Sensi - Revision history

Inthar: /* Patent vals */

2026-04-14T14:08:43Z

Patent vals

← Older revision		Revision as of 14:08, 14 April 2026
Line 109:		Line 109:
	The following patent vals support 2.3.5.7 Sensi. Vals contorted in the 7-limit are not included.		The following patent vals support 2.3.5.7 Sensi. Vals contorted in the 7-limit are not included.
	{\| class="wikitable sortable"		{\| class="wikitable sortable"
	!\|Edo!!13 extension!!Generator!!3/2 tuning!!5/4 tuning!!13/8 tuning		!\|Edo!!13 extension!!Generator!!3/2 tuning!!5/4 tuning!!7/4 tuning!!13/8 tuning
	\|-		\|-
	\|\|19\|\|19 & 27\|\|442.105\|\|694.737\|\|378.947\|\|947.368\|\|821.053		\|\|19\|\|19 & 27\|\|442.105\|\|694.737\|\|378.947\|\|947.368\|\|821.053

Inthar: /* Patent vals */

2026-04-14T14:08:32Z

Patent vals

← Older revision		Revision as of 14:08, 14 April 2026
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	== Patent vals ==		== Patent vals ==
	The following patent vals support 2.3.5.7 Sensi. Vals contorted in the 7-limit are not included.		The following patent vals support 2.3.5.7 Sensi. Vals contorted in the 7-limit are not included.
	{ class="wikitable sortable"		{\| class="wikitable sortable"
	!\|Edo!!13 extension!!Generator!!3/2 tuning!!5/4 tuning!!13/8 tuning		!\|Edo!!13 extension!!Generator!!3/2 tuning!!5/4 tuning!!13/8 tuning
	\|-		\|-

Inthar at 14:08, 14 April 2026

2026-04-14T14:08:17Z

← Older revision		Revision as of 14:08, 14 April 2026
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	}}		}}

	'''Sensi''', 19 & 27, is a rank-2 temperament generated by a sharpened 9/7 such that two of them are equated to 5/3. Distinctly from other sensamagic temperaments, 3/2 is also found at 7 generators, or equivalently the octave is found at 125/63. It is most accurately extended to add prime 31 (by equating the generator with 31/24), but less accurately prime 13 is canonically added (by equating the generator with 13/10).		'''Sensi''', 2.3.5.7[{{e\|19}} & {{e\|27}}], is a rank-2 temperament generated by a sharpened 9/7 such that two of them are equated to 5/3. Distinctly from other sensamagic temperaments, 3/2 is also found at 7 generators, or equivalently the octave is found at 125/63. It is most accurately extended to add prime 31 (by equating the generator with 31/24), but less accurately prime 13 is canonically added (by equating the generator with 13/10).

	== Interval chain ==		== Interval chain ==
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	\|}		\|}
	<nowiki/>* In 2.3.5.7.13 CWE tuning		<nowiki/>* In 2.3.5.7.13 CWE tuning
			== Patent vals ==
			The following patent vals support 2.3.5.7 Sensi. Vals contorted in the 7-limit are not included.
			{ class="wikitable sortable"
			!\|Edo!!13 extension!!Generator!!3/2 tuning!!5/4 tuning!!13/8 tuning
			\|-
			\|\|19\|\|19 & 27\|\|442.105\|\|694.737\|\|378.947\|\|947.368\|\|821.053
			\|-
			\|\|65\|\|\|\|443.077\|\|701.538\|\|387.692\|\|960.000\|\|849.231
			\|-
			\|\|46\|\|19 & 27\|\|443.478\|\|704.348\|\|391.304\|\|965.217\|\|834.783
			\|-
			\|\|73\|\|19 & 27\|\|443.836\|\|706.849\|\|394.521\|\|969.863\|\|838.356
			\|-
			\|\|27\|\|19 & 27\|\|444.444\|\|711.111\|\|400.000\|\|977.778\|\|844.444
			\|}
	{{Navbox regtemp}}		{{Navbox regtemp}}
	{{Cat\|temperaments}}		{{Cat\|temperaments}}

Vector at 07:01, 14 March 2026

2026-03-14T07:01:52Z

← Older revision		Revision as of 07:01, 14 March 2026
Line 10:		Line 10:
	}}		}}

	'''Sensi''', 19 & 27, is a rank-2 temperament generated by a sharpened 9/7 such that two of them are equated to 5/3. It is most accurately extended to add prime 31 (by equating the generator with 31/24), but less accurately prime 13 is canonically added (by equating the generator with 13/10).		'''Sensi''', 19 & 27, is a rank-2 temperament generated by a sharpened 9/7 such that two of them are equated to 5/3. Distinctly from other sensamagic temperaments, 3/2 is also found at 7 generators, or equivalently the octave is found at 125/63. It is most accurately extended to add prime 31 (by equating the generator with 31/24), but less accurately prime 13 is canonically added (by equating the generator with 13/10).

	== Interval chain ==		== Interval chain ==

Inthar at 05:19, 7 March 2026

2026-03-07T05:19:02Z

← Older revision		Revision as of 05:19, 7 March 2026
Line 10:		Line 10:
	}}		}}

	'''Sensi''', 19 & 27, is a rank-2 temperament generated by a sharpened 9/7 such that two of them are equated to 5/3. It is most accurately extended to add 31 (by equating the generator with 31/24), but less accurately 13 is canonically added (by equating the generator with 13/10).		'''Sensi''', 19 & 27, is a rank-2 temperament generated by a sharpened 9/7 such that two of them are equated to 5/3. It is most accurately extended to add prime 31 (by equating the generator with 31/24), but less accurately prime 13 is canonically added (by equating the generator with 13/10).

	== Interval chain ==		== Interval chain ==

Inthar at 05:17, 7 March 2026

2026-03-07T05:17:35Z

← Older revision		Revision as of 05:17, 7 March 2026
Line 10:		Line 10:
	}}		}}

	'''Sensi''', 19 & 27, is a rank-2 temperament generated by a sharpened 9/7 such that two of them are equated to 5/3. It is most accurately extended to add 31 (by equating the generator with 31/24) ~~and~~ less accurately 13 (by equating the generator with 13/10).		'''Sensi''', 19 & 27, is a rank-2 temperament generated by a sharpened 9/7 such that two of them are equated to 5/3. It is most accurately extended to add 31 (by equating the generator with 31/24), but less accurately 13 is canonically added (by equating the generator with 13/10).

	== Interval chain ==		== Interval chain ==

Inthar: /* Interval chain */

2026-03-07T05:11:59Z

Interval chain

← Older revision		Revision as of 05:11, 7 March 2026
Line 12:		Line 12:
	'''Sensi''', 19 & 27, is a rank-2 temperament generated by a sharpened 9/7 such that two of them are equated to 5/3. It is most accurately extended to add 31 (by equating the generator with 31/24) and less accurately 13 (by equating the generator with 13/10).		'''Sensi''', 19 & 27, is a rank-2 temperament generated by a sharpened 9/7 such that two of them are equated to 5/3. It is most accurately extended to add 31 (by equating the generator with 31/24) and less accurately 13 (by equating the generator with 13/10).

	=== Interval chain ===		== Interval chain ==
	In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''.		In the following table, odd harmonics and subharmonics 1–21 are in '''bold'''.

Inthar at 05:11, 7 March 2026

2026-03-07T05:11:41Z

@@ Line 10: / Line 10: @@
 }}
-'''Sensi''' is a rank-2 temperament generated by a sharpened 9/7 such that two of them are equated to 5/3. It is most accurately extended to add 31 (by equating the generator with 31/24) and less accurately 13 (by equating the generator with 13/10).
+'''Sensi''', 19 & 27, is a rank-2 temperament generated by a sharpened 9/7 such that two of them are equated to 5/3. It is most accurately extended to add 31 (by equating the generator with 31/24) and less accurately 13 (by equating the generator with 13/10).
 {{Navbox regtemp}}
 {{Cat|temperaments}}

Inthar at 05:09, 7 March 2026

2026-03-07T05:09:45Z

← Older revision		Revision as of 05:09, 7 March 2026
Line 10:		Line 10:
	}}		}}

	'''Sensi''' is a rank-2 temperament generated by a sharpened 9/7 such that two of them are equated to 5/3.		'''Sensi''' is a rank-2 temperament generated by a sharpened 9/7 such that two of them are equated to 5/3. It is most accurately extended to add 31 (by equating the generator with 31/24) and less accurately 13 (by equating the generator with 13/10).
	{{Navbox regtemp}}		{{Navbox regtemp}}
	{{Cat\|temperaments}}		{{Cat\|temperaments}}

Inthar at 05:06, 7 March 2026

2026-03-07T05:06:30Z

← Older revision		Revision as of 05:06, 7 March 2026
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	{{Infobox regtemp		{{Infobox regtemp
	\| Title = Sensi		\| Title = Sensi
	\| Subgroups = 2.3.5.7~~, 2.3.5.7.13~~		\| Subgroups = 2.3.5.7
	\| Comma basis = [[126/125]], [[245/243]] (7-limit~~); <br>[[91/90]], [[126/125]], [[169/168]] (2.3.5.7.13~~)		\| Comma basis = [[126/125]], [[245/243]] (7-limit)
	\| Edo join 1 = 19 \| Edo join 2 = 27		\| Edo join 1 = 19 \| Edo join 2 = 27
	\| Mapping = 1; 7 9 13 10		\| Mapping = 1; 7 9 13
	\| Generators = 9/7 \| Generators tuning = 443.3 \| Optimization method = CWE		\| Generators = 9/7 \| Generators tuning = 443.3 \| Optimization method = CWE
	\| MOS scales = [[3L 2s]], [[3L 5s]], [[8L 3s]], [[8L 11s]]		\| MOS scales = [[3L 2s]], [[3L 5s]], [[8L 3s]], [[8L 11s]]
	\| Odd limit 1 = 7 \| Mistuning 1 = 7.5 \| Complexity 1 = 19		\| Odd limit 1 = 7 \| Mistuning 1 = 7.5 \| Complexity 1 = 19
	~~\| Odd limit 2 = 2.3.5.7.13 21 \| Mistuning 2 = 11.1 \| Complexity 2 = 27~~
	}}		}}

			'''Sensi''' is a rank-2 temperament generated by a sharpened 9/7 such that two of them are equated to 5/3.
	{{Navbox regtemp}}		{{Navbox regtemp}}
	{{Cat\|temperaments}}		{{Cat\|temperaments}}