Try to create a meantone tuning that minimizes the overall error. You can adjust the value of α, which is the correction made to Pythagorean tuning, measured in cents. Commonly used values of α include 1/4 and 1/3. See the table below for more suggestions. Without any other qualification, meantone temperament refers to α = 1/4. The following matrix uses Eitz's notation for the comma adjustments to the Pythagorean scale.
| E-4α | B-5α | F♯-6α | C♯-7α | G♯-8α | ||||||
| C0 | G-α | D-2α | A-3α | E-4α | ||||||
| E♭+3α | B♭+2α | F+1α | C0 | |||||||
| Note | C | D | E | F | G | A | B | C |
| Py. ratios | 1:1 | 9:8 | 81:64 | 4:3 | 3:2 | 27:16 | 243:128 | 2:1 |
| Py. cents | 0 | 203.9 | 407.8 | 498.0 | 702.0 | 905.9 | 1109.8 | 1200 |
| Just cents | 0 | 203.9 | 386.3 | 498.0 | 702.0 | 884.4 | 1088.3 | 1200 |
| α cents | ||||||||
| Error |
Historical meantone α-comma temperaments:
| 0 | 0 | Pythagoras |
| 1/7 | 0.14 | Romieu, 1755 |
| 1/6 | 0.17 | Silbermann, 1748 |
| 1/5 | 0.20 | Verheijen, 1600 |
| 2/9 | 0.22 | Rossi, 1666 |
| 1/4 | 0.25 | Aaron, 1523 |
| 2/7 | 0.29 | Zarlino, 1558 |
| 1/3 | 0.33 | Salinas, 1577 |
Reference
Benson, Dave. 2008. Music: A Mathematical Offering. Pages 176–181. (Link)