User:Dummy index/3rd-tritave temperaments - Revision history

ArrowHead294: Replace {{scale link}} with {{mos scalesig}}

2025-03-08T00:41:13Z

Replace {{scale link}} with {{mos scalesig}}

← Older revision		Revision as of 00:41, 8 March 2025
Line 5:		Line 5:
	== "Threedie family" start from 3.5.7.13 ==		== "Threedie family" start from 3.5.7.13 ==

	=== BPS III (b30 & b9, b39 & b9) ===		=== BPS III (b30 & b9, b39 & b9) ===
	: ''Proposed names: [[User:Recentlymaterialized/Miscellaneous rank-2 temperaments #Tripierce (b30 & b39)]]''		: ''Proposed names: [[User:Recentlymaterialized/Miscellaneous rank-2 temperaments #Tripierce (b30 & b39)]]''

	[[Subgroup]]: 3.5.7.13		[[Subgroup]]: 3.5.7.13
Line 24:		Line 24:
	Badness (Dirichlet): 0.269		Badness (Dirichlet): 0.269

	* {{sl\|3L 6s}}		* {{mos scalesig\|3L 6s<3/1>\|link=1}}
	* {{sl\|9L 3s}} – This has 5:7:9:13.		* {{mos scalesig\|9L 3s<3/1>\|link=1}} – This has 5:7:9:13.

	==== 3.5.7.11.13 ====		==== 3.5.7.11.13 ====
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	Badness (Dirichlet): 0.525		Badness (Dirichlet): 0.525

	==== strong extension 3.5.7.11.13 (b39 & b30e) ====		==== strong extension 3.5.7.11.13 (b39 & b30e) ====

	Subgroup: 3.5.7.11.13		Subgroup: 3.5.7.11.13
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	Badness (Dirichlet): 0.713		Badness (Dirichlet): 0.713

	==== weak extension 3.5.7.11.13 (b39 & b60) ====		==== weak extension 3.5.7.11.13 (b39 & b60) ====

	Subgroup: 3.5.7.11.13		Subgroup: 3.5.7.11.13
Line 82:		Line 82:
	Badness (Dirichlet): 0.447		Badness (Dirichlet): 0.447

	* {{sl\|3L 15s}}		* {{mos scalesig\|3L 15s<3/1>\|link=1}}
	* {{sl\|18L 3s}} – This has 5:7:9:11:13.		* {{mos scalesig\|18L 3s<3/1>\|link=1}} – This has 5:7:9:11:13.

	=== Sirius III (b39 & b6, b39 & b45) ===		=== Sirius III (b39 & b6, b39 & b45) ===

	[[Subgroup]]: 3.5.7.13		[[Subgroup]]: 3.5.7.13
Line 103:		Line 103:
	Badness (Dirichlet): 0.832		Badness (Dirichlet): 0.832

	* {{sl\|3L 3s}}		* {{mos scalesig\|3L 3s<3/1>\|link=1}}
	* {{sl\|6L 3s}}		* {{mos scalesig\|6L 3s<3/1>\|link=1}}

	==== 3.5.7.11.13 (also deneb III) ====		==== 3.5.7.11.13 (also deneb III) ====
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	Badness (Dirichlet): 0.551		Badness (Dirichlet): 0.551

	=== Canopus III (b39 & b36, b39 & b75) ===		=== Canopus III (b39 & b36, b39 & b75) ===

	[[Subgroup]]: 3.5.7.13		[[Subgroup]]: 3.5.7.13
Line 144:		Line 144:
	{{main\|Suhail}}		{{main\|Suhail}}

	=== b9 & b6 ===		=== b9 & b6 ===

	[[Subgroup]]: 3.5.7.13		[[Subgroup]]: 3.5.7.13
Line 163:		Line 163:

	== "Threedie family" start from 3.7.11.13 ==		== "Threedie family" start from 3.7.11.13 ==
	=== Mintaka III (b39 & b66) ===		=== Mintaka III (b39 & b66) ===

	[[Subgroup]]: 3.7.11.13		[[Subgroup]]: 3.7.11.13
Line 181:		Line 181:
	Badness (Dirichlet): 0.237		Badness (Dirichlet): 0.237

	* {{sl\|3L 9s}} – This and the following have 7:9:11:13.		* {{mos scalesig\|3L 9s<3/1>\|link=1}} – This and the following have 7:9:11:13.
	* {{sl\|12L 3s}}		* {{mos scalesig\|12L 3s<3/1>\|link=1}}

	==== 3.5.7.11.13 (also procyon III) ====		==== 3.5.7.11.13 (also procyon III) ====
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	Badness (Dirichlet): 0.459		Badness (Dirichlet): 0.459

	==== ~~weak~~ extension 3.5.7.11.13 (b39 & b15, also arcturus III) ====		==== Weak extension 3.5.7.11.13 (b39 & b15, also arcturus III) ====
	:''See also: [[Tetrahanson #b39 & b15]]''		: ''See also: [[Tetrahanson #b39 & b15]]''

	Subgroup: 3.5.7.11.13		Subgroup: 3.5.7.11.13
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	Badness (Dirichlet): 0.588		Badness (Dirichlet): 0.588

	* {{sl\|6L 3s}}		* {{mos scalesig\|6L 3s<3/1>\|link=1}}
	* {{sl\|9L 6s}} – This has 5:9:11:13.		* {{mos scalesig\|9L 6s<3/1>\|link=1}} – This has 5:9:11:13.
	* {{sl\|15L 9s}} – This has 5:7:9:11:13.		* {{mos scalesig\|15L 9s<3/1>\|link=1}} – This has 5:7:9:11:13.

	~~=== b27 & b21 ===~~

			=== b27 & b21 ===
	Subgroup: 3.7.11.13		Subgroup: 3.7.11.13

Line 243:		Line 242:

	== External links ==		== External links ==
	*[https://x31eq.com/pyscript/more.html?r=2&limit=3_5_7_13&error=6.2]		* [https://x31eq.com/pyscript/more.html?r=2&limit=3_5_7_13&error=6.2]
	*[https://x31eq.com/pyscript/more.html?r=2&limit=3_5_7_11_13&error=4.0]		* [https://x31eq.com/pyscript/more.html?r=2&limit=3_5_7_11_13&error=4.0]

	<!-- b30 & b6, b30 & b45, b9 & b45 -->		<!-- b30 & b6, b30 & b45, b9 & b45 -->

Dummy index: /* weak extension 3.5.7.11.13 (b39 & b15, also arcturus III) */

2025-02-10T14:53:14Z

weak extension 3.5.7.11.13 (b39 & b15, also arcturus III)

← Older revision		Revision as of 14:53, 10 February 2025
Line 202:		Line 202:

	==== weak extension 3.5.7.11.13 (b39 & b15, also arcturus III) ====		==== weak extension 3.5.7.11.13 (b39 & b15, also arcturus III) ====
			:''See also: [[Tetrahanson #b39 & b15]]''

	Subgroup: 3.5.7.11.13		Subgroup: 3.5.7.11.13
Line 220:		Line 221:

	* {{sl\|6L 3s}}		* {{sl\|6L 3s}}
	* {{sl\|9L 6s}}		* {{sl\|9L 6s}} – This has 5:9:11:13.
	* {{sl\|15L 9s}} – This has 5:7:9:11:13.		* {{sl\|15L 9s}} – This has 5:7:9:11:13.

Dummy index: /* weak extension 3.5.7.11.13 (b39 & b15, also arcturus III) */ fix

2025-02-01T12:44:47Z

weak extension 3.5.7.11.13 (b39 & b15, also arcturus III): fix

← Older revision		Revision as of 12:44, 1 February 2025
Line 221:		Line 221:
	* {{sl\|6L 3s}}		* {{sl\|6L 3s}}
	* {{sl\|9L 6s}}		* {{sl\|9L 6s}}
	* {{sl\|15L 6s}} – This has 5:7:9:11:13.		* {{sl\|15L 9s}} – This has 5:7:9:11:13.

	=== b27 & b21 ===		=== b27 & b21 ===

Dummy index: /* Mintaka III (b39 & b66) */ fix

2025-02-01T12:19:30Z

Mintaka III (b39 & b66): fix

← Older revision		Revision as of 12:19, 1 February 2025
Line 181:		Line 181:
	Badness (Dirichlet): 0.237		Badness (Dirichlet): 0.237

	* {{sl\|3L 9s}} – This and the following have 5:7:9:13.		* {{sl\|3L 9s}} – This and the following have 7:9:11:13.
	* {{sl\|12L 3s}}		* {{sl\|12L 3s}}

Dummy index: +mos

2025-02-01T12:14:28Z

+mos

← Older revision		Revision as of 12:14, 1 February 2025
Line 23:		Line 23:

	Badness (Dirichlet): 0.269		Badness (Dirichlet): 0.269

			* {{sl\|3L 6s}}
			* {{sl\|9L 3s}} – This has 5:7:9:13.

	==== 3.5.7.11.13 ====		==== 3.5.7.11.13 ====
Line 78:		Line 81:

	Badness (Dirichlet): 0.447		Badness (Dirichlet): 0.447

			* {{sl\|3L 15s}}
			* {{sl\|18L 3s}} – This has 5:7:9:11:13.

	=== Sirius III (b39 & b6, b39 & b45) ===		=== Sirius III (b39 & b6, b39 & b45) ===
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	Badness (Dirichlet): 0.832		Badness (Dirichlet): 0.832

			* {{sl\|3L 3s}}
			* {{sl\|6L 3s}}

	==== 3.5.7.11.13 (also deneb III) ====		==== 3.5.7.11.13 (also deneb III) ====
Line 171:		Line 180:

	Badness (Dirichlet): 0.237		Badness (Dirichlet): 0.237

			* {{sl\|3L 9s}} – This and the following have 5:7:9:13.
			* {{sl\|12L 3s}}

	==== 3.5.7.11.13 (also procyon III) ====		==== 3.5.7.11.13 (also procyon III) ====
Line 206:		Line 218:

	Badness (Dirichlet): 0.588		Badness (Dirichlet): 0.588

			* {{sl\|6L 3s}}
			* {{sl\|9L 6s}}
			* {{sl\|15L 6s}} – This has 5:7:9:11:13.

	=== b27 & b21 ===		=== b27 & b21 ===

Dummy index: /* "Threedie family" start from 3.7.11.13 */

2025-01-27T13:30:54Z

"Threedie family" start from 3.7.11.13

← Older revision		Revision as of 13:30, 27 January 2025
Line 206:		Line 206:

	Badness (Dirichlet): 0.588		Badness (Dirichlet): 0.588

			=== b27 & b21 ===

			Subgroup: 3.7.11.13

			Comma list: 9477/9317, 2197/2187

			Sval mapping: {{mapping\| 3 1 8 7 \| 0 3 -1 0 }}

			Sval mapping (mingen): {{mapping\| 3 4 7 7 \| 0 3 -1 0 }}

			Sval mapping generators: ~13/9, ~243/143

			Optimal tuning (CWE): ~13/9 = 1\3edt, ~243/143 = 912.556

			Supporting ETs: 27, 6, 21, 48, 75, 15[-7], 33[+7], 69, 102, 123[+11], 60[+7], 129[+7], 90[+11], 117[+11]

			Badness (Dirichlet): 0.830

	== External links ==		== External links ==

Dummy index: -stub

2025-01-25T07:43:55Z

-stub

← Older revision		Revision as of 07:43, 25 January 2025
Line 212:		Line 212:

	<!-- b30 & b6, b30 & b45, b9 & b45 -->		<!-- b30 & b6, b30 & b45, b9 & b45 -->
	~~{{stub}}~~

Dummy index: +data(3/3)

2025-01-25T07:42:05Z

+data(3/3)

← Older revision		Revision as of 07:42, 25 January 2025
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	=== Mintaka III (b39 & b66) ===		=== Mintaka III (b39 & b66) ===

	Subgroup: 3.7.11.13		[[Subgroup]]: 3.7.11.13

	Comma list: 1331/1323, 2197/2187		[[Comma list]]: 1331/1323, 2197/2187

	Sval mapping: {{mapping\| 3 6 7 7 \| 0 -3 -2 0 }}		[[Sval]] [[mapping]]: {{mapping\| 3 0 3 7 \| 0 3 2 0 }}

			Sval mapping ([[mingen]]): {{mapping\| 3 6 7 7 \| 0 -3 -2 0 }}

			Sval mapping generators: ~13/9, ~21/11

			[[Optimal tuning]] ([[CWE]]): ~13/9 = 1\3edt, ~21/11 = 1122.959

			[[Support]]ing [[ET]]s: 39, 27, 12, 66, 105, 15, 144, 51, 93, 183, 171, 90, 42[+7], 222[-11]

			Badness (Dirichlet): 0.237

	==== 3.5.7.11.13 (also procyon III) ====		==== 3.5.7.11.13 (also procyon III) ====
Line 167:		Line 177:
	Subgroup: 3.5.7.11.13		Subgroup: 3.5.7.11.13

	Comma list: ~~823543~~/~~820125~~, ~~1331~~/~~1323~~, ~~2197~~/~~2187~~		Comma list: 4459/4455, 11011/10935, 847/845

	Sval mapping: {{mapping\| 3 6 6 7 7 \| 0 -7 -3 -2 0 }}		Sval mapping: {{mapping\| 3 6 6 7 7 \| 0 -7 -3 -2 0 }}

			Sval mapping generators: ~13/9, ~49/45

			Optimal tuning (CWE): ~13/9 = 1\3edt, ~49/45 = 145.470

			Supporting ETs: 39, 144, 105, 183, 66, 27, 12[-5], 222[-11], 261[-11], 51[-5], 249, 327[-11], 300[-11], 171

			Badness (Dirichlet): 0.459

	==== weak extension 3.5.7.11.13 (b39 & b15, also arcturus III) ====		==== weak extension 3.5.7.11.13 (b39 & b15, also arcturus III) ====
Line 175:		Line 193:
	Subgroup: 3.5.7.11.13		Subgroup: 3.5.7.11.13

	Comma list: ~~15625~~/~~15309~~, ~~1331~~/~~1323~~, ~~2197~~/~~2187~~		Comma list: 275/273, 1575/1573, 8125/8019

			Sval mapping: {{mapping\| 3 3 -3 1 7 \| 0 1 6 4 0 }}

			Sval mapping (mingen): {{mapping\| 3 4 3 5 7 \| 0 1 6 4 0 }}

			Sval mapping generators: ~13/9, ~5/3

			Optimal tuning (CWE): ~13/9 = 1\3edt, ~5/3 = 878.361

			Supporting ETs: 39, 15, 24[-7], 54, 93, 63[-7, -11], 132, 102[-7, -11], 171[-5], 69[+7], 141[-5, -7, -11], 210[-5], 147[+7], 180[-5, -7, -11]

	~~Sval mapping~~: ~~{{mapping\| 3 4 3 5 7 \|~~ 0 ~~1 6 4 0 }}~~		Badness (Dirichlet): 0.588

	== External links ==		== External links ==

Dummy index: +data(2/3)

2025-01-25T07:25:33Z

+data(2/3)

← Older revision		Revision as of 07:25, 25 January 2025
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	=== Sirius III (b39 & b6, b39 & b45) ===		=== Sirius III (b39 & b6, b39 & b45) ===

	Subgroup: 3.5.7.13		[[Subgroup]]: 3.5.7.13

	Comma list: 3125/3087, 2197/2187		[[Comma list]]: 3125/3087, 2197/2187

	Sval mapping: {{mapping\| 3 3 3 7 \| 0 3 5 0 }}		[[Sval]] [[mapping]]: {{mapping\| 3 0 -2 7 \| 0 3 5 0 }}

			Sval mapping ([[mingen]]): {{mapping\| 3 3 3 7 \| 0 3 5 0 }}

			Sval mapping generators: ~13/9, ~325/189

			[[Optimal tuning]] ([[CWE]]): ~13/9 = 1\3edt, ~325/189 = 927.630

			[[Support]]ing [[ET]]s: 39, 6, 45, 84, 33, 123, 162, 51[+7], 72[-7], 27[-5, -7], 129[+7], 201, 207, 111[-5, -7]

			Badness (Dirichlet): 0.832

	==== 3.5.7.11.13 (also deneb III) ====		==== 3.5.7.11.13 (also deneb III) ====
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	Subgroup: 3.5.7.11.13		Subgroup: 3.5.7.11.13

	Comma list: ~~3125~~/~~3087~~, ~~6655~~/~~6561~~, ~~2197~~/~~2187~~		Comma list: 275/273, 1625/1617, 11011/10935

			Sval mapping: {{mapping\| 3 0 -2 8 7 \| 0 3 5 -1 0 }}

	Sval mapping: {{mapping\| 3 3 3 7 7 \| 0 3 5 -1 0 }}		Sval mapping (mingen): {{mapping\| 3 3 3 7 7 \| 0 3 5 -1 0 }}

			Sval mapping generators: ~13/9, ~77/45

			Optimal tuning (CWE): ~13/9 = 1\3edt, ~77/45 = 927.277

			Supporting ETs: 39, 6, 45, 84, 33, 123, 72[-7], 162[-11], 27[-5, -7], 111[-5, -7], 201[-11], 240[-5, -11], 150[-5, -7], 279[-5, -11]

			Badness (Dirichlet): 0.551

	=== Canopus III (b39 & b36, b39 & b75) ===		=== Canopus III (b39 & b36, b39 & b75) ===

	Subgroup: 3.5.7.13		[[Subgroup]]: 3.5.7.13

	Comma list: 16875/16807, 2197/2187		[[Comma list]]: 16875/16807, 2197/2187

	Sval mapping: {{mapping\| 3 4 5 7 \| 0 5 4 0 }}		[[Sval]] [[mapping]]: {{mapping\| 3 4 5 7 \| 0 5 4 0 }}

			Sval mapping generators: ~13/9, ~65/63

			[[Optimal tuning]] ([[CWE]]): ~13/9 = 1\3edt, ~65/63 = 49.865

			[[Support]]ing [[ET]]s: 39, 114, 75, 153, 36, 192, 42[-5], 267, 189, 231, 33[+5, +7], 111, 81[-5], 345

			Badness (Dirichlet): 0.564

	==== 3.5.7.11.13 Suhail ====		==== 3.5.7.11.13 Suhail ====
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	=== b9 & b6 ===		=== b9 & b6 ===

	Subgroup: 3.5.7.13		[[Subgroup]]: 3.5.7.13

			[[Comma list]]: 65/63, 675/637

			[[Sval]] [[mapping]]: {{mapping\| 3 3 4 7 \| 0 1 1 0 }}

			Sval mapping ([[mingen]]): {{mapping\| 3 4 5 7 \| 0 1 1 0 }}

			Sval mapping generators: ~7/5, ~5/3

			[[Optimal tuning]] ([[CWE]]): ~7/5 = 1\3edt, ~5/3 = 864.428

	~~Comma list~~: ~~375/343~~, ~~2197/2187~~		[[Support]]ing [[ET]]s: 9, 6, 15, 12[-5], 24, 21[+7], 33[+7]

	~~Sval mapping~~: ~~{{mapping\| 3 4 5 7 \|~~ 0 ~~1 1 0 }}~~		Badness (Dirichlet): 0.508

	== "Threedie family" start from 3.7.11.13 ==		== "Threedie family" start from 3.7.11.13 ==

Dummy index: +data(1/3)

2025-01-25T07:00:54Z

+data(1/3)

← Older revision		Revision as of 07:00, 25 January 2025
Line 12:		Line 12:
	[[Comma list]]: 245/243, 2197/2187		[[Comma list]]: 245/243, 2197/2187

	[[Sval]] [[mapping]]: {{mapping\| 3 5 5 7 \| 0 -2 1 0 }}		[[Sval]] [[mapping]]: {{mapping\| 3 1 7 7 \| 0 2 -1 0 }}

			Sval mapping ([[mingen]]): {{mapping\| 3 5 5 7 \| 0 -2 1 0 }}

			Sval mapping generators: ~13/9, ~13/7

			[[Optimal tuning]] ([[CWE]]): ~13/9 = 1\3edt, ~13/7 = 1074.663

			[[Support]]ing [[ET]]s: 39, 9, 30, 69, 21, 108, 48, 99, 12, 51, 147, 87, 57[-5], 129

			Badness (Dirichlet): 0.269

	==== 3.5.7.11.13 ====		==== 3.5.7.11.13 ====
			This tempers out threedie, DPC(5/3,9/7) and DPC(5:7:11).

	Subgroup: 3.5.7.11.13		Subgroup: 3.5.7.11.13

	Comma list: 245/243, ~~****~~, ~~2197~~/~~2187~~		Comma list: 245/243, 275/273, 9295/9261

	Sval mapping: {{mapping\| 3 5 5 5 7 \| 0 -2 1 5 0 }}		Sval mapping: {{mapping\| 3 1 7 15 7 \| 0 2 -1 -5 0 }}

			Sval mapping (mingen): {{mapping\| 3 5 5 5 7 \| 0 -2 1 5 0 }}

			Sval mapping generators: ~13/9, ~13/7

			Optimal tuning (CWE): ~13/9 = 1\3edt, ~13/7 = 1073.060

			Supporting ETs: 39, 9, 30, 48, 69[-11], 108[-11], 87, 21[-11], 147[-11], 126[-5], 99[-11], 186[-11], 165[-5], 225[-5, -7, -11]

			Badness (Dirichlet): 0.525

	==== strong extension 3.5.7.11.13 (b39 & b30e) ====		==== strong extension 3.5.7.11.13 (b39 & b30e) ====
Line 26:		Line 47:
	Subgroup: 3.5.7.11.13		Subgroup: 3.5.7.11.13

	Comma list: 245/243, ~~****~~, ~~2197~~/~~2187~~		Comma list: 245/243, 1625/1617, 1875/1859

			Sval mapping: {{mapping\| 3 1 7 -7 7 \| 0 2 -1 8 0 }}

			Sval mapping (mingen): {{mapping\| 3 5 5 9 7 \| 0 -2 1 -8 0 }}

			Sval mapping generators: ~13/9, ~13/7

			Optimal tuning (CWE): ~13/9 = 1\3edt, ~13/7 = 1073.481

			Supporting ETs: 39, 9[-11], 30[+11], 69, 108, 48[-11], 147, 87[-11], 186, 225[-5, -7], 126[-5, -11], 264[-5, -7], 165[-5, -11], 303[-5, -7]

	~~Sval mapping~~: ~~{{mapping\| 3 5 5 9 7 \|~~ 0 ~~-2 1 -8 0 }}~~		Badness (Dirichlet): 0.713

	==== weak extension 3.5.7.11.13 (b39 & b60) ====		==== weak extension 3.5.7.11.13 (b39 & b60) ====
Line 34:		Line 65:
	Subgroup: 3.5.7.11.13		Subgroup: 3.5.7.11.13

	Comma list: 245/243, ~~****~~, ~~2197~~/~~2187~~		Comma list: 245/243, 1575/1573, 847/845

	Sval mapping: {{mapping\| 3 5 5 7 7 \| 0 -4 2 -3 0 }}		Sval mapping: {{mapping\| 3 1 7 4 7 \| 0 4 -2 3 0 }}

			Sval mapping (mingen): {{mapping\| 3 5 5 7 7 \| 0 -4 2 -3 0 }}

			Sval mapping generators: ~13/9, ~15/11

			Optimal tuning (CWE): ~13/9 = 1\3edt, ~15/11 = 537.359

			Supporting ETs: 39, 21, 60, 99, 18, 138, 177[-7], 57[-5], 216[-7], 81, 159[-7], 96[-5, -11], 237[-7], 255[-5, -7, -11]

			Badness (Dirichlet): 0.447

	=== Sirius III (b39 & b6, b39 & b45) ===		=== Sirius III (b39 & b6, b39 & b45) ===
Line 64:		Line 105:

	==== 3.5.7.11.13 Suhail ====		==== 3.5.7.11.13 Suhail ====
	{{main\|~~No-twos subgroup temperaments #~~Suhail}}		{{main\|Suhail}}

	=== b9 & b6 ===		=== b9 & b6 ===
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	Sval mapping: {{mapping\| 3 4 3 5 7 \| 0 1 6 4 0 }}		Sval mapping: {{mapping\| 3 4 3 5 7 \| 0 1 6 4 0 }}

			== External links ==
			*[https://x31eq.com/pyscript/more.html?r=2&limit=3_5_7_13&error=6.2]
			*[https://x31eq.com/pyscript/more.html?r=2&limit=3_5_7_11_13&error=4.0]

	<!-- b30 & b6, b30 & b45, b9 & b45 -->		<!-- b30 & b6, b30 & b45, b9 & b45 -->
	{{stub}}		{{stub}}