Gentle region
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author JosephRuhf and made on 2012-10-02 18:59:15 UTC.
- The original revision id was 369712382.
- The revision comment was:
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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. We can consider this region to extend from fifths of size 17\29 to 64\109. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the gentle region include multiples of [[29edo]], [[46edo]], [[75edo]], [[104edo]], [[109edo]], [[121edo]], [[145edo|133edo]], [[155edo]], [[162edo]], [[167edo]], [[179edo]], [[191edo]], [[201edo]], [[213edo]], [[225edo]] and [[237edo]]. || 17\29 || || || || || || || 703.44828 || || || || || || || || 112\191 || 703.66492 || || || || || || || 95\162 || || 703.__703__ || || || || || || || || 173\295 || 703.72881 || || || || || || 78\133 || || || 703.7594 || || || || || || || || 217\370 || 703.__783__ || || || || || || || 139\237 || || 703.79747 || || || || || || || || 200\341 || 703.81232 || || || || || 61\104 || || || || 703.84615 || || || || || || || || 227\387 || 703.87597 || || || || || || || 166\283 || || 703.88693 || || || || || || || || 271\462 || 703.8961 || || || || || || 105\179 || || || 703.91061 || || || || || || || || 254\433 || 703.9261 || || || || || || || 149\254 || || 703.93701 || || || || || || || || 193\329 || 703.95137 || || || || 44\75 || || || || || 704 || || || || || || || || 203\346 || 704.04624 || || || || || || || 159\271 || || 704.__05904__ || || || || || || || || 274\467 || 704.06852 || || || || || || 115\196 || || || 704.08163 || || || || || || || || 301\513 || 704.09357 || || || || || || || 186\317 || || 704.10095 || || || || || || || || 257\438 || 704.10959 || || || || || 71\121 || || || || 704.13223 || || || || || || || || 240\409 || 704.15648 || || || || || || || 169\288 || || 704.1__6__ || || || || || || || || 267\455 || 704.17582 || || || || || || 98\167 || || || 704.19162 || || || || || || || || 223\380 || 704.21053 || || || || || || || 125\213 || || 704.22535 || || || || || || || || 152\259 || 704.2471 || || || 27\46 || || || || || || 704.34783 || || || || || || || || 199\339 || 704.42478 || || || || || || || 172\293 || || 704.43686 || || || || || || || || 317\540 || 704.__4__ || || || || || || 145\247 || || || 704.45344 || || || || || || || || 408\695 || 704.46043 || || || || || || || 263\448 || || 704.46429 || || || || || || || || 381\649 || 704.46841 || || || || || 118\201 || || || || 704.47761 || || || || || || || || 445\758 || 704.48549 || || || || || || || 327\557 || || 704.48833 || || || || || || || || 536\913 || 704.49069 || || || || || || 209\356 || || || 704.49438 || || || || || || || || 509\867 || 704.49827 || || || || || || || 300\511 || || 704.50098 || || || || || || || || 391\666 || 704.__504__ || || || || 91\155 || || || || || 704.51613 || || || || || || || || 428\729 || 704.52675 || || || || || || || 337\574 || || 704.52962 || || || || || || || || 583\993 || 704.53172 || || || || || || 246\419 || || || 704.53461 || || || || || || || || 647\1102 || 704.537205 || || || || || || || 401\683 || || 704.5388 || || || || || || || || 556\947 || 704.540655 || || || || || 155\264 || || || || 704.__54__ || || || || || || || || 529\901 || 704.5505 || || || || || || || 374\637 || || 704.55259 || || || || || || || || 593\1010 || 704.__5544__ || || || || || || 219\373 || || || 704.55764 || || || || || || || || 502\855 || 704.5614 || || || || || || || 283\482 || || 704.564315 || || || || || || || || 347\591 || 704.56853 || || 64\109 || || || || || || || 704.58716 ||
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 "gentle region" of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp. We can consider this region to extend from fifths of size 17\29 to 64\109. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the 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>.<br />
<br />
<table class="wiki_table">
<tr>
<td>17\29<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>703.44828<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>112\191<br />
</td>
<td>703.66492<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>95\162<br />
</td>
<td><br />
</td>
<td>703.<u>703</u><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>173\295<br />
</td>
<td>703.72881<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>78\133<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>703.7594<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>217\370<br />
</td>
<td>703.<u>783</u><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>139\237<br />
</td>
<td><br />
</td>
<td>703.79747<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>200\341<br />
</td>
<td>703.81232<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>61\104<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>703.84615<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>227\387<br />
</td>
<td>703.87597<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>166\283<br />
</td>
<td><br />
</td>
<td>703.88693<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>271\462<br />
</td>
<td>703.8961<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>105\179<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>703.91061<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>254\433<br />
</td>
<td>703.9261<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>149\254<br />
</td>
<td><br />
</td>
<td>703.93701<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>193\329<br />
</td>
<td>703.95137<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>44\75<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>704<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>203\346<br />
</td>
<td>704.04624<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>159\271<br />
</td>
<td><br />
</td>
<td>704.<u>05904</u><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>274\467<br />
</td>
<td>704.06852<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>115\196<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>704.08163<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>301\513<br />
</td>
<td>704.09357<br />
</td>
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<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>186\317<br />
</td>
<td><br />
</td>
<td>704.10095<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>257\438<br />
</td>
<td>704.10959<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>71\121<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>704.13223<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>240\409<br />
</td>
<td>704.15648<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
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</td>
<td>169\288<br />
</td>
<td><br />
</td>
<td>704.1<u>6</u><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>267\455<br />
</td>
<td>704.17582<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>98\167<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>704.19162<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>223\380<br />
</td>
<td>704.21053<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>125\213<br />
</td>
<td><br />
</td>
<td>704.22535<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
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</td>
<td>152\259<br />
</td>
<td>704.2471<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>27\46<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>704.34783<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>199\339<br />
</td>
<td>704.42478<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>172\293<br />
</td>
<td><br />
</td>
<td>704.43686<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>317\540<br />
</td>
<td>704.<u>4</u><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>145\247<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>704.45344<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>408\695<br />
</td>
<td>704.46043<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>263\448<br />
</td>
<td><br />
</td>
<td>704.46429<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>381\649<br />
</td>
<td>704.46841<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>118\201<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>704.47761<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>445\758<br />
</td>
<td>704.48549<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>327\557<br />
</td>
<td><br />
</td>
<td>704.48833<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>536\913<br />
</td>
<td>704.49069<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>209\356<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>704.49438<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>509\867<br />
</td>
<td>704.49827<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>300\511<br />
</td>
<td><br />
</td>
<td>704.50098<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>391\666<br />
</td>
<td>704.<u>504</u><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>91\155<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>704.51613<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>428\729<br />
</td>
<td>704.52675<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>337\574<br />
</td>
<td><br />
</td>
<td>704.52962<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>583\993<br />
</td>
<td>704.53172<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>246\419<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>704.53461<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>647\1102<br />
</td>
<td>704.537205<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>401\683<br />
</td>
<td><br />
</td>
<td>704.5388<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>556\947<br />
</td>
<td>704.540655<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>155\264<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>704.<u>54</u><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>529\901<br />
</td>
<td>704.5505<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>374\637<br />
</td>
<td><br />
</td>
<td>704.55259<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>593\1010<br />
</td>
<td>704.<u>5544</u><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>219\373<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>704.55764<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>502\855<br />
</td>
<td>704.5614<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>283\482<br />
</td>
<td><br />
</td>
<td>704.564315<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>347\591<br />
</td>
<td>704.56853<br />
</td>
</tr>
<tr>
<td>64\109<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>704.58716<br />
</td>
</tr>
</table>
</body></html>