User:MisterShafXen/Tuning all ETs: Difference between revisions

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 Here is where I will be listing my approaches for tuning various ETs, octave-repeating or otherwise.
+== ED8/7s ==
+=== 23ed8/7 ===
+steps of this tuning differs from 256/243 by 0.234 cents, resulting in an error of 5.392 cents or 53.65%.
+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 ===
+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 ===
+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 ===
+step of this tuning differs from 64/63 by 1.671 cents, resulting in an error of 28.405 cents or 111%.
+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 ===
-steps of this tuning differs from 9/8 by 1.169 cents, resulting in an error of 19.873 cents.
+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 ===
+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 ===
+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 ===
+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 ===
+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 ===
+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 ===
+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 ===
+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 ===
+step of 5edo differs from 8/7 by 8.826 cents, resulting in an error of 44.13 cents or 18.4%.
+=== 6edo ===
+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 ===
+step of 10edo differs from 15/14 by 0.557 cents, resulting in an error of 5.572 cents or 4.64%.
 === 17edo ===
-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.
+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%.
-steps of 17edo is 3.925 cents sharp of 3/2, which results in a comma of 52.725 cents. Not great.
+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 ===
-step of 30edo differs from 128/125 by 1.058 cents, resulting in a comma of 31.74 cents.
+step of 30edo differs from 128/125 by 1.059 cents, resulting in a comma of 31.766 cents or 79.41%.
-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.
+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 ===
+steps of 31eddo differs from 5/4 by 0.783 cents, resulting in an error of 24.266 cents or 62.7%.
 === 32edo ===
-steps of 32edo differs from 16/15 by 0.769 cents, resulting in a comma of 24.608 cents.
+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 ===
+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 ===
+steps of this tuning differs from 6/5 by 1.351 cents, resulting in an error of 16.215 cents or 10.23%.
+=== 30ed3 ===
+steps of this tuning differs from 3/2 by 4.571 cents, resulting in an error of 137.145 cents or 216.3%.
+=== 34ed3 ===
+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 ===
-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.
+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 ===
+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 ===
+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 ===
+steps of this tuning differs from 43/32 by 0.036 cents, resulting in an error of 2 cents or 4.3%.
+== ED9s ==
+=== 7ed9 ===
+step of this tuning differs from 11/8 by 7.902 cents, resulting in an error of 55.316 cents or 10.2%.
+steps of this tuning differs from 15/8 by 1.412 cents, resulting in an error of 9.884 cents or 2%.
+=== 29ed9 ===
+steps of this tuning differs from 11/6 by 0.008 cents, resulting in an error of 0.245 cents or 0.2%.
+=== 59ed9 ===
+steps of this tuning differs from 5/4 by 0.524 cents, resulting in an error of 30.934 cents or 48%.