the natural scale
- here's the scale, so far:
| freq | ratio to the base pitch |
|---|---|
| 800 | 2/1 |
| 600 | 3/2 |
| 533 | 4/3 |
| 400 | 1/1 |
- now we add two more pitches, filling in the gaps we've left, while still using the simplest ratios we can find:
| step | freq | ratio to the base pitch |
|---|---|---|
| 1 | 800 | 2/1 |
| 7 | ||
| 6 | 666 | 5/3 |
| 5 | 600 | 3/2 |
| 4 | 533 | 4/3 |
| 3 | 500 | 5/4 |
| 2 | 450 | 9/8 |
| 1 | 400 | 1/1 |
- we've also numbered these pitches
- 1 through 7
- these are the scale steps or scale degrees
- the last scale step - 7 - has a somewhat less consonant ratio to the base pitch
- numbering the scale steps, rather than giving their frequencies, allows us to describe a piece of music in such a way that if we change the base frequency our description of the piece of music does not have to change
| step | freq | ratio | ratio in 24ths |
|---|---|---|---|
| 1 | 800 | 2/1 | 48/24 |
| 7 | 750 | 15/8 | 45/24 |
| 6 | 666 | 5/3 | 40/24 |
| 5 | 600 | 3/2 | 36/24 |
| 4 | 533 | 4/3 | 32/24 |
| 3 | 500 | 5/4 | 30/24 |
| 2 | 450 | 9/8 | 27/24 |
| 1 | 400 | 1/1 | 24/24 |
- we have now generated the steps that make up the most common scale (in the west): the natural scale
- very little popular music in the west uses anything other than this scale