feat: add custom tempo/BPM converter with musical note units

Add comprehensive tempo conversion system supporting:
- BPM (beats per minute) as base unit
- Musical note durations: whole, half, quarter, eighth, sixteenth, thirty-second
- Dotted notes (1.5x duration): dotted-half, dotted-quarter, dotted-eighth, dotted-sixteenth
- Triplet notes (2/3 duration): quarter-triplet, eighth-triplet, sixteenth-triplet
- Time units: milliseconds, seconds, Hertz

Technical implementation:
- Created lib/tempo.ts with custom measure definition
- Extended lib/units.ts with tempo integration and reciprocal conversion logic
- Added tempo category color (orange #F97316) to globals.css
- Conversion formula: milliseconds per beat = 60000 / BPM
- Special handling for BPM ↔ time unit conversions using reciprocal relationship

The tempo converter integrates seamlessly with existing UX:
- Appears as "Tempo / BPM" category in category selector
- Supports all features: search, favorites, history, visual comparison, draggable bars
- Enables musicians to convert between BPM and note durations for tempo calculations

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

app/globals.css

@@ -74,6 +74,7 @@
   --color-category-reactive-power: oklch(74.5% 0.233 316.8);
   --color-category-speed: oklch(72.4% 0.159 165.1);
   --color-category-temperature: oklch(62.8% 0.257 29.2);
+  --color-category-tempo: oklch(70% 0.18 30);
   --color-category-time: oklch(58.5% 0.238 293.1);
   --color-category-voltage: oklch(75.5% 0.159 55.3);
   --color-category-volume: oklch(64.8% 0.190 293.6);

lib/tempo.ts

@@ -0,0 +1,117 @@
+/**
+ * Custom tempo/BPM measure for convert-units
+ *
+ * Converts between BPM and note durations in milliseconds.
+ * Uses a reciprocal relationship where BPM (beats per minute) is the base unit.
+ *
+ * Formula: milliseconds per beat = 60000 / BPM
+ *
+ * The to_anchor value represents the conversion factor:
+ * - For BPM → time units: multiply by to_anchor to get milliseconds
+ * - For time units → BPM: divide by to_anchor to get BPM
+ */
+
+export const tempoMeasure = {
+  tempo: {
+    systems: {
+      metric: {
+        // BPM as the base unit (1 BPM = 60000 ms per beat)
+        'BPM': {
+          name: { singular: 'Beat per Minute', plural: 'Beats per Minute' },
+          to_anchor: 1
+        },
+
+        // Whole note (4 beats) = 240000 / BPM
+        'whole': {
+          name: { singular: 'Whole Note', plural: 'Whole Notes' },
+          to_anchor: 240000
+        },
+
+        // Half note (2 beats) = 120000 / BPM
+        'half': {
+          name: { singular: 'Half Note', plural: 'Half Notes' },
+          to_anchor: 120000
+        },
+
+        // Quarter note (1 beat) = 60000 / BPM
+        'quarter': {
+          name: { singular: 'Quarter Note', plural: 'Quarter Notes' },
+          to_anchor: 60000
+        },
+
+        // Eighth note (0.5 beats) = 30000 / BPM
+        'eighth': {
+          name: { singular: 'Eighth Note', plural: 'Eighth Notes' },
+          to_anchor: 30000
+        },
+
+        // Sixteenth note (0.25 beats) = 15000 / BPM
+        'sixteenth': {
+          name: { singular: 'Sixteenth Note', plural: 'Sixteenth Notes' },
+          to_anchor: 15000
+        },
+
+        // Thirty-second note (0.125 beats) = 7500 / BPM
+        'thirty-second': {
+          name: { singular: 'Thirty-Second Note', plural: 'Thirty-Second Notes' },
+          to_anchor: 7500
+        },
+
+        // Dotted notes (1.5x the duration)
+        'dotted-half': {
+          name: { singular: 'Dotted Half Note', plural: 'Dotted Half Notes' },
+          to_anchor: 180000 // 3 beats
+        },
+
+        'dotted-quarter': {
+          name: { singular: 'Dotted Quarter Note', plural: 'Dotted Quarter Notes' },
+          to_anchor: 90000 // 1.5 beats
+        },
+
+        'dotted-eighth': {
+          name: { singular: 'Dotted Eighth Note', plural: 'Dotted Eighth Notes' },
+          to_anchor: 45000 // 0.75 beats
+        },
+
+        'dotted-sixteenth': {
+          name: { singular: 'Dotted Sixteenth Note', plural: 'Dotted Sixteenth Notes' },
+          to_anchor: 22500 // 0.375 beats
+        },
+
+        // Triplet notes (2/3 of the duration)
+        'quarter-triplet': {
+          name: { singular: 'Quarter Note Triplet', plural: 'Quarter Note Triplets' },
+          to_anchor: 40000 // 2/3 beat
+        },
+
+        'eighth-triplet': {
+          name: { singular: 'Eighth Note Triplet', plural: 'Eighth Note Triplets' },
+          to_anchor: 20000 // 1/3 beat
+        },
+
+        'sixteenth-triplet': {
+          name: { singular: 'Sixteenth Note Triplet', plural: 'Sixteenth Note Triplets' },
+          to_anchor: 10000 // 1/6 beat
+        },
+
+        // Milliseconds as direct time unit
+        'ms': {
+          name: { singular: 'Millisecond', plural: 'Milliseconds' },
+          to_anchor: 60000 // Same as quarter note
+        },
+
+        // Seconds
+        's': {
+          name: { singular: 'Second', plural: 'Seconds' },
+          to_anchor: 60 // 60 seconds per beat at 1 BPM
+        },
+
+        // Hertz (beats per second)
+        'Hz': {
+          name: { singular: 'Hertz', plural: 'Hertz' },
+          to_anchor: 1 / 60 // 1 BPM = 1/60 Hz
+        }
+      }
+    }
+  }
+};

lib/units.ts

@@ -4,6 +4,7 @@
  */
 
 import convert from 'convert-units';
+import { tempoMeasure } from './tempo';
 
 export type Measure =
   | 'angle'
@@ -25,6 +26,7 @@ export type Measure =
   | 'reactivePower'
   | 'speed'
   | 'temperature'
+  | 'tempo'
   | 'time'
   | 'voltage'
   | 'volume'
@@ -48,13 +50,17 @@ export interface ConversionResult {
  * Get all available measures/categories
  */
 export function getAllMeasures(): Measure[] {
-  return convert().measures() as Measure[];
+  const standardMeasures = convert().measures() as Measure[];
+  return [...standardMeasures, 'tempo'];
 }
 
 /**
  * Get all units for a specific measure
  */
 export function getUnitsForMeasure(measure: Measure): string[] {
+  if (measure === 'tempo') {
+    return Object.keys(tempoMeasure.tempo.systems.metric);
+  }
   return convert().possibilities(measure);
 }
 
@@ -63,6 +69,19 @@ export function getUnitsForMeasure(measure: Measure): string[] {
  */
 export function getUnitInfo(unit: string): UnitInfo | null {
   try {
+    // Check if it's a tempo unit
+    const tempoUnits = tempoMeasure.tempo.systems.metric;
+    if (unit in tempoUnits) {
+      const tempoUnit = tempoUnits[unit as keyof typeof tempoUnits];
+      return {
+        abbr: unit,
+        measure: 'tempo',
+        system: 'metric',
+        singular: tempoUnit.name.singular,
+        plural: tempoUnit.name.plural,
+      };
+    }
+
     const description = convert().describe(unit);
     return description as UnitInfo;
   } catch {
@@ -79,6 +98,34 @@ export function convertUnit(
   toUnit: string
 ): number {
   try {
+    // Handle tempo conversions
+    const tempoUnits = tempoMeasure.tempo.systems.metric;
+    const isFromTempo = fromUnit in tempoUnits;
+    const isToTempo = toUnit in tempoUnits;
+
+    if (isFromTempo && isToTempo) {
+      const fromAnchor = tempoUnits[fromUnit as keyof typeof tempoUnits].to_anchor;
+      const toAnchor = tempoUnits[toUnit as keyof typeof tempoUnits].to_anchor;
+
+      // Special handling for BPM conversions (reciprocal relationship)
+      if (fromUnit === 'BPM') {
+        // BPM → time unit: divide anchor by BPM value
+        // Example: 120 BPM → quarter = 60000 / 120 = 500ms
+        return toAnchor / value;
+      } else if (toUnit === 'BPM') {
+        // Time unit → BPM: divide anchor by time value
+        // Example: 500ms quarter → BPM = 60000 / 500 = 120
+        return fromAnchor / value;
+      } else {
+        // Time unit → time unit: convert through BPM
+        // Example: 500ms quarter → eighth
+        // Step 1: 500ms → BPM = 60000 / 500 = 120
+        // Step 2: 120 BPM → eighth = 30000 / 120 = 250ms
+        const bpm = fromAnchor / value;
+        return toAnchor / bpm;
+      }
+    }
+
     return convert(value).from(fromUnit).to(toUnit);
   } catch (error) {
     console.error('Conversion error:', error);
@@ -139,6 +186,7 @@ export function getCategoryColor(measure: Measure): string {
     reactivePower: 'category-reactive-power',
     speed: 'category-speed',
     temperature: 'category-temperature',
+    tempo: 'category-tempo',
     time: 'category-time',
     voltage: 'category-voltage',
     volume: 'category-volume',
@@ -172,6 +220,7 @@ export function getCategoryColorHex(measure: Measure): string {
     reactivePower: '#E879F9',
     speed: '#10B981',
     temperature: '#EF4444',
+    tempo: '#F97316', // Orange for music/tempo
     time: '#7C3AED',
     voltage: '#FB923C',
     volume: '#8B5CF6',
@@ -205,6 +254,7 @@ export function formatMeasureName(measure: Measure): string {
     reactivePower: 'Reactive Power',
     speed: 'Speed',
     temperature: 'Temperature',
+    tempo: 'Tempo / BPM',
     time: 'Time',
     voltage: 'Voltage',
     volume: 'Volume',