User:MisterShafXen/Tuning all ETs: Difference between revisions
Created page with "Here is where I will be listing my approaches for tuning various ETs, octave-repeating or otherwise. == 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. == EDOs == === 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. 10 steps of 17edo is 3.925 cents sharp of 3/2, which results in a comm..." Tags: Visual edit Mobile edit Mobile web edit Advanced mobile edit |
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Here is where I will be listing my approaches for tuning various ETs, octave-repeating or otherwise. | 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 == | |||
=== 10ed9/7 === | |||
9 steps of this tuning differs from 2744/2187 by 1.217 cents. This results in an error of 12.17 cents or 28%. | |||
=== 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 == | == ED4/3s == | ||
=== 17ed4/3 === | === 17ed4/3 === | ||
7 steps of this tuning differs from 9/8 by 1. | 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%. | |||
== ED9/5s == | |||
=== 7ed9/5 === | |||
3 steps of this tuning differs from 9/7 by 1.029 cents, resulting in an error of 7.2 cents or 4.95%. | |||
== EDOs == | == 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 === | === 17edo === | ||
1 step of 17edo is very near 25/24, differing from it by only 0. | 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. | 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 === | === 30edo === | ||
1 step of 30edo differs from 128/125 by 1. | 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%. | |||
3 steps of | === 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%. | |||
=== 34ed3 === | |||
15 steps of this tuning differs from 13/8 by 1.43 cents, resulting in an error of 48.615 cents or 86.9%. | |||
== ED7/2s == | == ED7/2s == | ||
=== 35ed7/2 === | === 35ed7/2 === | ||
7 steps of this tuning differs from 9/7 by 1. | 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 == | |||
=== 31ed9/2 === | |||
24 steps of this tuning differs from 16/5 by 2.244 cents, resulting in an error of 69.565 cents or 82.8%. | |||
=== 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%. | |||
=== 29ed9 === | |||
8 steps of this tuning differs from 11/6 by 0.008 cents, resulting in an error of 0.245 cents or 0.2%. | |||
=== 59ed9 === | |||
6 steps of this tuning differs from 5/4 by 0.524 cents, resulting in an error of 30.934 cents or 48%. | |||
Latest revision as of 11:30, 17 May 2026
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
10ed9/7
9 steps of this tuning differs from 2744/2187 by 1.217 cents. This results in an error of 12.17 cents or 28%.
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%.
ED9/5s
7ed9/5
3 steps of this tuning differs from 9/7 by 1.029 cents, resulting in an error of 7.2 cents or 4.95%.
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%.
34ed3
15 steps of this tuning differs from 13/8 by 1.43 cents, resulting in an error of 48.615 cents or 86.9%.
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
31ed9/2
24 steps of this tuning differs from 16/5 by 2.244 cents, resulting in an error of 69.565 cents or 82.8%.
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%.
29ed9
8 steps of this tuning differs from 11/6 by 0.008 cents, resulting in an error of 0.245 cents or 0.2%.
59ed9
6 steps of this tuning differs from 5/4 by 0.524 cents, resulting in an error of 30.934 cents or 48%.