Gentle region: Difference between revisions

Revision as of 15:28, 30 October 2015

IMPORTED REVISION FROM WIKISPACES

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This revision was by author JosephRuhf and made on 2015-10-30 15:28:09 UTC.

The original revision id was 564511617.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

[[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.

|| 17\29 ||   ||   || 703.448 || < 29 46 81| ||= 2\29
82.759 ||= 3\29
124.138 ||||= 6\29
248.276 ||   ||
||   || 61\104 ||   || 703.846 || < 104 165 292| ||= 20\312
76.923 ||= 33\208
132.692 ||= 20\104 (5\26)
230.769 ||= 33\104
265.385 ||   ||
||   || 44\75 ||   || 704 || < 7<span style="line-height: 1.5;">5 119 211|</span> ||= 14\225
74.667 ||= 17\150
136 ||= 14\75
224 ||= 17\75
272 ||   ||
||   ||   ||   || 704.0585 || < 17 27 48|*pi+<span style="background-color: #ffffff;">< 24 38 67|</span> ||= 69.372 ||= 143.912 ||= 208.117 ||= 287.824 ||   ||
||   ||   || 115\196 || 704.082 || <<span style="line-height: 1.5;"> 196 311 551|</span> ||= 37/588
75.51 ||= 22/196 (11/98)
134.694 ||= 37/196
226.531 ||= 44/196 (11/49)
269.388 ||   ||
||   ||   ||   || 704.095 || < 17 27 48|<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span><span style="line-height: 1.5;">+</span>
<span style="background-color: #ffffff;">< 12 19 34|</span> ||= 69.397 ||= 143.857 ||= 208.191 ||= 287.731 ||   ||
||   || 71\121 ||   || 704.132 || < 121 192 340| ||= 23\363
76.033 ||= 27\242
133.884 ||= 23\121
228.099 ||= 27\121
267.769 ||   ||
|| 27\46 ||   ||   || 704.348 || < 46 73 129| ||= 3\46
78.261 ||= 5\46
130.435 ||= 9\46
234.783 ||= 10\46 (5\23)
260.87 ||   ||
||   ||   ||   || 704.426 || < 29 46 81|+
< 109 173 306|
<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span> ||= 77.868 ||= 130.984 ||= 233.605 ||= 261.969 ||   ||
||   || 118\201 ||   || 704.478 || < 201 319 564| ||= 13\201
77.612 ||= 22\201
131.343 ||= 39\201 (13\67)
232.836 ||= 44\201
262.687 ||   ||
||   || 91\155 ||   || 704.516 || < 155 246 435| ||= 10\155 (2\31)
77.419 ||= 17\155
131.613 ||= 30\155 (6\31)
232.258 ||= 34\155
263.226 ||   ||
||   ||   ||   ||   || < 17 27 48|<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span>+
<span style="background-color: #ffffff;">< 29 46 81|</span> ||   ||   ||   ||   ||   ||
||   || 155\264 ||   || 704.5455 || < 264 419 741| ||= 17\264
77.273 ||= 29\264
131.818 ||= 51\264 (17\88)
231.818 ||= 58\264 (29\132)
263.636 ||   ||
|| 64\109 ||   ||   || 704.587 || < 109 173 306| ||= 7\109
77.064 ||= 12\109
132.11 ||= 21\109
231.192 ||= 24\109
264.22 || Boundary of smaller "gentle region" ||
||   || 165\281 ||   || 704.626 || < 281 446 789| ||= 18\281
76.868 ||= 31\281
132.384 ||= 54\281
230.605 ||= 62\281
264.769 ||   ||
||   || 101\172 ||   || 704.651 || < 172 273 483| ||= 11\172
76.744 ||= 19\172
132.558 ||= 33\172
230.232 ||= 38\172 (19\86)
265.116 ||   ||
||   || 138\235 ||   || 704.681 || < 235 373 660| ||= 15\235 (3\47)
76.596 ||= 26\235
132.766 ||= 45\235 (9/45)
229.787 ||= 52\235
265.532 ||   ||
||   ||   ||   || 704.716 || < 80 127 225|
+
< 109 173 306|
<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span> ||= 76.42 ||= 133.012 ||= 229.26 ||= 266.024 ||   ||
|| 37\63 ||   ||   || 704.762 || < 63 100 177| ||= 4\63
76.1905 ||= 7\63 (1\9)
133.333 ||= 12\63 (4\21)
228.571 ||= 14\63 (2\9)
266.667 ||   ||
||   || 121\206 ||   || 704.854 || < 206 327 578| ||= 40\618 (20\309)
77.67 ||= 45\412
131.068 ||= 40\206 (20\103)
233.01 ||= 45\206
262.136 ||   ||
||   || 84\143 ||   || 704.895 || < 143 227 401| ||= 28\429
78.322 ||= 31\286
130.07 ||= 28\143
234.965 ||= 31\143
260.14 ||   ||
||   || 131\223 ||   || 704.933 || < 223 354 626| ||= 43\669
77.13 ||= 49\446
131.839 ||= 43\223
231.39 ||= 49\223
263.667 ||   ||
|| 47\80 ||   ||   || 705 || < 80 127 225| ||= 5\80 (1\16)
75 ||= 9\80
135 ||= 15\80 (3\16)
225 ||= 18\80 (9\40)
270 || Boundary of larger "gentle region" ||

Original HTML content:

<html><head><title>Gentle region</title></head><body><a class="wiki_link" href="/Margo%20Schulter">Margo Schulter</a>, in a <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/38721" rel="nofollow">tuning list posting</a>, defined the &quot;gentle region&quot; of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp; later <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/105172" rel="nofollow">amending that</a> 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 <a class="wiki_link" href="/29edo">29edo</a>, <a class="wiki_link" href="/46edo">46edo</a>, <a class="wiki_link" href="/75edo">75edo</a>, <a class="wiki_link" href="/104edo">104edo</a>, <a class="wiki_link" href="/109edo">109edo</a>, <a class="wiki_link" href="/121edo">121edo</a>, <a class="wiki_link" href="/145edo">133edo</a>, <a class="wiki_link" href="/155edo">155edo</a>, <a class="wiki_link" href="/162edo">162edo</a>, <a class="wiki_link" href="/167edo">167edo</a>, <a class="wiki_link" href="/179edo">179edo</a>, <a class="wiki_link" href="/191edo">191edo</a>, <a class="wiki_link" href="/201edo">201edo</a>, <a class="wiki_link" href="/213edo">213edo</a>, <a class="wiki_link" href="/225edo">225edo</a> and <a class="wiki_link" href="/237edo">237edo</a>, plus <a class="wiki_link" href="/63edo">63edo</a> and <a class="wiki_link" href="/80edo">80edo</a> in the extended region.<br />
<br />


<table class="wiki_table">
    <tr>
        <td>17\29<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>703.448<br />
</td>
        <td>&lt; 29 46 81|<br />
</td>
        <td style="text-align: center;">2\29<br />
82.759<br />
</td>
        <td style="text-align: center;">3\29<br />
124.138<br />
</td>
        <td colspan="2" style="text-align: center;">6\29<br />
248.276<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>61\104<br />
</td>
        <td><br />
</td>
        <td>703.846<br />
</td>
        <td>&lt; 104 165 292|<br />
</td>
        <td style="text-align: center;">20\312<br />
76.923<br />
</td>
        <td style="text-align: center;">33\208<br />
132.692<br />
</td>
        <td style="text-align: center;">20\104 (5\26)<br />
230.769<br />
</td>
        <td style="text-align: center;">33\104<br />
265.385<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>44\75<br />
</td>
        <td><br />
</td>
        <td>704<br />
</td>
        <td>&lt; 7<span style="line-height: 1.5;">5 119 211|</span><br />
</td>
        <td style="text-align: center;">14\225<br />
74.667<br />
</td>
        <td style="text-align: center;">17\150<br />
136<br />
</td>
        <td style="text-align: center;">14\75<br />
224<br />
</td>
        <td style="text-align: center;">17\75<br />
272<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>704.0585<br />
</td>
        <td>&lt; 17 27 48|*pi+<span style="background-color: #ffffff;">&lt; 24 38 67|</span><br />
</td>
        <td style="text-align: center;">69.372<br />
</td>
        <td style="text-align: center;">143.912<br />
</td>
        <td style="text-align: center;">208.117<br />
</td>
        <td style="text-align: center;">287.824<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>115\196<br />
</td>
        <td>704.082<br />
</td>
        <td>&lt;<span style="line-height: 1.5;"> 196 311 551|</span><br />
</td>
        <td style="text-align: center;">37/588<br />
75.51<br />
</td>
        <td style="text-align: center;">22/196 (11/98)<br />
134.694<br />
</td>
        <td style="text-align: center;">37/196<br />
226.531<br />
</td>
        <td style="text-align: center;">44/196 (11/49)<br />
269.388<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>704.095<br />
</td>
        <td>&lt; 17 27 48|<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span><span style="line-height: 1.5;">+</span><br />
<span style="background-color: #ffffff;">&lt; 12 19 34|</span><br />
</td>
        <td style="text-align: center;">69.397<br />
</td>
        <td style="text-align: center;">143.857<br />
</td>
        <td style="text-align: center;">208.191<br />
</td>
        <td style="text-align: center;">287.731<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>71\121<br />
</td>
        <td><br />
</td>
        <td>704.132<br />
</td>
        <td>&lt; 121 192 340|<br />
</td>
        <td style="text-align: center;">23\363<br />
76.033<br />
</td>
        <td style="text-align: center;">27\242<br />
133.884<br />
</td>
        <td style="text-align: center;">23\121<br />
228.099<br />
</td>
        <td style="text-align: center;">27\121<br />
267.769<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>27\46<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>704.348<br />
</td>
        <td>&lt; 46 73 129|<br />
</td>
        <td style="text-align: center;">3\46<br />
78.261<br />
</td>
        <td style="text-align: center;">5\46<br />
130.435<br />
</td>
        <td style="text-align: center;">9\46<br />
234.783<br />
</td>
        <td style="text-align: center;">10\46 (5\23)<br />
260.87<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>704.426<br />
</td>
        <td>&lt; 29 46 81|+<br />
&lt; 109 173 306|<br />
<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span><br />
</td>
        <td style="text-align: center;">77.868<br />
</td>
        <td style="text-align: center;">130.984<br />
</td>
        <td style="text-align: center;">233.605<br />
</td>
        <td style="text-align: center;">261.969<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>118\201<br />
</td>
        <td><br />
</td>
        <td>704.478<br />
</td>
        <td>&lt; 201 319 564|<br />
</td>
        <td style="text-align: center;">13\201<br />
77.612<br />
</td>
        <td style="text-align: center;">22\201<br />
131.343<br />
</td>
        <td style="text-align: center;">39\201 (13\67)<br />
232.836<br />
</td>
        <td style="text-align: center;">44\201<br />
262.687<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>91\155<br />
</td>
        <td><br />
</td>
        <td>704.516<br />
</td>
        <td>&lt; 155 246 435|<br />
</td>
        <td style="text-align: center;">10\155 (2\31)<br />
77.419<br />
</td>
        <td style="text-align: center;">17\155<br />
131.613<br />
</td>
        <td style="text-align: center;">30\155 (6\31)<br />
232.258<br />
</td>
        <td style="text-align: center;">34\155<br />
263.226<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>&lt; 17 27 48|<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span>+<br />
<span style="background-color: #ffffff;">&lt; 29 46 81|</span><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>155\264<br />
</td>
        <td><br />
</td>
        <td>704.5455<br />
</td>
        <td>&lt; 264 419 741|<br />
</td>
        <td style="text-align: center;">17\264<br />
77.273<br />
</td>
        <td style="text-align: center;">29\264<br />
131.818<br />
</td>
        <td style="text-align: center;">51\264 (17\88)<br />
231.818<br />
</td>
        <td style="text-align: center;">58\264 (29\132)<br />
263.636<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>64\109<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>704.587<br />
</td>
        <td>&lt; 109 173 306|<br />
</td>
        <td style="text-align: center;">7\109<br />
77.064<br />
</td>
        <td style="text-align: center;">12\109<br />
132.11<br />
</td>
        <td style="text-align: center;">21\109<br />
231.192<br />
</td>
        <td style="text-align: center;">24\109<br />
264.22<br />
</td>
        <td>Boundary of smaller &quot;gentle region&quot;<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>165\281<br />
</td>
        <td><br />
</td>
        <td>704.626<br />
</td>
        <td>&lt; 281 446 789|<br />
</td>
        <td style="text-align: center;">18\281<br />
76.868<br />
</td>
        <td style="text-align: center;">31\281<br />
132.384<br />
</td>
        <td style="text-align: center;">54\281<br />
230.605<br />
</td>
        <td style="text-align: center;">62\281<br />
264.769<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>101\172<br />
</td>
        <td><br />
</td>
        <td>704.651<br />
</td>
        <td>&lt; 172 273 483|<br />
</td>
        <td style="text-align: center;">11\172<br />
76.744<br />
</td>
        <td style="text-align: center;">19\172<br />
132.558<br />
</td>
        <td style="text-align: center;">33\172<br />
230.232<br />
</td>
        <td style="text-align: center;">38\172 (19\86)<br />
265.116<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>138\235<br />
</td>
        <td><br />
</td>
        <td>704.681<br />
</td>
        <td>&lt; 235 373 660|<br />
</td>
        <td style="text-align: center;">15\235 (3\47)<br />
76.596<br />
</td>
        <td style="text-align: center;">26\235<br />
132.766<br />
</td>
        <td style="text-align: center;">45\235 (9/45)<br />
229.787<br />
</td>
        <td style="text-align: center;">52\235<br />
265.532<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>704.716<br />
</td>
        <td>&lt; 80 127 225|<br />
+<br />
&lt; 109 173 306|<br />
<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span><br />
</td>
        <td style="text-align: center;">76.42<br />
</td>
        <td style="text-align: center;">133.012<br />
</td>
        <td style="text-align: center;">229.26<br />
</td>
        <td style="text-align: center;">266.024<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>37\63<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>704.762<br />
</td>
        <td>&lt; 63 100 177|<br />
</td>
        <td style="text-align: center;">4\63<br />
76.1905<br />
</td>
        <td style="text-align: center;">7\63 (1\9)<br />
133.333<br />
</td>
        <td style="text-align: center;">12\63 (4\21)<br />
228.571<br />
</td>
        <td style="text-align: center;">14\63 (2\9)<br />
266.667<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>121\206<br />
</td>
        <td><br />
</td>
        <td>704.854<br />
</td>
        <td>&lt; 206 327 578|<br />
</td>
        <td style="text-align: center;">40\618 (20\309)<br />
77.67<br />
</td>
        <td style="text-align: center;">45\412<br />
131.068<br />
</td>
        <td style="text-align: center;">40\206 (20\103)<br />
233.01<br />
</td>
        <td style="text-align: center;">45\206<br />
262.136<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>84\143<br />
</td>
        <td><br />
</td>
        <td>704.895<br />
</td>
        <td>&lt; 143 227 401|<br />
</td>
        <td style="text-align: center;">28\429<br />
78.322<br />
</td>
        <td style="text-align: center;">31\286<br />
130.07<br />
</td>
        <td style="text-align: center;">28\143<br />
234.965<br />
</td>
        <td style="text-align: center;">31\143<br />
260.14<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>131\223<br />
</td>
        <td><br />
</td>
        <td>704.933<br />
</td>
        <td>&lt; 223 354 626|<br />
</td>
        <td style="text-align: center;">43\669<br />
77.13<br />
</td>
        <td style="text-align: center;">49\446<br />
131.839<br />
</td>
        <td style="text-align: center;">43\223<br />
231.39<br />
</td>
        <td style="text-align: center;">49\223<br />
263.667<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>47\80<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>705<br />
</td>
        <td>&lt; 80 127 225|<br />
</td>
        <td style="text-align: center;">5\80 (1\16)<br />
75<br />
</td>
        <td style="text-align: center;">9\80<br />
135<br />
</td>
        <td style="text-align: center;">15\80 (3\16)<br />
225<br />
</td>
        <td style="text-align: center;">18\80 (9\40)<br />
270<br />
</td>
        <td>Boundary of larger &quot;gentle region&quot;<br />
</td>
    </tr>
</table>

</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-10-30 13:54:27 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-10-30 15:28:09 UTC</tt>.<br>
-: The original revision id was <tt>564501787</tt>.<br>
+: The original revision id was <tt>564511617</tt>.<br>
 : 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>
@@ Line 8: / Line 8: @@
 <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">[[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.
-|| 17\29 ||   || 703.448 || &lt; 29 46 81| ||= 2\29
+|| 17\29 ||   ||   || 703.448 || &lt; 29 46 81| ||= 2\29
 .759 ||= 3\29
 .138 ||||= 6\29
 .276 ||   ||
-||   || 61\104 || 703.846 || &lt; 104 165 292| ||= 20\312
+||   || 61\104 ||   || 703.846 || &lt; 104 165 292| ||= 20\312
 .923 ||= 33\208
 .692 ||= 20\104 (5\26)
 .769 ||= 33\104
 .385 ||   ||
-||   || 44\75 || 704 || &lt; 75 119 211| ||= 14\225
+||   || 44\75 ||   || 704 || &lt; 7&lt;span style="line-height: 1.5;"&gt;5 119 211|&lt;/span&gt; ||= 14\225
 .667 ||= 17\150
 ||= 14\75
 ||= 17\75
 ||   ||
-||   || 71\121 || 704.132 || &lt; 121 192 340| ||= 23\363
+||   ||   ||   || 704.0585 || &lt; 17 27 48|*pi+&lt;span style="background-color: #ffffff;"&gt;&lt; 24 38 67|&lt;/span&gt; ||= 69.372 ||= 143.912 ||= 208.117 ||= 287.824 ||   ||
+||   ||   || 115\196 || 704.082 || &lt;&lt;span style="line-height: 1.5;"&gt; 196 311 551|&lt;/span&gt; ||= 37/588
+.51 ||= 22/196 (11/98)
+.694 ||= 37/196
+.531 ||= 44/196 (11/49)
+.388 ||   ||
+||   ||   ||   || 704.095 || &lt; 17 27 48|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;+&lt;/span&gt;
+&lt;span style="background-color: #ffffff;"&gt;&lt; 12 19 34|&lt;/span&gt; ||= 69.397 ||= 143.857 ||= 208.191 ||= 287.731 ||   ||
+||   || 71\121 ||   || 704.132 || &lt; 121 192 340| ||= 23\363
 .033 ||= 27\242
 .884 ||= 23\121
 .099 ||= 27\121
 .769 ||   ||
-|| 27\46 ||   || 704.348 || &lt; 46 73 129| ||= 3\46
+|| 27\46 ||   ||   || 704.348 || &lt; 46 73 129| ||= 3\46
 .261 ||= 5\46
 .435 ||= 9\46
 .783 ||= 10\46 (5\23)
 .87 ||   ||
-||   ||   || 704.426 || &lt; 29 46 81|+
+||   ||   ||   || 704.426 || &lt; 29 46 81|+
 &lt; 109 173 306|
 &lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt; ||= 77.868 ||= 130.984 ||= 233.605 ||= 261.969 ||   ||
-||   || 118\201 || 704.478 || &lt; 201 319 564| ||= 13\201
+||   || 118\201 ||   || 704.478 || &lt; 201 319 564| ||= 13\201
 .612 ||= 22\201
 .343 ||= 39\201 (13\67)
 .836 ||= 44\201
 .687 ||   ||
-||   || 91\155 || 704.516 || &lt; 155 246 435| ||= 10\155 (2\31)
+||   || 91\155 ||   || 704.516 || &lt; 155 246 435| ||= 10\155 (2\31)
 .419 ||= 17\155
 .613 ||= 30\155 (6\31)
 .258 ||= 34\155
 .226 ||   ||
-||   || 155\264 || 704.5455 || &lt; 264 419 741| ||= 17\264
+||   ||   ||   ||   || &lt; 17 27 48|&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: #ffffff;"&gt;&lt; 29 46 81|&lt;/span&gt; ||   ||   ||   ||   ||   ||
+||   || 155\264 ||   || 704.5455 || &lt; 264 419 741| ||= 17\264
 .273 ||= 29\264
 .818 ||= 51\264 (17\88)
 .818 ||= 58\264 (29\132)
 .636 ||   ||
-|| 64\109 ||   || 704.587 || &lt; 109 173 306| ||= 7\109
+|| 64\109 ||   ||   || 704.587 || &lt; 109 173 306| ||= 7\109
 .064 ||= 12\109
 .11 ||= 21\109
 .192 ||= 24\109
 .22 || Boundary of smaller "gentle region" ||
-||   || 165\281 || 704.626 || &lt; 281 446 789| ||= 18\281
+||   || 165\281 ||   || 704.626 || &lt; 281 446 789| ||= 18\281
 .868 ||= 31\281
 .384 ||= 54\281
 .605 ||= 62\281
 .769 ||   ||
-||   || 101\172 || 704.651 || &lt; 172 273 483| ||= 11\172
+||   || 101\172 ||   || 704.651 || &lt; 172 273 483| ||= 11\172
 .744 ||= 19\172
 .558 ||= 33\172
 .232 ||= 38\172 (19\86)
 .116 ||   ||
-||   || 138\235 || 704.681 || &lt; 235 373 660| ||= 15\235 (3\47)
+||   || 138\235 ||   || 704.681 || &lt; 235 373 660| ||= 15\235 (3\47)
 .596 ||= 26\235
 .766 ||= 45\235 (9/45)
 .787 ||= 52\235
 .532 ||   ||
-||   ||   || 704.716 || &lt; 80 127 225|
+||   ||   ||   || 704.716 || &lt; 80 127 225|
 +
 &lt; 109 173 306|
 &lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt; ||= 76.42 ||= 133.012 ||= 229.26 ||= 266.024 ||   ||
-|| 37\63 ||   || 704.762 || &lt; 63 100 177| ||= 4\63
+|| 37\63 ||   ||   || 704.762 || &lt; 63 100 177| ||= 4\63
 .1905 ||= 7\63 (1\9)
 .333 ||= 12\63 (4\21)
 .571 ||= 14\63 (2\9)
 .667 ||   ||
-||   || 121\206 || 704.854 || &lt; 206 327 578| ||= 40\618 (20\309)
+||   || 121\206 ||   || 704.854 || &lt; 206 327 578| ||= 40\618 (20\309)
 .67 ||= 45\412
 .068 ||= 40\206 (20\103)
 .01 ||= 45\206
 .136 ||   ||
-||   || 84\143 || 704.895 || &lt; 143 227 401| ||= 28\429
+||   || 84\143 ||   || 704.895 || &lt; 143 227 401| ||= 28\429
 .322 ||= 31\286
 .07 ||= 28\143
 .965 ||= 31\143
 .14 ||   ||
-||   || 131\223 || 704.933 || &lt; 223 354 626| ||= 43\669
+||   || 131\223 ||   || 704.933 || &lt; 223 354 626| ||= 43\669
 .13 ||= 49\446
 .839 ||= 43\223
 .39 ||= 49\223
 .667 ||   ||
-|| 47\80 ||   || 705 || &lt; 80 127 225| ||= 5\80 (1\16)
+|| 47\80 ||   ||   || 705 || &lt; 80 127 225| ||= 5\80 (1\16)
 ||= 9\80
 ||= 15\80 (3\16)
@@ Line 107: / Line 117: @@
      &lt;tr&gt;
          &lt;td&gt;17\29&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 130: / Line 142: @@
 &lt;/td&gt;
          &lt;td&gt;61\104&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;703.846&lt;br /&gt;
@@ Line 154: / Line 168: @@
 &lt;/td&gt;
          &lt;td&gt;44\75&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;704&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&amp;lt; 75 119 211|&lt;br /&gt;
+         &lt;td&gt;&amp;lt; 7&lt;span style="line-height: 1.5;"&gt;5 119 211|&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;14\225&lt;br /&gt;
@@ Line 170: / Line 186: @@
          &lt;td style="text-align: center;"&gt;17\75&lt;br /&gt;
 &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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;704.0585&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&amp;lt; 17 27 48|*pi+&lt;span style="background-color: #ffffff;"&gt;&amp;lt; 24 38 67|&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;69.372&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;143.912&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;208.117&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;287.824&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;115\196&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;704.082&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&amp;lt;&lt;span style="line-height: 1.5;"&gt; 196 311 551|&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;37/588&lt;br /&gt;
+.51&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;22/196 (11/98)&lt;br /&gt;
+.694&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;37/196&lt;br /&gt;
+.531&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;44/196 (11/49)&lt;br /&gt;
+.388&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;704.095&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&amp;lt; 17 27 48|&lt;span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"&gt;φ&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;+&lt;/span&gt;&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;&amp;lt; 12 19 34|&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;69.397&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;143.857&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;208.191&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;287.731&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 178: / Line 265: @@
 &lt;/td&gt;
          &lt;td&gt;71\121&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;704.132&lt;br /&gt;
@@ Line 200: / Line 289: @@
      &lt;tr&gt;
          &lt;td&gt;27\46&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 223: / Line 314: @@
      &lt;/tr&gt;
      &lt;tr&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
@@ Line 248: / Line 341: @@
 &lt;/td&gt;
          &lt;td&gt;118\201&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;704.478&lt;br /&gt;
@@ Line 272: / Line 367: @@
 &lt;/td&gt;
          &lt;td&gt;91\155&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;704.516&lt;br /&gt;
@@ Line 288: / Line 385: @@
          &lt;td style="text-align: center;"&gt;34\155&lt;br /&gt;
 .226&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&amp;lt; 17 27 48|&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;span style="background-color: #ffffff;"&gt;&amp;lt; 29 46 81|&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 296: / Line 416: @@
 &lt;/td&gt;
          &lt;td&gt;155\264&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;704.5455&lt;br /&gt;
@@ Line 318: / Line 440: @@
      &lt;tr&gt;
          &lt;td&gt;64\109&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 344: / Line 468: @@
 &lt;/td&gt;
          &lt;td&gt;165\281&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;704.626&lt;br /&gt;
@@ Line 368: / Line 494: @@
 &lt;/td&gt;
          &lt;td&gt;101\172&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;704.651&lt;br /&gt;
@@ Line 392: / Line 520: @@
 &lt;/td&gt;
          &lt;td&gt;138\235&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;704.681&lt;br /&gt;
@@ Line 413: / Line 543: @@
      &lt;/tr&gt;
      &lt;tr&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
@@ Line 437: / Line 569: @@
      &lt;tr&gt;
          &lt;td&gt;37\63&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 463: / Line 597: @@
 &lt;/td&gt;
          &lt;td&gt;121\206&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;704.854&lt;br /&gt;
@@ Line 487: / Line 623: @@
 &lt;/td&gt;
          &lt;td&gt;84\143&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;704.895&lt;br /&gt;
@@ Line 511: / Line 649: @@
 &lt;/td&gt;
          &lt;td&gt;131\223&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;704.933&lt;br /&gt;
@@ Line 533: / Line 673: @@
      &lt;tr&gt;
          &lt;td&gt;47\80&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;

Gentle region: Difference between revisions

Revision as of 15:28, 30 October 2015

IMPORTED REVISION FROM WIKISPACES

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Original HTML content:

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