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 0.234 cents, resulting in an error of 5.392 cents or 53.65%.

15 steps of this tuning differs from 12/11 by 0.129 cents, resulting in an error of 2.959 cents or 29.44%.

ED6/5s

16ed6/5

5 steps of this tuning differs from 18/17 by 0.317 cents, resulting in an error of 5.065 cents or 25.67%.

ED9/7s

17ed9/7

1 step of this tuning differs from 64/63 by 1.671 cents, resulting in an error of 28.405 cents or 111%.

8 steps of this tuning differs from 9/8 by 0.835 cents, resulting in an error of 14.203 cents or 55.5%.

ED4/3s

17ed4/3

7 steps of this tuning differs from 9/8 by 1.167 cents, resulting in an error of 19.845 cents or 67.74%.

26ed4/3

19 steps of this tuning differs from 100/81 by 0.852 cents, resulting in an error of 22.153 cents or 115.65%.

ED7/5s

9ed7/5

7 steps of this tuning differs from 13/10 by 1.149 cents, resulting in an error of 10.341 cents or 15.98%.

ED3/2s

5ed3/2

6 steps of this tuning differs from 13/8 by 1.818 cents, resulting in an error of 9.092 cents or 6.48%.

6ed3/2

1 step of this tuning differs from 31/29 by 1.534 cents, resulting in a comma of 9.204 cents or 7.9%.

18ed3/2

4 steps of this tuning differs from 35/32 by 0.85 cents, resulting in an error of 7.653 cents. 7 steps of this tuning differs from 7/6 by 6.112 cents, resulting in an error of 55.004 cents. The combined error is 62.657 cents or 160.7%.

ED8/5s

31ed8/5

4 steps of this tuning differs from 17/16 by 0.037 cents, resulting in an error of 1.14 cents or 4.34%.

EDOs

5edo

1 step of 5edo differs from 8/7 by 8.826 cents, resulting in an error of 44.13 cents or 18.4%.

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 11.73%.

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

10edo

1 step of 10edo differs from 15/14 by 0.557 cents, resulting in an error of 5.572 cents or 4.64%.

17edo

1 step of 17edo is very near 25/24, differing from it by only 0.084 cents. Thus, 17edo can be tuned as a stack of 25/24s with a comma of 1.424 cents or 2.02%.

10 steps of 17edo is 3.927 cents sharp of 3/2, which results in a comma of 66.765 cents or 94.58%. Not great.

30edo

1 step of 30edo differs from 128/125 by 1.059 cents, resulting in a comma of 31.766 cents or 79.41%.

3 steps of 30edo differs from 15/14 by 0.557 cents. When a stack of 10 of these is combined with 20 128/125s, the comma is 26.752 cents or 66.88%.

31edo

10 steps of 31eddo differs from 5/4 by 0.783 cents, resulting in an error of 24.266 cents or 62.7%.

32edo

3 steps of 32edo differs from 16/15 by 0.769 cents, resulting in a comma of 24.599 cents or 65.6%.

ED8/3s

35ed8/3

8 steps of this tuning differs from 5/4 by 1.811 cents, resulting in an error of 63.37 cents or 130.6%.

ED3s

12ed3

2 steps of this tuning differs from 6/5 by 1.351 cents, resulting in an error of 16.215 cents or 10.23%.

30ed3

11 steps of this tuning differs from 3/2 by 4.571 cents, resulting in an error of 137.145 cents or 216.3%.

ED7/2s

35ed7/2

7 steps of this tuning differs from 9/7 by 1.319 cents. Stacking 5 of these results in a comma of 6.595 cents. 8 steps of this tuning differs from 4/3 by 2.313 cents. Stacking 30 of these has an error of 69.401 cents. The total error becomes 75.996 cents or 122.64%.

ED4s

39ed4

10 steps of this tuning differs from 10/7 by 2.103 cents, resulting in an error of 82.009 cents or 133.265%.

ED9/2s

56ed9/2

11 steps of this tuning differs from 43/32 by 0.036 cents, resulting in an error of 2 cents or 4.3%.

ED9s

7ed9

1 step of this tuning differs from 11/8 by 7.902 cents, resulting in an error of 55.316 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%.

59ed9

6 steps of this tuning differs from 5/4 by 0.524 cents, resulting in an error of 30.934 cents or 48%.