Gentle region (extended version): Difference between revisions

Latest revision as of 15:16, 16 January 2025

This is an extended version of the Gentle region article.

Margo Schulter, in a tuning list posting, defined the "gentle region" of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp; later amending that to from 1.49 to 3.04 cents sharp.

Gentle-tempered tone systems are thus "mild" (or, as the name says, "gentle") versions of Superpyth temperament. They allow harmony in the style of medieval Pythagorean harmony, usable for "Neo-gothic" harmony systems; besides, they are possible temperament frameworks for middle-eastern (Arabic, Turkish, Persian) tuning systems, with the special property of delivering a common framework for both Arabic and Turkish music, differing in the degree of tempering. When the tempering of the fifth is "very gentle"/near-just, the interval notated as C-Fb in standard sheet notation (8 fifths down) will be close to a 5/4 major third, as used in Turkish music; while sharper tempering will give this interval the character of a neutral third, as important in Arabic music. (The interval notated as C-E will have the character of a larger Pythagorean—or super-Pythagorean—major third.)

We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of 29, 46, 75, 104, 109, 121, 145, 155, 162, 167, 179, 191, 201, 213, 225 and 237, plus 63 and 80 in the extended region.

Generator		Cents	2-3-7(b)-11-13(b)	Half 8/7+ 1\3 7/61\3 8/7+ Half 7/6	8/7+7/6	Notes
(7+10)\29		289.655+413.793	⟨29 46 81 100 107]	2\29+3\29 82.759+124.138	6\29+6\29 248.276+248.276
(25+36)\104		288.4615+415.385	⟨104 165 292 360 385]	5\52+23\312 115.385+88.4615 5\78+23\208 76.923+132.692	5\52+23\104 230.769+265.385
(18+26)\75		288+416		7\75+17\225 112+90.667 14\225+17\150 74.667+136	14\75+17\75 224+272
	(47+68)\196	287.755+416.3265		37\392+44\588 113.265+89.796 37/588+11/98 75.51+134.694	37/196+44/196 226.531+269.388
		287.713+416.382	⟨29 46 81 100 107] + ⟨46 73 129 159 170]φ	119.283+85.7795 79.522+128.769	238.566+257.3385
	(29+42)\121	287.603+416.529	⟨121 192 339~340 419 448]	23\242+9\121 114.05+89.256 23\363+27\242 76.033+133.884	23\121+27\121 228.099+267.769
		287.267+416.978	⟨29 46 81 100 107] + ⟨109 173 306 377 403]φ	116.8205+87.323 78.617+130.984	235.85+261.969
(11+16)\46		286.9565+417.391	⟨46 73 129 159 170]	9\92+5\69 117.391+86.9565 3\46+5\46 78.261+130.435	9\46+5\23 234.783+260.87
		286.587+417.884	⟨29 46 81 100 107] + ⟨63 100 177 218 233]φ	117.925+88.626 77.635+132.9395	232.936+265.879
	(48+70)\201	286.567+417.91	⟨201 319 564 695 703]	13\134+44\603 116.418+87.56 13\201+22\201 77.612+131.343	39\201+44\201 232.836+262.687
	(37+54)\155	286.452+418.0645	⟨155 246 435 536 573]	3\31+34\465 116.129+87.742 2\31+17\155 77.419+131.613	30\155+34\155 232.258+263.226
		286.387+418.151	⟨46 73 129 159 170] + ⟨109 173 306 377 403]φ	115.968+87.842 77.312+131.7365	231.935+263.527
	(63+92)\264	286.364+418.182	⟨264 419 741 913 976]	51\528+29\396 115.909+87.87 17\264+29\264 77.273+131.818	51\264+58\264 231.818+263.636
(26+38)\109		286.2385+418.349	⟨109 173 306 377 403]	21\218+8\109 115.596+88.07 7\109+12\109 77.064+132.11	21\109+24\109 231.192+264.22	Boundary of smaller "gentle region"
	(67+98)\281	286.121+418.505	⟨281 446 789 972 1039]	27\281+62\843 115.3025+88.256 18\281+31\281 76.868+132.384	54\281+62\281 230.605+264.769
		286.101+418.533	⟨46 73 129 159 170] + ⟨63 100 177 218 233]φ	116.526+89.264 77.684+133.8965	233.052+267.793
	(41+60)\172	286.0465+418.605	⟨172 273 483 595 636]	33\344+19\258 115.116+88.372 11\172+19\172 76.744+132.558	33\172+38\172 230.232+265.116
	(56+82)\235	285.957+418.723	⟨235 373 660 813 869]	9\94+52\705 114.894+81.511 3\47+26\235 76.596+132.766	9\47+52\235 229.787+265.532
		285.852+418.864	⟨109 173 306 377 403] + ⟨63 100 177 218 233]φ	114.963+88.4675 76.642+132.701	229.926+265.402
(15+22)\63		285.714+419.048	⟨63 100 177 218 233]	2\21+2\27 114.286+88.889 4\63+1\9 76.1905+133.333	4\21+2\9 228.571+266.667
		285.513+419.316	⟨46 73 129 159 170] + ⟨80 127 225 277 296]φ	113.7825+89.2075.855+133.80	227.565+267.606
	(49+72)\206	285.437+419.4175	⟨206 327 578~579 713 762]	10\103+15\206 116.505+87.37 20\309+45\412 77.67+131.068	20\103+45\206 233.01+262.136
(34+50)\143		285.315+419.58	⟨143 227 401~402 495 529]	14\143+31\429 117.4825+86.71 28\429+31\286 78.322+130.07	28\143+31\143 234.965+260.14
		285.234+419.688	⟨63 100 177 218 233] + ⟨80 127 225 277 296]φ	113.085+89.636 75.39+134.454	226.169+268.909
(54+78)\223		285.202+419.731	⟨223 354 626~627 771 825]	43\446+49\669 115.695+87.892 43\669+49\446 77.13+131.839	43\223+49\223 231.39+263.677
(19+28)\80		285+420	⟨80 127 225 277 296]	3\32+3\40 112.5+90 1\16+9\80 75+135	3\16+9\40 225+270	Boundary of larger "gentle region"
(4+6)\17		282.353+423.529	< 17 27 48 60 63\|	1\17+4\51 70.588+93.1765 3\34+1\17 105.882+70.588	3\17+4\17 211.765+282.353

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+''This is an extended version of the '''[[Gentle_region|Gentle region]] article.'''''
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-29 12:17:24 UTC</tt>.<br>
+-----
-: The original revision id was <tt>602895168</tt>.<br>
+[[Margo_Schulter|Margo Schulter]], in a [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105200.html#105202 tuning list posting], defined the "gentle region" of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp; later [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_106239.html#106239 amending that] to from 1.49 to 3.04 cents sharp.
-: The revision comment was: <tt></tt><br>
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
+Gentle-tempered tone systems are thus "mild" (or, as the name says, "gentle") versions of [[Superpyth]] temperament. They allow harmony in the style of medieval Pythagorean harmony, usable for "Neo-gothic" harmony systems; besides, they are possible temperament frameworks for [[Arabic, Turkish, Persian| middle-eastern (Arabic, Turkish, Persian)]] tuning systems, with the special property of delivering a common framework for both Arabic and Turkish music, differing in the degree of tempering. When the tempering of the fifth is "very gentle"/near-just, the interval notated as C-Fb in standard sheet notation (8 fifths down) will be close to a 5/4 major third, as used in Turkish music; while sharper tempering will give this interval the character of a neutral third, as important in Arabic music. (The interval notated as C-E will have the character of a larger Pythagorean—or super-Pythagorean—major third.)
-<h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">//This is an extended version of the **[[Gentle region]] article. **//
+We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of {{EDOs| 29, 46, 75, 104, 109, 121, 145, 155, 162, 167, 179, 191, 201, 213, 225 and 237, plus 63 and 80 }} in the extended region.
-----
-[[@Margo Schulter]], in a [[@http://launch.groups.yahoo.com/group/tuning/message/38721|tuning list posting]], defined the "gentle region" of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp; later [[@http://launch.groups.yahoo.com/group/tuning/message/105172|amending that]] to from 1.49 to 3.04 cents sharp. We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of [[@29edo]], [[@46edo]], [[@75edo]], [[@104edo]], [[@109edo]], [[@121edo]], [[@145edo|133edo]], [[@155edo]], [[@162edo]], [[@167edo]], [[@179edo]], [[@191edo]], [[@201edo]], [[@213edo]], [[@225edo]] and [[@237edo]], plus [[@63edo]] and [[@80edo]] in the extended region.
+{| class="wikitable"
+|-
+! colspan="2" | Generator
+! Cents
+! 2-3-7(b)-11-13(b)
+! <span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"><span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">Half 8/7+ 1\3 7/6<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">1\3 8/7+ Half 7/6</span></span></span>
+! 8/7+7/6
+! Notes
+|-
+| (7+10)\29
+|
+| style="text-align: center;" | 289.655+413.793
+| {{val| 29 46 81 100 107 }}
+| style="text-align: center;" | 2\29+3\29
+.759+124.138
+| style="text-align: center;" | 6\29+6\29
+.276+248.276
+|
+|-
+| (25+36)\104
+|
+| style="text-align: center;" | 288.4615+415.385
+| {{val| 104 165 292 360 385 }}
+| style="text-align: center;" | 5\52+''23\312''
+.385+''88.4615''
+<span style="background-color: rgba(255,255,255,0); text-align: start;">''5\78+23\208''</span>
+<span style="background-color: rgba(255,255,255,0); text-align: start;">''76.923+132.692''</span>
+| style="text-align: center;" | 5\52+23\104
+.769+265.385
+|
+|-
+| (18+26)\75
+|
+| style="text-align: center;" | 288+416
+| &lt; 75 119 210~211 259 277|
+| style="text-align: center;" | 7\75+''17\225''
++''90.667''
+<span style="background-color: rgba(255,255,255,0); text-align: start;">''14\225+17\150''</span>
+<span style="background-color: rgba(255,255,255,0); text-align: start;">''74.667+136''</span>
+| style="text-align: center;" | 14\75+17\75
++272
+|
+|-
+|
+| (47+68)\196
+| style="text-align: center;" | 287.755+416.3265
+| &lt; 196 311 549-551 678 725|
+| style="text-align: center;" | ''37\392+44\588''
+''113.265+89.796''
+<span style="background-color: rgba(255,255,255,0); text-align: start;">''37/588''+11/98</span>
+<span style="background-color: rgba(255,255,255,0); text-align: start;">''75.51''+134.694</span>
+| style="text-align: center;" | 37/196+44/196
+.531+269.388
+|
+|-
+|
+|
+| style="text-align: center;" | 287.713+416.382
+| {{val| 29 46 81 100 107 }} + {{val| 46 73 129 159 170 }}</span><span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small; line-height: 1.5;">φ</span>
+| style="text-align: center;" | 119.283+85.7795
+<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">79.522+128.769</span>
+| style="text-align: center;" | 238.566+257.3385
+|
+|-
+|
+| (29+42)\121
+| style="text-align: center;" | 287.603+416.529
+| {{val| 121 192 339~340 419 448 }}
+| style="text-align: center;" | ''23\242''+9\121
+''114.05''+89.256
+<span style="background-color: rgba(255,255,255,0);">''23\363+27\242''</span>
+<span style="background-color: rgba(255,255,255,0);">''76.033+133.884''</span>
+| style="text-align: center;" | 23\121+27\121
+.099+267.769
+|
+|-
+|
+|
+| style="text-align: center;" | 287.267+416.978
+| {{val| 29 46 81 100 107 }} + {{val| 109 173 306 377 403 }}<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span>
+| style="text-align: center;" | 116.8205+87.323
+<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">78.617+130.984</span>
+| style="text-align: center;" | 235.85+261.969
+|
+|-
+| (11+16)\46
+|
+| style="text-align: center;" | 286.9565+417.391
+| {{val| 46 73 129 159 170 }}
+| style="text-align: center;" | ''9\92+5\69''
+''117.391+86.9565''
+<span style="background-color: rgba(255,255,255,0);">3\46+5\46</span>
+<span style="background-color: rgba(255,255,255,0);">78.261+130.435</span>
+| style="text-align: center;" | 9\46+5\23
+.783+260.87
+|
+|-
+|
+|
+| style="text-align: center;" | 286.587+417.884
+| {{val| 29 46 81 100 107 }} + {{val| 63 100 177 218 233 }}<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span>
+| style="text-align: center;" | 117.925+88.626
+<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">77.635+132.9395</span>
+| style="text-align: center;" | 232.936+265.879
+|
+|-
+|
+| (48+70)\201
+| style="text-align: center;" | 286.567+417.91
+| {{val| 201 319 564 695 703 }}
+| style="text-align: center;" | ''13\134+44\603''
+''116.418+87.56''
+<span style="background-color: rgba(255,255,255,0);">13\201+22\201</span>
+<span style="background-color: rgba(255,255,255,0);">77.612+131.343</span>
+| style="text-align: center;" | 39\201+44\201
+.836+262.687
+|
+|-
+|
+| (37+54)\155
+| style="text-align: center;" | 286.452+418.0645
+| {{val| 155 246 435 536 573 }}
+| style="text-align: center;" | 3\31+''34\465''
+.129+''87.742''
+<span style="background-color: rgba(255,255,255,0);">2\31+17\155</span>
+<span style="background-color: rgba(255,255,255,0);">77.419+131.613</span>
+| style="text-align: center;" | 30\155+34\155
+.258+263.226
+|
+|-
+|
+|
+| style="text-align: center;" | 286.387+418.151
+| {{val| 46 73 129 159 170 }} + {{val| 109 173 306 377 403 }}<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span>
+| style="text-align: center;" | 115.968+87.842
+<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">77.312+131.7365</span>
+| style="text-align: center;" | 231.935+263.527
+|
+|-
+|
+| (63+92)\264
+| style="text-align: center;" | 286.364+418.182
+| {{val| 264 419 741 913 976 }}
+| style="text-align: center;" | ''51\528+29\396''
+''115.909+87.87''
+<span style="background-color: rgba(255,255,255,0);">17\264+29\264</span>
+<span style="background-color: rgba(255,255,255,0);">77.273+131.818</span>
+| style="text-align: center;" | 51\264+58\264
+.818+263.636
+|
+|-
+| (26+38)\109
+|
+| style="text-align: center;" | 286.2385+418.349
+| {{val| 109 173 306 377 403 }}
+| style="text-align: center;" | ''21\218''+8\109
+''115.596''+88.07
+<span style="background-color: rgba(255,255,255,0);">7\109+12\109</span>
+<span style="background-color: rgba(255,255,255,0);">77.064+132.11</span>
+| style="text-align: center;" | 21\109+24\109
+.192+264.22
+| Boundary of smaller "gentle region"
+|-
+|
+| (67+98)\281
+| style="text-align: center;" | 286.121+418.505
+| {{val| 281 446 789 972 1039 }}
+| style="text-align: center;" | 27\281+''62\843''
+.3025+''88.256''
+<span style="background-color: rgba(255,255,255,0);">18\281+31\281</span>
+<span style="background-color: rgba(255,255,255,0);">76.868+132.384</span>
+| style="text-align: center;" | 54\281+62\281
+.605+264.769
+|
+|-
+|
+|
+| style="text-align: center;" | 286.101+418.533
+| {{val| 46 73 129 159 170 }} + {{val| 63 100 177 218 233 }}<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span>
+| style="text-align: center;" | 116.526+89.264
+<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">77.684+133.8965</span>
+| style="text-align: center;" | 233.052+267.793
+|
+|-
+|
+| (41+60)\172
+| style="text-align: center;" | 286.0465+418.605
+| {{val| 172 273 483 595 636 }}
+| style="text-align: center;" | ''33\344+19\258''
+''115.116+88.372''
+<span style="background-color: rgba(255,255,255,0);">11\172+19\172</span>
+<span style="background-color: rgba(255,255,255,0);">76.744+132.558</span>
+| style="text-align: center;" | 33\172+38\172
+.232+265.116
+|
+|-
+|
+| (56+82)\235
+| style="text-align: center;" | 285.957+418.723
+| {{val| 235 373 660 813 869 }}
+| style="text-align: center;" | ''9\94+52\705''
-||||~ Geneator ||~ Cents ||~ 2-3-7(b)-11-13(b) ||||~ &lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;Half 8/7+ 1\3 7/6&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;1\3 8/7+ Half 7/6&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; ||~ 8/7+7/6 ||~   ||
-|| (7+10)\29 ||   ||= 289.655+413.793 || &lt; 29 46 81 100 107| ||||= 2\29+&lt;span style="line-height: 1.5;"&gt;3\29&lt;/span&gt;
-.759+124.138 ||= 6\29+6\29
-.276+248.276 ||   ||
-|| (25+36)\104 ||   ||= 288.4615+415.385 || &lt; 104 165 292 360 385| ||||= 10\104+23\312
-.385+88.4615
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;20\312+23\208&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;76.923+132.692&lt;/span&gt; ||= 20\104+23\104
-.769+265.385 ||   ||
-|| (18+26)\75 ||   ||= 288+416 || &lt; 7&lt;span style="line-height: 1.5;"&gt;5 119 210~211 259 277|&lt;/span&gt; ||||= 7\75+17\225
-+90.667
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;14\225+17\150&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;74.667+136&lt;/span&gt; ||= 14\75+17\75
-+272 ||   ||
-||   || (47+68)\196 ||= 287.755+416.3265 || &lt;&lt;span style="line-height: 1.5;"&gt; 196 311 549-551 678 725|&lt;/span&gt; ||||= 37\392+44\588
-.265+89.796
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;37/588+22/196&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;75.51+134.694&lt;/span&gt; ||= 37/196+44/196
-.531+269.388 ||   ||
-||   ||   ||= 287.713+416.382 || &lt; 29 46 81 100 107|+&lt; &lt;span style="line-height: 1.5;"&gt;46 73 129 159 170|&lt;/span&gt;&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small; line-height: 1.5;"&gt;φ&lt;/span&gt; ||||= 119.283+85.7795
-&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;79.522+128.769&lt;/span&gt; ||= 238.566+257.3385 ||   ||
-||   || (29+42)\121 ||= 287.603+416.529 || &lt; 121 192 339~340 419 448| ||||= 23\242+9\121
-.05+89.256
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;23\363+27\242&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;76.033+133.884&lt;/span&gt; ||= 23\121+27\121
-.099+267.769 ||   ||
-||   ||   ||= 287.267+416.978 || &lt; 29 46 81 100 107|+&lt; 109 173 306 377 403|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt; ||||= 116.8205+87.323
-&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;78.617+130.984&lt;/span&gt; ||= 235.85+261.969 ||   ||
-|| (11+16)\46 ||   ||= 286.9565+417.391 || &lt; 46 73 129 159 170| ||||= 9\92+10\138
-.391+86.9565
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;3\46+5\46&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;78.261+130.435&lt;/span&gt; ||= 9\46+10\46
-.783+260.87 ||   ||
-||   ||   ||= 286.587+417.884 || &lt; 29 46 81 100 107|+&lt;63 100 177 218 233|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt; ||||= 117.925+88.626
-&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;77.635+132.9395&lt;/span&gt; ||= 232.936+265.879 ||   ||
-||   || (48+70)\201 ||= 286.567+417.91 || &lt; 201 319 564 695 703| ||||= 39\402+44\603
-.418+87.56
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;13\201+22\201&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;77.612+131.343&lt;/span&gt; ||= 39\201+44\201
-.836+262.687 ||   ||
-||   || (37+54)\155 ||= 286.452+418.0645 || &lt; 155 246 435 536 573| ||||= 15\155+34\465
-.129+87.742
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;10\155+17\15&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;77.419+131.613&lt;/span&gt; ||= 30\155+34\155
-.258+263.226 ||   ||
-||   ||   ||= 286.387+418.151 || &lt; 46 73 129 159 170|+&lt; 109 173 306 377 403|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt; ||||= 115.968+87.842
-&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;77.312+131.7365&lt;/span&gt; ||= 231.935+263.527 ||   ||
-||   || (63+92)\264 ||= 286.364+418.182 || &lt; 264 419 741 913 976| ||||= 51\528+58\792
-.909+87.87
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;17\264+29\264&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;77.273+131.818&lt;/span&gt; ||= 51\264+58\264
-.818+263.636 ||   ||
-|| (26+38)\109 ||   ||= 286.2385+418.349 || &lt; 109 173 306 377 403| ||||= 21\218+8\109
-.596+88.07
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;7\109+12\10&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;77.064+132.11&lt;/span&gt; ||= 21\109+24\109
-.192+264.22 || Boundary of smaller "gentle region" ||
-||   || (67+98)\281 ||= 286.121+418.505 || &lt; 281 446 789 972 1039| ||||= 27\281+62\843
-.3025+88.256
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;18\281+31\28&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;76.868+132.384&lt;/span&gt; ||= 54\281+62\281
-.605+264.769 ||   ||
-||   ||   ||= 286.101+418.533 || &lt; 46 73 129 159 170|+&lt; 63 100 177 218 233|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt; ||||= 116.526+89.264
-&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;77.684+133.8965&lt;/span&gt; ||= 233.052+267.793 ||   ||
-||   || (41+60)\172 ||= 286.0465+418.605 || &lt; 172 273 483 595 636| ||||= 33\344+38\516
-.116+88.372
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;11\172+19\17&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;76.744+132.558&lt;/span&gt; ||= 33\172+38\172
-.232+265.116 ||   ||
-||   || (56+82)\235 ||= 285.957+418.723 || &lt; 235 373 660 813 869| ||||= 45\470+52\705
 .894+81.511
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;15\235+26\23&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;76.596+132.766&lt;/span&gt; ||= 45\235+52\235
+<span style="background-color: rgba(255,255,255,0);">3\47+26\235</span>
-.787+265.532 ||   ||
-||   ||   ||= 285.852+418.864 || &lt; &lt;span style="line-height: 1.5;"&gt;109 173 306 377 403|+&lt;/span&gt;&lt; 63 100 177 218 233|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt; ||||= 114.963+88.4675
+<span style="background-color: rgba(255,255,255,0);">76.596+132.766</span>
-&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;76.642+132.701&lt;/span&gt; ||= 229.926+265.402 ||   ||
+| style="text-align: center;" | 9\47+52\235
-|| &lt;span style="display: block; text-align: center;"&gt;(15+22)\63&lt;/span&gt; ||   ||= &lt;span style="display: block; text-align: center;"&gt;285.714+419.048&lt;/span&gt; || &lt; 63 100 177 218 233| ||||= 6\63+14\189
-.286+88.88
+.787+265.532
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;4\63+7\63&lt;/span&gt;
+|
-&lt;span style="text-align: start;"&gt;&lt;span style="background-color: rgba(255,255,255,0);"&gt;76.1905+133.333&lt;/span&gt;&lt;/span&gt; ||= 12\63+14\63
+|-
-.571+266.667 ||   ||
+|
-||   ||   ||= 285.513+419.316 || &lt; 46 73 129 159 170|+&lt; 80 127 225 277 296|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt; ||||= &lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;113.7825+89.20&lt;/span&gt;&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;&lt;span style="background-color: rgba(255,255,255,0);"&gt;75.855+133.80&lt;/span&gt;&lt;/span&gt;&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;
+|
-&lt;/span&gt; ||= 227.565+267.606 ||   ||
+| style="text-align: center;" | 285.852+418.864
-||   || &lt;span style="display: block; text-align: center;"&gt;(49+72)\206&lt;/span&gt; ||= &lt;span style="display: block; text-align: center;"&gt;285.437+419.4175&lt;/span&gt; || &lt; 206 327 578~579 713 762| ||||= 20\206+15\206
+| {{val| 109 173 306 377 403 }} + {{val| 63 100 177 218 233 }}<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span>
+| style="text-align: center;" | 114.963+88.4675
+<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">76.642+132.701</span>
+| style="text-align: center;" | 229.926+265.402
+|
+|-
+| <span style="display: block; text-align: center;">(15+22)\63</span>
+|
+| style="text-align: center;" | <span style="display: block; text-align: center;">285.714+419.048</span>
+| {{val| 63 100 177 218 233 }}
+| style="text-align: center;" | 2\21+''2\27''
+.286+''88.889''
+<span style="background-color: rgba(255,255,255,0);">4\63+1\9</span>
+<span style="background-color: rgba(255,255,255,0); text-align: start;">76.1905+133.333</span>
+| style="text-align: center;" | 4\21+2\9
+.571+266.667
+|
+|-
+|
+|
+| style="text-align: center;" | 285.513+419.316
+| {{val| 46 73 129 159 170 }} + {{val| 80 127 225 277 296 }}<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span>
+| style="text-align: center;" | <span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">113.7825+89.20</span><span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"><span style="background-color: rgba(255,255,255,0);">75.855+133.80</span></span><span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"></span>
+| style="text-align: center;" | 227.565+267.606
+|
+|-
+|
+| <span style="display: block; text-align: center;">(49+72)\206</span>
+| style="text-align: center;" | <span style="display: block; text-align: center;">285.437+419.4175</span>
+| {{val| 206 327 578~579 713 762 }}
+| style="text-align: center;" | 10\103+15\206
 .505+87.37
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;40\618+45\41&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;77.67+131.068&lt;/span&gt; ||= 40\206+45\206
+<span style="background-color: rgba(255,255,255,0);">''20\309+45\412''</span>
-.01+262.136 ||   ||
-|| &lt;span style="display: block; text-align: center;"&gt;(34+50)\143&lt;/span&gt; ||   ||= &lt;span style="display: block; text-align: center;"&gt;285.315+419.58&lt;/span&gt; || &lt; 143 227 401~402 495 529| ||||= 14\143+31\429
+<span style="background-color: rgba(255,255,255,0);">''77.67+131.068''</span>
+| style="text-align: center;" | 20\103+45\206
+.01+262.136
+|
+|-
+| <span style="display: block; text-align: center;">(34+50)\143</span>
+|
+| style="text-align: center;" | <span style="display: block; text-align: center;">285.315+419.58</span>
+| {{val| 143 227 401~402 495 529 }}
+| style="text-align: center;" | ''14\143+31\429''
 .4825+86.71
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;28\429+31\28&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;78.322+130.07&lt;/span&gt; ||= 28\143+31\143
+<span style="background-color: rgba(255,255,255,0);">''28\429+31\286''</span>
-.965+260.14 ||   ||
-||   ||   ||= 285.234+419.688 || &lt; 63 100 177 218 233|+&lt; 80 127 225 277 296|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt; ||||= 113.085+89.636
+<span style="background-color: rgba(255,255,255,0);">''78.322+130.07''</span>
-&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;75.39+134.454&lt;/span&gt; ||= 226.169+268.909 ||   ||
+| style="text-align: center;" | 28\143+31\143
-|| &lt;span style="display: block; text-align: center;"&gt;(54+78)\223&lt;/span&gt; ||   ||= &lt;span style="display: block; text-align: center;"&gt;285.202+419.731&lt;/span&gt; || &lt; 223 354 626~627 771 825| ||||= 43\446+49\669
+.965+260.14
+|
+|-
+|
+|
+| style="text-align: center;" | 285.234+419.688
+| {{val| 63 100 177 218 233 }} + {{val| 80 127 225 277 296 }}<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span>
+| style="text-align: center;" | 113.085+89.636
+<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">75.39+134.454</span>
+| style="text-align: center;" | 226.169+268.909
+|
+|-
+| <span style="display: block; text-align: center;">(54+78)\223</span>
+|
+| style="text-align: center;" |
+<span style="display: block; text-align: center;">285.202+419.731</span>
+| {{val| 223 354 626~627 771 825 }}
+| style="text-align: center;" | ''43\446+49\669''
 .695+87.892
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;43\669+49\44&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;77.13+131.839&lt;/span&gt; ||= 43\223+49\223
-.39+263.677 ||   ||
-|| &lt;span style="display: block; text-align: center;"&gt;(19+28)\80&lt;/span&gt; ||   ||= &lt;span style="display: block; text-align: center;"&gt;285+420&lt;/span&gt; || &lt; 80 127 225 277 296| ||||= 15\160+6\80
-.5+90
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;5\80+9\80&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;75+135&lt;/span&gt; ||= 15\80+18\80
-+270 || Boundary of larger "gentle region" ||</pre></div>
-<h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Gentle region (extended version)&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;This is an extended version of the &lt;strong&gt;&lt;a class="wiki_link" href="/Gentle%20region"&gt;Gentle region&lt;/a&gt; article. &lt;/strong&gt;&lt;/em&gt;&lt;br /&gt;
-&lt;hr /&gt;
-&lt;a class="wiki_link" href="/Margo%20Schulter" target="_blank"&gt;Margo Schulter&lt;/a&gt;, in a &lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/38721" rel="nofollow" target="_blank"&gt;tuning list posting&lt;/a&gt;, defined the &amp;quot;gentle region&amp;quot; of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp; later &lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/105172" rel="nofollow" target="_blank"&gt;amending that&lt;/a&gt; to from 1.49 to 3.04 cents sharp. We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of &lt;a class="wiki_link" href="/29edo" target="_blank"&gt;29edo&lt;/a&gt;, &lt;a class="wiki_link" href="/46edo" target="_blank"&gt;46edo&lt;/a&gt;, &lt;a class="wiki_link" href="/75edo" target="_blank"&gt;75edo&lt;/a&gt;, &lt;a class="wiki_link" href="/104edo" target="_blank"&gt;104edo&lt;/a&gt;, &lt;a class="wiki_link" href="/109edo" target="_blank"&gt;109edo&lt;/a&gt;, &lt;a class="wiki_link" href="/121edo" target="_blank"&gt;121edo&lt;/a&gt;, &lt;a class="wiki_link" href="/145edo" target="_blank"&gt;133edo&lt;/a&gt;, &lt;a class="wiki_link" href="/155edo" target="_blank"&gt;155edo&lt;/a&gt;, &lt;a class="wiki_link" href="/162edo" target="_blank"&gt;162edo&lt;/a&gt;, &lt;a class="wiki_link" href="/167edo" target="_blank"&gt;167edo&lt;/a&gt;, &lt;a class="wiki_link" href="/179edo" target="_blank"&gt;179edo&lt;/a&gt;, &lt;a class="wiki_link" href="/191edo" target="_blank"&gt;191edo&lt;/a&gt;, &lt;a class="wiki_link" href="/201edo" target="_blank"&gt;201edo&lt;/a&gt;, &lt;a class="wiki_link" href="/213edo" target="_blank"&gt;213edo&lt;/a&gt;, &lt;a class="wiki_link" href="/225edo" target="_blank"&gt;225edo&lt;/a&gt; and &lt;a class="wiki_link" href="/237edo" target="_blank"&gt;237edo&lt;/a&gt;, plus &lt;a class="wiki_link" href="/63edo" target="_blank"&gt;63edo&lt;/a&gt; and &lt;a class="wiki_link" href="/80edo" target="_blank"&gt;80edo&lt;/a&gt; in the extended region.&lt;br /&gt;
-&lt;br /&gt;
+<span style="background-color: rgba(255,255,255,0);">''43\669+49\446''</span>
+<span style="background-color: rgba(255,255,255,0);">''77.13+131.839''</span>
+| style="text-align: center;" | 43\223+49\223
+.39+263.677
+|
+|-
+| <span style="display: block; text-align: center;">(19+28)\80</span>
+|
+| style="text-align: center;" | <span style="display: block; text-align: center;">285+420</span>
+| {{val| 80 127 225 277 296 }}
+| style="text-align: center;" | ''3\32+3\40''
+''112.5+90''
+<span style="background-color: rgba(255,255,255,0);">1\16+9\80</span>
+<span style="background-color: rgba(255,255,255,0);">75+135</span>
+| style="text-align: center;" | 3\16+9\40
++270
+| Boundary of larger "gentle region"
+|-
+| style="text-align: center;" | (4+6)\17
+|
+| style="text-align: center;" | 282.353+423.529
+|<nowiki>< 17 27 48 60 63|</nowiki>
+| style="text-align: center;" | 1\17+''4\51''
+.588+''93.1765''
+''3\34''+1\17
-&lt;table class="wiki_table"&gt;
+''105.882''+70.588
-    &lt;tr&gt;
+| style="text-align: center;" | 3\17+4\17
-        &lt;th colspan="2"&gt;Geneator&lt;br /&gt;
+.765+282.353
-&lt;/th&gt;
+|
-        &lt;th&gt;Cents&lt;br /&gt;
+|}
-&lt;/th&gt;
-        &lt;th&gt;2-3-7(b)-11-13(b)&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th colspan="2"&gt;&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;Half 8/7+ 1\3 7/6&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;1\3 8/7+ Half 7/6&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;8/7+7/6&lt;br /&gt;
-&lt;/th&gt;
-        &lt;th&gt;&lt;br /&gt;
-&lt;/th&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;(7+10)\29&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;289.655+413.793&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&amp;lt; 29 46 81 100 107|&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td colspan="2" style="text-align: center;"&gt;2\29+&lt;span style="line-height: 1.5;"&gt;3\29&lt;/span&gt;&lt;br /&gt;
-.759+124.138&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;6\29+6\29&lt;br /&gt;
-.276+248.276&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;(25+36)\104&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;288.4615+415.385&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&amp;lt; 104 165 292 360 385|&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td colspan="2" style="text-align: center;"&gt;10\104+23\312&lt;br /&gt;
-.385+88.4615&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;20\312+23\208&lt;/span&gt;&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;76.923+132.692&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;20\104+23\104&lt;br /&gt;
-.769+265.385&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;(18+26)\75&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;288+416&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&amp;lt; 7&lt;span style="line-height: 1.5;"&gt;5 119 210~211 259 277|&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td colspan="2" style="text-align: center;"&gt;7\75+17\225&lt;br /&gt;
-+90.667&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;14\225+17\150&lt;/span&gt;&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0); text-align: start;"&gt;74.667+136&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;14\75+17\75&lt;br /&gt;
-+272&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;(47+68)\196&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;287.755+416.3265&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&amp;lt;&lt;span style="line-height: 1.5;"&gt; 196 311 549-551 678 725|&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td colspan="2" style="text-align: center;"&gt;37\392+44\588&lt;br /&gt;
-.265+89.796&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;37/196+44/196&lt;br /&gt;
-.531+269.388&lt;br /&gt;
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-        &lt;td&gt;&lt;br /&gt;
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-        &lt;td&gt;&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;287.713+416.382&lt;br /&gt;
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-        &lt;td&gt;&amp;lt; 29 46 81 100 107|+&amp;lt; &lt;span style="line-height: 1.5;"&gt;46 73 129 159 170|&lt;/span&gt;&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small; line-height: 1.5;"&gt;φ&lt;/span&gt;&lt;br /&gt;
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-        &lt;td colspan="2" style="text-align: center;"&gt;119.283+85.7795&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;238.566+257.3385&lt;br /&gt;
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-        &lt;td&gt;(29+42)\121&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;287.603+416.529&lt;br /&gt;
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-        &lt;td&gt;&amp;lt; 121 192 339~340 419 448|&lt;br /&gt;
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-        &lt;td colspan="2" style="text-align: center;"&gt;23\242+9\121&lt;br /&gt;
-.05+89.256&lt;br /&gt;
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-&lt;span style="background-color: rgba(255,255,255,0);"&gt;76.033+133.884&lt;/span&gt;&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;23\121+27\121&lt;br /&gt;
-.099+267.769&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;287.267+416.978&lt;br /&gt;
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-        &lt;td&gt;&amp;lt; 29 46 81 100 107|+&amp;lt; 109 173 306 377 403|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt;&lt;br /&gt;
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-        &lt;td colspan="2" style="text-align: center;"&gt;116.8205+87.323&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;235.85+261.969&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;286.9565+417.391&lt;br /&gt;
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-        &lt;td&gt;&amp;lt; 46 73 129 159 170|&lt;br /&gt;
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-&lt;span style="background-color: rgba(255,255,255,0);"&gt;78.261+130.435&lt;/span&gt;&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;9\46+10\46&lt;br /&gt;
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-        &lt;td&gt;&amp;lt; 29 46 81 100 107|+&amp;lt;63 100 177 218 233|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt;&lt;br /&gt;
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-        &lt;td&gt;(48+70)\201&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;286.567+417.91&lt;br /&gt;
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-        &lt;td&gt;&amp;lt; 201 319 564 695 703|&lt;br /&gt;
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-&lt;span style="background-color: rgba(255,255,255,0);"&gt;77.612+131.343&lt;/span&gt;&lt;br /&gt;
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-        &lt;td&gt;(37+54)\155&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;286.452+418.0645&lt;br /&gt;
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-        &lt;td&gt;&amp;lt; 155 246 435 536 573|&lt;br /&gt;
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-.129+87.742&lt;br /&gt;
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-.258+263.226&lt;br /&gt;
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-        &lt;td colspan="2" style="text-align: center;"&gt;115.968+87.842&lt;br /&gt;
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-        &lt;td&gt;(63+92)\264&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;286.364+418.182&lt;br /&gt;
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-        &lt;td&gt;&amp;lt; 264 419 741 913 976|&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;286.0465+418.605&lt;br /&gt;
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-        &lt;td&gt;&amp;lt; 172 273 483 595 636|&lt;br /&gt;
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-        &lt;td&gt;(56+82)\235&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;285.957+418.723&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;45\235+52\235&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;229.926+265.402&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;285.714+419.048&lt;/span&gt;&lt;br /&gt;
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-        &lt;td&gt;&amp;lt; 63 100 177 218 233|&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;12\63+14\63&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;285.513+419.316&lt;br /&gt;
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-        &lt;td&gt;&amp;lt; 46 73 129 159 170|+&amp;lt; 80 127 225 277 296|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt;&lt;br /&gt;
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-        &lt;td colspan="2" style="text-align: center;"&gt;&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;113.7825+89.20&lt;/span&gt;&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;&lt;span style="background-color: rgba(255,255,255,0);"&gt;75.855+133.80&lt;/span&gt;&lt;/span&gt;&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;285.437+419.4175&lt;/span&gt;&lt;br /&gt;
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-&lt;span style="background-color: rgba(255,255,255,0);"&gt;40\618+45\41&lt;/span&gt;&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;40\206+45\206&lt;br /&gt;
-.01+262.136&lt;br /&gt;
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-        &lt;td&gt;&lt;br /&gt;
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-    &lt;tr&gt;
-        &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;(34+50)\143&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;285.315+419.58&lt;/span&gt;&lt;br /&gt;
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-        &lt;td&gt;&amp;lt; 143 227 401~402 495 529|&lt;br /&gt;
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-        &lt;td colspan="2" style="text-align: center;"&gt;14\143+31\429&lt;br /&gt;
-.4825+86.71&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;28\429+31\28&lt;/span&gt;&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;78.322+130.07&lt;/span&gt;&lt;br /&gt;
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-        &lt;td style="text-align: center;"&gt;28\143+31\143&lt;br /&gt;
-.965+260.14&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
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-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;285.234+419.688&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&amp;lt; 63 100 177 218 233|+&amp;lt; 80 127 225 277 296|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td colspan="2" style="text-align: center;"&gt;113.085+89.636&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"&gt;75.39+134.454&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;226.169+268.909&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;(54+78)\223&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;285.202+419.731&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&amp;lt; 223 354 626~627 771 825|&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td colspan="2" style="text-align: center;"&gt;43\446+49\669&lt;br /&gt;
-.695+87.892&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;43\669+49\44&lt;/span&gt;&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;77.13+131.839&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;43\223+49\223&lt;br /&gt;
-.39+263.677&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;(19+28)\80&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;285+420&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&amp;lt; 80 127 225 277 296|&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td colspan="2" style="text-align: center;"&gt;15\160+6\80&lt;br /&gt;
-.5+90&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;5\80+9\80&lt;/span&gt;&lt;br /&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;75+135&lt;/span&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;15\80+18\80&lt;br /&gt;
-+270&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Boundary of larger &amp;quot;gentle region&amp;quot;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-&lt;/table&gt;
-&lt;/body&gt;&lt;/html&gt;</pre></div>
+[[Category:Gentle]]
+[[Category:Interval region]]
+[[Category:Tables]]

Gentle region (extended version): Difference between revisions

Latest revision as of 15:16, 16 January 2025

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