User:MisterShafXen/Tuning all ETs - Revision history

MisterShafXen at 11:30, 17 May 2026

2026-05-17T11:30:34Z

← Older revision		Revision as of 11:30, 17 May 2026
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	=== 30ed3 ===		=== 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%.		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 ==
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	== ED9/2s ==		== 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 ===		=== 56ed9/2 ===
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	2 steps of this tuning differs from 15/8 by 1.412 cents, resulting in an error of 9.884 cents or 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 ===		=== 59ed9 ===
	6 steps of this tuning differs from 5/4 by 0.524 cents, resulting in an error of 30.934 cents or 48%.		6 steps of this tuning differs from 5/4 by 0.524 cents, resulting in an error of 30.934 cents or 48%.

MisterShafXen at 12:05, 15 May 2026

2026-05-15T12:05:56Z

← Older revision		Revision as of 12:05, 15 May 2026
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	== ED9/7s ==		== 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 ===		=== 17ed9/7 ===

MisterShafXen at 12:02, 15 May 2026

2026-05-15T12:02:10Z

← Older revision		Revision as of 12:02, 15 May 2026
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	=== 31ed8/5 ===		=== 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%.		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 ==

MisterShafXen at 09:54, 21 April 2026

2026-04-21T09:54:09Z

← Older revision		Revision as of 09:54, 21 April 2026
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	15 steps of this tuning differs from 12/11 by 0.129 cents, resulting in an error of 2.959 cents or 29.44%.		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 ==		== ED9/7s ==
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	== ED3/2s ==		== 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 ===		=== 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%.		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 ==		== ED8/5s ==
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	== 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 ===		=== 6edo ===

MisterShafXen at 21:47, 20 April 2026

2026-04-20T21:47:27Z

← Older revision		Revision as of 21:47, 20 April 2026
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	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 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 ===		=== 32edo ===
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	=== 12ed3 ===		=== 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%.		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 ==		== ED7/2s ==
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	=== 39ed4 ===		=== 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%.		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 ==		== ED9s ==
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	2 steps of this tuning differs from 15/8 by 1.412 cents, resulting in an error of 9.884 cents or 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%.

MisterShafXen at 16:33, 20 April 2026

2026-04-20T16:33:33Z

← Older revision		Revision as of 16:33, 20 April 2026
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	=== 35ed8/3 ===		=== 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%.		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%.

	== ED7/2s ==		== ED7/2s ==

MisterShafXen at 14:43, 20 April 2026

2026-04-20T14:43:40Z

← Older revision		Revision as of 14:43, 20 April 2026
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	Another approach is to use 64/57, which results in an error of 2.808 cents or 1.404%.		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 ===
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	=== 35ed7/2 ===		=== 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%.		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 ==		== ED4s ==

	=== 39ed4 ===		=== 39ed4 ===
	10 steps of this tuning differs from 10/7 by 3.~~101~~ cents, resulting in an error of ~~120~~.~~939~~ cents or ~~nearly 200~~%.		10 steps of this tuning differs from 10/7 by 2.103 cents, resulting in an error of 82.009 cents or 133.265%.

	== ED9s ==		== ED9s ==

	=== 7ed9 ===		=== 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%.		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%.		2 steps of this tuning differs from 15/8 by 1.412 cents, resulting in an error of 9.884 cents or 2%.

MisterShafXen at 13:39, 20 April 2026

2026-04-20T13:39:40Z

← Older revision		Revision as of 13:39, 20 April 2026
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	=== 23ed8/7 ===		=== 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%.		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.~~015~~ cents, resulting in an error of 0.~~345~~ cents or 3.45%.		15 steps of this tuning differs from 12/11 by 0.129 cents, resulting in an error of 2.959 cents or 29.44%.

	== ED9/7s ==		== ED9/7s ==

	=== 17ed9/7 ===		=== 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~~%.		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.~~796~~ cents, resulting in an error of 13.~~532~~ cents or 52.73%.		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.~~169~~ cents, resulting in an error of 19.~~873~~ cents or 69%.		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 ===		=== 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%.		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 ==		== ED7/5s ==

	=== 9ed7/5 ===		=== 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%.		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 ==		== ED3/2s ==

	=== 6ed3/2 ===		=== 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%.		1 step of this tuning differs from 31/29 by 1.534 cents, resulting in a comma of 9.204 cents or 7.9%.

	== ED8/5s ==		== ED8/5s ==

	=== 31ed8/5 ===		=== 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%.		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 ==		== EDOs ==

	=== 6edo ===		=== 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%.		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%.		Another approach is to use 64/57, which results in an error of 2.808 cents or 1.404%.

	=== 17edo ===		=== 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%.		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.~~925~~ cents sharp of 3/2, which results in a comma of 52.~~725~~ cents or 75%. Not great.		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.~~058~~ cents, resulting in a comma of 31.74 cents or 79.35%.		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.~~657~~ cents. When a stack of 10 of these is combined with 20 128/125s, the comma is 27.73 cents or 69.~~325~~%.		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%.

	=== 32edo ===		=== 32edo ===
	3 steps of 32edo differs from 16/15 by 0.769 cents, resulting in a comma of 24.~~608~~ cents or 65.6%.		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 ==		== ED8/3s ==

	=== 35ed8/3 ===		=== 35ed8/3 ===
	8 steps of this tuning differs from 5/4 by 1.8 cents, resulting in an error of 63 cents or ~~140~~%.		8 steps of this tuning differs from 5/4 by 1.811 cents, resulting in an error of 63.37 cents or 130.6%.

	== ED7/2s ==		== ED7/2s ==

MisterShafXen at 11:36, 20 April 2026

2026-04-20T11:36:58Z

← Older revision		Revision as of 11:36, 20 April 2026
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	=== 32edo ===		=== 32edo ===
	3 steps of 32edo differs from 16/15 by 0.769 cents, resulting in a comma of 24.608 cents or 65.6%.		3 steps of 32edo differs from 16/15 by 0.769 cents, resulting in a comma of 24.608 cents or 65.6%.

			== ED8/3s ==

			=== 35ed8/3 ===
			8 steps of this tuning differs from 5/4 by 1.8 cents, resulting in an error of 63 cents or 140%.

	== ED7/2s ==		== ED7/2s ==
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	=== 35ed7/2 ===		=== 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%.		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%.

			== ED4s ==

			=== 39ed4 ===
			10 steps of this tuning differs from 10/7 by 3.101 cents, resulting in an error of 120.939 cents or nearly 200%.

	== ED9s ==		== ED9s ==

MisterShafXen at 11:27, 20 April 2026

2026-04-20T11:27:23Z

@@ Line 1: / Line 1: @@
 Here is where I will be listing my approaches for tuning various ETs, octave-repeating or otherwise.
 == ED4/3s ==
@@ Line 5: / Line 19: @@
 === 17ed4/3 ===
 steps of this tuning differs from 9/8 by 1.169 cents, resulting in an error of 19.873 cents or 69%.
 == ED3/2s ==
@@ Line 10: / Line 32: @@
 === 6ed3/2 ===
 step of this tuning differs from 31/29 by 1.541 cents, resulting in a comma of 9.246 cents or 7.7%.
 == EDOs ==
@@ Line 35: / Line 62: @@
 === 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 or 122.6%.