Implement ratio and cents methods for Scale to bypass complex monzo c…

…alculations

ref xenharmonic-devs/scale-workshop#528

src/__tests__/scale.spec.ts

@@ -1077,4 +1077,21 @@ describe('Scale', () => {
     ]).approximateEqualTemperament(22);
     expect(scale.getName(0)).toBe('0\\22<1>');
   });
+
+  it('can calculate the ratio and cents gamuts of a complex scale', () => {
+    const scale = Scale.fromIntervalArray([
+      new Interval(
+        ExtendedMonzo.fromFraction('3001/3000', 7),
+        'ratio',
+        '3001/3000'
+      ),
+    ]);
+    for (let i = 0; i < 128; ++i) {
+      const idx = i - 69;
+      const ratio = scale.getRatio(idx);
+      const cents = scale.getCents(idx);
+      expect(ratio).toBeCloseTo(1.000333333333333 ** idx);
+      expect(cents).toBeCloseTo(0.5769818580538413 * idx);
+    }
+  });
 });

src/scale.ts

@@ -594,6 +594,33 @@ export class Scale {
     return this.intervals[index].monzo.add(this.equave.monzo.mul(numEquaves));
   }
 
+  /**
+   * Obtain the total cents of an interval in the scale (repeats at equaves).
+   * @param index Zero-based index of the interval.
+   * @returns Cents associated with the given index.
+   */
+  getCents(index: number) {
+    const numEquaves = Math.floor(index / this.size);
+    index -= numEquaves * this.size;
+    return (
+      this.intervals[index].totalCents() + this.equave.totalCents() * numEquaves
+    );
+  }
+
+  /**
+   * Obtain the ratio of an interval in the scale (repeats at equaves).
+   * @param index Zero-based index of the interval.
+   * @returns Ratio associated with the given index.
+   */
+  getRatio(index: number) {
+    const numEquaves = Math.floor(index / this.size);
+    index -= numEquaves * this.size;
+    return (
+      this.intervals[index].monzo.valueOf() *
+      this.equave.monzo.valueOf() ** numEquaves
+    );
+  }
+
   /**
    * Obtain the frequency of an interval in the scale (repeats at equaves).
    * @param index Zero-based index of the interval.