5L 8s: Difference between revisions

Revision as of 20:54, 23 May 2015

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 2015-05-23 20:54:42 UTC.

The original revision id was 551983422.

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:

This MOS, representing tempered chains of the 21st harmonic, is the chromatic scale of Semisept/A-team and Vulture temperaments. The major problematic of approaching it from a traditional tonality point of view is that, at best, it partially misses syntonic root-third-fifth triads unless you are extremely generous with the definition of the category of a "third". However, it does hit the correct syntonic second and seventh, so that insofar as the major second/minor seventh is a consonance, stacks of it (occasionally mixed with the "minor third/major sixth") are typically the most consonant harmonies of the scale.
|| (2+3)/13 ||   ||   || 184 8/13+<span style="font-size: 12.8000001907349px;">276 12/13</span> ||
|| (9+13)/57 ||   ||   || 189 9/19+273 13/19 ||
|| (7+10)/44 ||   ||   || 190 10/11+272 8/11 ||
||   || (19+27)/119 ||   || 191 71/119+272 32/119 ||
||   || (12+17)/75 ||   || 192+272 ||
||   || (17+24)/106 ||   || 192 25/53+271 37/53 ||
|| (5+7)/31 ||   ||   || 193 17/31+270 30/31 ||
||   || (18+25)/111 ||   || 194 22/37+270 10/37 ||
||   || (13+18)/80 ||   || 195+270 ||
||   || (8+11)/49 ||   || 195 45/49+269 19/49 ||
||   ||   || (19+26)/116 || 196 16/29+268 28/29 ||
||   || (11+15)/67 ||   || 197 1/67+268 44/67 ||
||   || (14+19)/85 ||   || 197 11/17+268 4/17 ||
||   || (17+23)/103 ||   || 198 6/103+267 99/103 ||
||   || (20+27)/121 ||   || 198 42/121+267 93/121 ||
||   || (23+31)/139 ||   || 198 78/139+267 87/139 ||
||   || (26+35)/157 ||   || 198 114/157+267 81/157 ||
||   || (29+39)/175 ||   || 198 6/7+267 3/7 ||
||   || (32+43)/193 ||   || 198 186/193+267 69/193 ||
||   || (35+47)/211 ||   || 199 11/211+267 63/211 ||
|| (3+4)/18 ||   ||   || 200+266 2/3 ||
||   || (19+25)/113 ||   || 201 87/113+265 50/113 ||
||   || (16+21)/95 ||   || 202 2/19+265 4/19 ||
||   || (13+17)/77 ||   || 202 46/77+264 72/77 ||
||   || (10+13)/59 ||   || 203 23/59+264 24/59 ||
||   || (7+9)/41 ||   || 204 36/41+263 17/41 ||
||   ||   || (18+23)/105 || 205 5/7+262 6/7 ||
||   || (11+14)/64 ||   || 206.25+262.5 ||
||   ||   ||   || 206.653404+262.231064 ||
||   || (15+19)/87 ||   || 206 26/29+262 2/29 ||
||   || (19+24)/110 ||   || 207 3/11+261 9/11 ||
|| (4+5)/23 ||   ||   || 208 16/23+260 20/23 ||
||   ||   ||   || 209.630457+260.246362 ||
||   || (13+16)/74 ||   || 210 30/37+259 17/37 ||
||   || (9+11)/51 ||   || 211 13/17+258 14/17 ||
||   || (14+17)/79 ||   || 212 52/79+258 18/79 ||
|| (5+6)/28 ||   ||   || 214 2/7+257 1/7 ||
||   || (16+19)/89 ||   || 215 65/89+256 16/89 ||
||   || <span style="font-size: 12.8000001907349px;">(11+13)/61</span> ||   || 216 24/61+255 45/61 ||
||   || (17+20)/94 ||   || 217 1/47+255 15/47 ||
|| (6+7)/33 ||   ||   || 218 2/11+254 6/11 ||
|| (1+1)/5 ||   ||   || 240+240 ||

Original HTML content:

<html><head><title>5L 8s</title></head><body>This MOS, representing tempered chains of the 21st harmonic, is the chromatic scale of Semisept/A-team and Vulture temperaments. The major problematic of approaching it from a traditional tonality point of view is that, at best, it partially misses syntonic root-third-fifth triads unless you are extremely generous with the definition of the category of a &quot;third&quot;. However, it does hit the correct syntonic second and seventh, so that insofar as the major second/minor seventh is a consonance, stacks of it (occasionally mixed with the &quot;minor third/major sixth&quot;) are typically the most consonant harmonies of the scale.<br />


<table class="wiki_table">
    <tr>
        <td>(2+3)/13<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>184 8/13+<span style="font-size: 12.8000001907349px;">276 12/13</span><br />
</td>
    </tr>
    <tr>
        <td>(9+13)/57<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>189 9/19+273 13/19<br />
</td>
    </tr>
    <tr>
        <td>(7+10)/44<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>190 10/11+272 8/11<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(19+27)/119<br />
</td>
        <td><br />
</td>
        <td>191 71/119+272 32/119<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(12+17)/75<br />
</td>
        <td><br />
</td>
        <td>192+272<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(17+24)/106<br />
</td>
        <td><br />
</td>
        <td>192 25/53+271 37/53<br />
</td>
    </tr>
    <tr>
        <td>(5+7)/31<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>193 17/31+270 30/31<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(18+25)/111<br />
</td>
        <td><br />
</td>
        <td>194 22/37+270 10/37<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(13+18)/80<br />
</td>
        <td><br />
</td>
        <td>195+270<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(8+11)/49<br />
</td>
        <td><br />
</td>
        <td>195 45/49+269 19/49<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>(19+26)/116<br />
</td>
        <td>196 16/29+268 28/29<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(11+15)/67<br />
</td>
        <td><br />
</td>
        <td>197 1/67+268 44/67<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(14+19)/85<br />
</td>
        <td><br />
</td>
        <td>197 11/17+268 4/17<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(17+23)/103<br />
</td>
        <td><br />
</td>
        <td>198 6/103+267 99/103<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(20+27)/121<br />
</td>
        <td><br />
</td>
        <td>198 42/121+267 93/121<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(23+31)/139<br />
</td>
        <td><br />
</td>
        <td>198 78/139+267 87/139<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(26+35)/157<br />
</td>
        <td><br />
</td>
        <td>198 114/157+267 81/157<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(29+39)/175<br />
</td>
        <td><br />
</td>
        <td>198 6/7+267 3/7<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(32+43)/193<br />
</td>
        <td><br />
</td>
        <td>198 186/193+267 69/193<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(35+47)/211<br />
</td>
        <td><br />
</td>
        <td>199 11/211+267 63/211<br />
</td>
    </tr>
    <tr>
        <td>(3+4)/18<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>200+266 2/3<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(19+25)/113<br />
</td>
        <td><br />
</td>
        <td>201 87/113+265 50/113<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(16+21)/95<br />
</td>
        <td><br />
</td>
        <td>202 2/19+265 4/19<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(13+17)/77<br />
</td>
        <td><br />
</td>
        <td>202 46/77+264 72/77<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(10+13)/59<br />
</td>
        <td><br />
</td>
        <td>203 23/59+264 24/59<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(7+9)/41<br />
</td>
        <td><br />
</td>
        <td>204 36/41+263 17/41<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>(18+23)/105<br />
</td>
        <td>205 5/7+262 6/7<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(11+14)/64<br />
</td>
        <td><br />
</td>
        <td>206.25+262.5<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>206.653404+262.231064<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(15+19)/87<br />
</td>
        <td><br />
</td>
        <td>206 26/29+262 2/29<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(19+24)/110<br />
</td>
        <td><br />
</td>
        <td>207 3/11+261 9/11<br />
</td>
    </tr>
    <tr>
        <td>(4+5)/23<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>208 16/23+260 20/23<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>209.630457+260.246362<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(13+16)/74<br />
</td>
        <td><br />
</td>
        <td>210 30/37+259 17/37<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(9+11)/51<br />
</td>
        <td><br />
</td>
        <td>211 13/17+258 14/17<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(14+17)/79<br />
</td>
        <td><br />
</td>
        <td>212 52/79+258 18/79<br />
</td>
    </tr>
    <tr>
        <td>(5+6)/28<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>214 2/7+257 1/7<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(16+19)/89<br />
</td>
        <td><br />
</td>
        <td>215 65/89+256 16/89<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><span style="font-size: 12.8000001907349px;">(11+13)/61</span><br />
</td>
        <td><br />
</td>
        <td>216 24/61+255 45/61<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>(17+20)/94<br />
</td>
        <td><br />
</td>
        <td>217 1/47+255 15/47<br />
</td>
    </tr>
    <tr>
        <td>(6+7)/33<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>218 2/11+254 6/11<br />
</td>
    </tr>
    <tr>
        <td>(1+1)/5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>240+240<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>2015-02-12 12:36:00 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-23 20:54:42 UTC</tt>.<br>
-: The original revision id was <tt>540775490</tt>.<br>
+: The original revision id was <tt>551983422</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 35: / Line 35: @@
 ||   ||   || (18+23)/105 || 205 5/7+262 6/7 ||
 ||   || (11+14)/64 ||   || 206.25+262.5 ||
+||   ||   ||   || 206.653404+262.231064 ||
 ||   || (15+19)/87 ||   || 206 26/29+262 2/29 ||
 ||   || (19+24)/110 ||   || 207 3/11+261 9/11 ||
-||   ||   ||   || 208.506705+260.99553 ||
 || (4+5)/23 ||   ||   || 208 16/23+260 20/23 ||
-||   ||   ||   || 208.884069+260.734954 ||
+||   ||   ||   || 209.630457+260.246362 ||
 ||   || (13+16)/74 ||   || 210 30/37+259 17/37 ||
 ||   || (9+11)/51 ||   || 211 13/17+258 14/17 ||
@@ Line 337: / Line 337: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;(15+19)/87&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;206 26/29+262 2/29&lt;br /&gt;
+         &lt;td&gt;206.653404+262.231064&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 347: / Line 347: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;(19+24)/110&lt;br /&gt;
+         &lt;td&gt;(15+19)/87&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;207 3/11+261 9/11&lt;br /&gt;
+         &lt;td&gt;206 26/29+262 2/29&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 357: / Line 357: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;(19+24)/110&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;208.506705+260.99553&lt;br /&gt;
+         &lt;td&gt;207 3/11+261 9/11&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 381: / Line 381: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;208.884069+260.734954&lt;br /&gt;
+         &lt;td&gt;209.630457+260.246362&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

5L 8s: Difference between revisions

Revision as of 20:54, 23 May 2015

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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