User:MisterShafXen/Tuning all ETs

Here is where I will be listing my approaches for tuning various ETs, octave-repeating or otherwise.

ED8/7s

23ed8/7

9 steps of this tuning differs from 256/243 by 0.18 cents, resulting in an error of 4.14 cents or 41.4%.

15 steps of this tuning differs from 12/11 by 0.015 cents, resulting in an error of 0.345 cents or 3.45%.

ED9/7s

17ed9/7

1 step of this tuning differs from 64/63 by 1.676 cents, resulting in an error of 28.492 cents or 107.7%.

8 steps of this tuning differs from 9/8 by 0.796 cents, resulting in an error of 13.532 cents or 52.73%.

ED4/3s

17ed4/3

7 steps of this tuning differs from 9/8 by 1.169 cents, resulting in an error of 19.873 cents or 69%.

26ed4/3

19 steps of this tuning differs from 100/81 by 0.885 cents, resulting in an error of 23.01 cents or 121.1%.

ED7/5s

9ed7/5

7 steps of this tuning differs from 13/10 by 0.77 cents, resulting in an error of 6.93 cents or 10.6%.

ED3/2s

6ed3/2

1 step of this tuning differs from 31/29 by 1.541 cents, resulting in a comma of 9.246 cents or 7.7%.

ED8/5s

31ed8/5

4 steps of this tuning differs from 17/16 by 0.077 cents, resulting in an error of 2.387 cents or 9.23%.

EDOs

6edo

1 step of 6edo differs from 9/8 by 3.91 cents, resulting in an error of 23.46 cents (Pythagorean comma, 531441/524288) or 12.73%.

Another approach is to use 64/57, which results in an error of 2.808 cents or 1.404%.

17edo

1 step of 17edo is very near 25/24, differing from it by only 0.085 cents. Thus, 17edo can be tuned as a stack of 25/24s with a comma of 1.445 cents or 2%.

10 steps of 17edo is 3.925 cents sharp of 3/2, which results in a comma of 52.725 cents or 75%. Not great.

30edo

1 step of 30edo differs from 128/125 by 1.058 cents, resulting in a comma of 31.74 cents or 79.35%.

3 steps of 30edo differs from 15/14 by 0.657 cents. When a stack of 10 of these is combined with 20 128/125s, the comma is 27.73 cents or 69.325%.

32edo

3 steps of 32edo differs from 16/15 by 0.769 cents, resulting in a comma of 24.608 cents or 65.6%.

ED7/2s

35ed7/2

7 steps of this tuning differs from 9/7 by 1.322 cents. Stacking 5 of these results in a comma of 6.661 cents. 8 steps of this tuning differs from 4/3 by 2.317 cents. Stacking 30 of these has an error of 69.51 cents. The total error becomes 76.171 cents or 122.6%.

ED9s

7ed9

1 step of this tuning differs from 11/8 by 7.89 cents, resulting in an error of 55.23 cents or 10.2%.

2 steps of this tuning differs from 15/8 by 1.412 cents, resulting in an error of 9.884 cents or 2%.