translating scale steps to frequencies
- to play this melody, we must
- pick a base frequency
- translate each scale step into a frequency, using the ratios given above (in 2.3 the natural scale)
- substitute a frequency for each scale step in the melody
For example, using 400 Hz as the base frequency:
| step | freq | ratio |
|---|---|---|
| 1 | 800 | 2/1 |
| 7 | 750 | 15/8 |
| 6 | 666 | 5/3 |
| 5 | 600 | 3/2 |
| 4 | 533 | 4/3 |
| 3 | 500 | 5/4 |
| 2 | 450 | 9/8 |
| 1 | 400 | 1/1 |
And here's the melody, with frequencies in place of scale steps:
500 450 400 450 500 500 500 Ma- ry had a li- ttle lamb 450 450 450 li- ttle lamb 500 600 600 li- ttle lamb 500 450 400 450 500 500 500 500 Ma- ry had a li- ttle lamb, its 450 450 500 450 400 fleece was white as snow