User:BudjarnLambeth/Table of stretched 42edo tunings - Revision history

BudjarnLambeth at 00:13, 2 August 2025

2025-08-02T00:13:59Z

← Older revision		Revision as of 00:13, 2 August 2025
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			{{Editable user page}}
	[[42edo]] has almost 50% relative error on harmonics 3/1 and 5/1. This means that whether one [[Octave stretch\|stretches]] or [[Octave shrinking\|compresses]] the octave, either way it will improve 42edo’s approximations of [[JI]], but in opposite directions.		[[42edo]] has almost 50% relative error on harmonics 3/1 and 5/1. This means that whether one [[Octave stretch\|stretches]] or [[Octave shrinking\|compresses]] the octave, either way it will improve 42edo’s approximations of [[JI]], but in opposite directions.

BudjarnLambeth: BudjarnLambeth moved page Table of stretched 42edo tunings to User:BudjarnLambeth/Table of stretched 42edo tunings: XW:NG

2025-08-02T00:13:43Z

BudjarnLambeth moved page Table of stretched 42edo tunings to User:BudjarnLambeth/Table of stretched 42edo tunings: XW:NG

← Older revision	Revision as of 00:13, 2 August 2025
(No difference)

BudjarnLambeth at 02:44, 13 December 2024

2024-12-13T02:44:54Z

← Older revision		Revision as of 02:44, 13 December 2024
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	[[42edo]] has almost 50% relative error on harmonics 3/1 and 5/1. This means that whether one [[Octave stretch\|stretches]] or [[Octave shrinking\|compresses]] the octave, either way it will improve 42edo’s approximations of [[JI]], but in opposite directions.		[[42edo]] has almost 50% relative error on harmonics 3/1 and 5/1. This means that whether one [[Octave stretch\|stretches]] or [[Octave shrinking\|compresses]] the octave, either way it will improve 42edo’s approximations of [[JI]], but in opposite directions.

	This table provides a detailed comparison of three stretched- and ~~two~~ compressed-octave tunings for 42edo.		This table provides a detailed comparison of three stretched- and three compressed-octave tunings for 42edo.

	{\| class="wikitable"		{\| class="wikitable"

BudjarnLambeth at 02:41, 13 December 2024

2024-12-13T02:41:58Z

← Older revision		Revision as of 02:41, 13 December 2024
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	\| <small>ex: 5 <br>gd: 2, 13 <br>ok: 3, 11 <br>ba: 7</small>		\| <small>ex: 5 <br>gd: 2, 13 <br>ok: 3, 11 <br>ba: 7</small>
	\| '''<small>ex: 2, 7 <br>gd: <br>ok: 11 <br>ba: 3, 5, 13</small>'''		\| '''<small>ex: 2, 7 <br>gd: <br>ok: 11 <br>ba: 3, 5, 13</small>'''
	\| <small>ex: 2 <br>gd: 3, 5, 7, 13 <br>ok: 11 <br>ba:</small>		\| <small>ex: 2 <br>gd: 5, 7, 13 <br>ok: 3, 11 <br>ba:</small>
	\| <small>ex: 5, 11, 13 <br>gd: 2, 3 <br>ok: <br>ba: 7</small>		\| <small>ex: 5, 11, 13 <br>gd: 2, 3 <br>ok: <br>ba: 7</small>
	\| <small>ex: 3, 5, 11 <br>gd: 2 <br>ok: 13 <br>ba: 7</small>		\| <small>ex: 3, 5, 11 <br>gd: 2 <br>ok: 13 <br>ba: 7</small>
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	\| 173 <br>(5)		\| 173 <br>(5)
	\|-		\|-
	\| colspan="8" \| <small><div style="text-align: center;">''ex = “excellent”, 0-~~12.5~~% relative error • gd = “good”, ~~12.5~~-27.5% • ok = “okay”, 27.5-40% • bd = “bad”, 40-50%''</div></small>		\| colspan="8" \| <small><div style="text-align: center;">''ex = “excellent”, 0-13% relative error • gd = “good”, 13-27% • ok = “okay”, 27-40% • bd = “bad”, 40-50%''</div></small>
	\|}		\|}

	[[Category:42edo]][[Category:Tables]]		[[Category:42edo]][[Category:Tables]]

BudjarnLambeth at 02:38, 13 December 2024

2024-12-13T02:38:23Z

← Older revision		Revision as of 02:38, 13 December 2024
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	\|-		\|-
	! Overview		! Overview
	\| ex: 5 <br>gd: 2, 3, 7 <br>ok: <br>ba: 11, 13		\| <small>ex: 5 <br>gd: 2, 3, 7 <br>ok: <br>ba: 11, 13</small>
	\| ex: 5 <br>gd: 2, 3 <br>ok: 7, 11, 13 <br>ba:		\| <small>ex: 5 <br>gd: 2, 3 <br>ok: 7, 11, 13 <br>ba:</small>
	\| ex: 5 <br>gd: 2, 13 <br>ok: 3, 11 <br>ba: 7		\| <small>ex: 5 <br>gd: 2, 13 <br>ok: 3, 11 <br>ba: 7</small>
	\| '''ex: 2, 7 <br>gd: <br>ok: 11 <br>ba: 3, 5, 13'''		\| '''<small>ex: 2, 7 <br>gd: <br>ok: 11 <br>ba: 3, 5, 13</small>'''
	\| ex: 2 <br>gd: 3, 5, 7, 13 <br>ok: 11 <br>ba:		\| <small>ex: 2 <br>gd: 3, 5, 7, 13 <br>ok: 11 <br>ba:</small>
	\| ex: 5, 11, 13 <br>gd: 2, 3 <br>ok: <br>ba: 7		\| <small>ex: 5, 11, 13 <br>gd: 2, 3 <br>ok: <br>ba: 7</small>
	\| ex: 3, 5, 11 <br>gd: 2 <br>ok: 13 <br>ba: 7		\| <small>ex: 3, 5, 11 <br>gd: 2 <br>ok: 13 <br>ba: 7</small>
	\|-		\|-
	! 2/1 error		! 2/1 error

BudjarnLambeth at 02:37, 13 December 2024

2024-12-13T02:37:51Z

← Older revision		Revision as of 02:37, 13 December 2024
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	\|-		\|-
	! Overview		! Overview
	\| ~~great~~: 5 <br>~~good~~: 2, 3, 7 <br>~~okay~~: <br>~~bad~~: 11, 13		\| ex: 5 <br>gd: 2, 3, 7 <br>ok: <br>ba: 11, 13
	\| ~~great~~: 5 <br>~~good~~: 2, 3 <br>~~okay~~: 7, 11, 13 <br>~~bad~~:		\| ex: 5 <br>gd: 2, 3 <br>ok: 7, 11, 13 <br>ba:
	\| ~~great~~: 5 <br>~~good~~: 2, 13 <br>~~okay~~: 3, 11 <br>~~bad~~: 7		\| ex: 5 <br>gd: 2, 13 <br>ok: 3, 11 <br>ba: 7
	\| '''~~great~~: 2, 7 <br>~~good~~: <br>~~okay~~: 11 <br>~~bad~~: 3, 5, 13'''		\| '''ex: 2, 7 <br>gd: <br>ok: 11 <br>ba: 3, 5, 13'''
	\| ~~great~~: 2 <br>~~good~~: 3, 5, 7, 13 <br>~~okay~~: 11 <br>~~bad~~:		\| ex: 2 <br>gd: 3, 5, 7, 13 <br>ok: 11 <br>ba:
	\| ~~great~~: 5, 11, 13 <br>~~good~~: 2, 3 <br>~~okay~~: <br>~~bad~~: 7		\| ex: 5, 11, 13 <br>gd: 2, 3 <br>ok: <br>ba: 7
	\| ~~great~~: 3, 5, 11 <br>~~good~~: 2 <br>~~okay~~: 13 <br>~~bad~~: 7		\| ex: 3, 5, 11 <br>gd: 2 <br>ok: 13 <br>ba: 7
	\|-		\|-
	! 2/1 error		! 2/1 error
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	\| 173 <br>(5)		\| 173 <br>(5)
	\|-		\|-
	\| colspan="8" \| <small><div style="text-align: center;">''~~“great”~~ = 0-12.5% relative error • “good” = 12.5-27.5% • “okay” = 27.5-40% • “bad” = 40-50%''</div></small>		\| colspan="8" \| <small><div style="text-align: center;">''ex = “excellent”, 0-12.5% relative error • gd = “good”, 12.5-27.5% • ok = “okay”, 27.5-40% • bd = “bad”, 40-50%''</div></small>
	\|}		\|}

	[[Category:42edo]][[Category:Tables]]		[[Category:42edo]][[Category:Tables]]

BudjarnLambeth at 02:11, 13 December 2024

2024-12-13T02:11:10Z

← Older revision		Revision as of 02:11, 13 December 2024
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	\|+		\|+
	!Tuning		!Tuning
	! [[42ed257/128]]		! '''[[42ed257/128]]'''
	! [[1ed28.7c\|APS720jot]]		! [[1ed28.7c\|'''APS720jot''']]
	! [[zpi\|189zpi]]		! [[zpi\|'''189zpi''']]
	! [[42edo]]		! [[42edo]]
	! [[1ed28.5c\|APS715jot]]		! [[1ed28.5c\|APS715jot]]
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	\| ~41.81		\| ~41.81
	\| ~41.83		\| ~41.83
	\| 42.00		\| '''42.00'''
	\| ~42.10		\| ~42.10
	\| ~42.19		\| ~42.19
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	\| ~28.70¢		\| ~28.70¢
	\| ~28.69¢		\| ~28.69¢
	\| ~28.57¢		\| '''~28.57¢'''
	\| ~28.50¢		\| ~28.50¢
	\| ~28.44¢		\| ~28.44¢
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	\| great: 5 <br>good: 2, 3 <br>okay: 7, 11, 13 <br>bad:		\| great: 5 <br>good: 2, 3 <br>okay: 7, 11, 13 <br>bad:
	\| great: 5 <br>good: 2, 13 <br>okay: 3, 11 <br>bad: 7		\| great: 5 <br>good: 2, 13 <br>okay: 3, 11 <br>bad: 7
	\| great: 2, 7 <br>good: <br>okay: 11 <br>bad: 3, 5, 13		\| '''great: 2, 7 <br>good: <br>okay: 11 <br>bad: 3, 5, 13'''
	\| great: 2 <br>good: 3, 5, 7, 13 <br>okay: 11 <br>bad:		\| great: 2 <br>good: 3, 5, 7, 13 <br>okay: 11 <br>bad:
	\| great: 5, 11, 13 <br>good: 2, 3 <br>okay: <br>bad: 7		\| great: 5, 11, 13 <br>good: 2, 3 <br>okay: <br>bad: 7
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	\| +19.0% <br>(5.5¢)		\| +19.0% <br>(5.5¢)
	\| +17.2% <br>(4.9¢)		\| +17.2% <br>(4.9¢)
	\| 0.0% <br>(0.0¢)		\| '''0.0% <br>(0.0¢)'''
	\| -10.2% <br>(2.9¢)		\| -10.2% <br>(2.9¢)
	\| −18.8% <br>(5.3¢)		\| −18.8% <br>(5.3¢)
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	\| −26.7% <br>(7.7¢)		\| −26.7% <br>(7.7¢)
	\| −29.6% <br>(8.5¢)		\| −29.6% <br>(8.5¢)
	\| +43.2% <br>(12.3¢)		\| '''+43.2% <br>(12.3¢)'''
	\| +27.0% <br>(7.7¢)		\| +27.0% <br>(7.7¢)
	\| +13.4% <br>(3.8¢)		\| +13.4% <br>(3.8¢)
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	\| −7.9% <br>(2.3¢)		\| −7.9% <br>(2.3¢)
	\| −12.2% <br>(3.5¢)		\| −12.2% <br>(3.5¢)
	\| +47.9% <br>(13.7¢)		\| '''+47.9% <br>(13.7¢)'''
	\| +24.2% <br>(6.9¢)		\| +24.2% <br>(6.9¢)
	\| +4.3% <br>(1.2¢)		\| +4.3% <br>(1.2¢)
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	\| −37.5% <br>(10.8¢)		\| −37.5% <br>(10.8¢)
	\| −42.6% <br>(12.2¢)		\| −42.6% <br>(12.2¢)
	\| +9.1% <br>(2.6¢)		\| '''+9.1% <br>(2.6¢)'''
	\| -19.6% <br>(5.6¢)		\| -19.6% <br>(5.6¢)
	\| −43.6% <br>(12.4¢)		\| −43.6% <br>(12.4¢)
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	\| +36.2% <br>(10.4¢)		\| +36.2% <br>(10.4¢)
	\| +29.8% <br>(8.6¢)		\| +29.8% <br>(8.6¢)
	\| −29.6% <br>(8.5¢)		\| '''−29.6% <br>(8.5¢)'''
	\| +35.1% <br>(10.0¢)		\| +35.1% <br>(10.0¢)
	\| +5.5% <br>(1.6¢)		\| +5.5% <br>(1.6¢)
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	\| +28.6% <br>(8.2¢)		\| +28.6% <br>(8.2¢)
	\| +21.7% <br>(6.2¢)		\| +21.7% <br>(6.2¢)
	\| −41.8% <br>(12.0¢)		\| '''−41.8% <br>(12.0¢)'''
	\| +20.4% <br>(5.8¢)		\| +20.4% <br>(5.8¢)
	\| −11.3% <br>(3.2¢)		\| −11.3% <br>(3.2¢)
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	\| +10.4% <br>(3.0¢)		\| +10.4% <br>(3.0¢)
	\| +2.9% <br>(0.8¢)		\| +2.9% <br>(0.8¢)
	\| +32.7% <br>(9.3¢)		\| '''+32.7% <br>(9.3¢)'''
	\| -9.1% <br>(2.5¢)		\| -9.1% <br>(2.5¢)
	\| -44.0% <br>(12.5¢)		\| -44.0% <br>(12.5¢)
Line 108:		Line 108:
	\| 42 <br>(0)		\| 42 <br>(0)
	\| 42 <br>(0)		\| 42 <br>(0)
	\| 42 <br>(0)		\| '''42 <br>(0)'''
	\| 42 <br>(0)		\| 42 <br>(0)
	\| 42 <br>(0)		\| 42 <br>(0)
Line 117:		Line 117:
	\| 66 <br>(24)		\| 66 <br>(24)
	\| 66 <br>(24)		\| 66 <br>(24)
	\| 67 <br>(25)		\| '''67 <br>(25)'''
	\| 67 <br>(25)		\| 67 <br>(25)
	\| 67 <br>(25)		\| 67 <br>(25)
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	\| 97 <br>(13)		\| 97 <br>(13)
	\| 97 <br>(13)		\| 97 <br>(13)
	\| 98 <br>(14)		\| '''98 <br>(14)'''
	\| 98 <br>(14)		\| 98 <br>(14)
	\| 98 <br>(14)		\| 98 <br>(14)
Line 135:		Line 135:
	\| 117 <br>(33)		\| 117 <br>(33)
	\| 117 <br>(33)		\| 117 <br>(33)
	\| 118 <br>(34)		\| '''118 <br>(34)'''
	\| 118 <br>(34)		\| 118 <br>(34)
	\| 118 <br>(34)		\| 118 <br>(34)
Line 144:		Line 144:
	\| 145 <br>(19)		\| 145 <br>(19)
	\| 145 <br>(19)		\| 145 <br>(19)
	\| 145 <br>(19)		\| '''145 <br>(19)'''
	\| 146 <br>(20)		\| 146 <br>(20)
	\| 146 <br>(20)		\| 146 <br>(20)
Line 153:		Line 153:
	\| 155 <br>(29)		\| 155 <br>(29)
	\| 155 <br>(29)		\| 155 <br>(29)
	\| 155 <br>(29)		\| '''155 <br>(29)'''
	\| 156 <br>(30)		\| 156 <br>(30)
	\| 156 <br>(30)		\| 156 <br>(30)
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	\| 171 <br>(3)		\| 171 <br>(3)
	\| 171 <br>(3)		\| 171 <br>(3)
	\| 172 <br>(4)		\| '''172 <br>(4)'''
	\| 172 <br>(4)		\| 172 <br>(4)
	\| 172 <br>(4)		\| 172 <br>(4)

BudjarnLambeth at 02:10, 13 December 2024

2024-12-13T02:10:03Z

← Older revision		Revision as of 02:10, 13 December 2024
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	\| +35.1% <br>(10.0¢)		\| +35.1% <br>(10.0¢)
	\| +5.5% <br>(1.6¢)		\| +5.5% <br>(1.6¢)
	\| −12.1% <br>3.4¢)		\| −12.1% <br>(3.4¢)
	\|-		\|-
	! 13/1 error		! 13/1 error

BudjarnLambeth: Add 17/1

2024-12-13T02:03:44Z

Add 17/1

@@ Line 94: / Line 94: @@
 | −11.3% <br>(3.2¢)
 | −30.1% <br>(8.6¢)
 |-
 ! 2/1 val <br>(& reduced)
@@ Line 148: / Line 157: @@
 | 156 <br>(30)
 | 156 <br>(30)
 |-
 | colspan="8" | <small><div style="text-align: center;">''“great” = 0-12.5% relative error • “good” = 12.5-27.5% • “okay” = 27.5-40% • “bad” = 40-50%''</div></small>

BudjarnLambeth at 01:52, 13 December 2024

2024-12-13T01:52:50Z

← Older revision		Revision as of 01:52, 13 December 2024
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	\| 156 <br>(30)		\| 156 <br>(30)
	\|-		\|-
	\| colspan="7" \| <small><div style="text-align: center;">''“great” = 0-12.5% relative error • “good” = 12.5-27.5% • “okay” = 27.5-40% • “bad” = 40-50%''</div></small>		\| colspan="8" \| <small><div style="text-align: center;">''“great” = 0-12.5% relative error • “good” = 12.5-27.5% • “okay” = 27.5-40% • “bad” = 40-50%''</div></small>
	\|}		\|}

	[[Category:42edo]][[Category:Tables]]		[[Category:42edo]][[Category:Tables]]