECK(almostEqual(secondsToMs(1.5), 1500.0));
+    CHECK(almostEqual(msToSeconds(secondsToMs(0.037)), 0.037));
+}
+
+int main() {
+    testUsableBpmIsAccepted();
+    testUnusableBpmIsRejected();
+
+    testSecondsPerBeatFollowsBpm();
+    testBeatsToSecondsAtAKnownTempo();
+    testBeatsToMsAtAKnownTempo();
+    testMsAndBeatsRoundTripAcrossTemposAndSigns();
+    testSecondsRoundTrip();
+
+    testHalvingTheTempoDoublesEveryBeatDuration();
+    testSecondsScaleInverselyWithBpm();
+    testMillisecondsAreTempoFree();
+
+    if (g_fail == 0) std::printf("tempo: all tests passed\n");
+    else std::printf("tempo: %d FAILED\n", g_fail);
+    return g_fail == 0 ? 0 : 1;
+}