Isoharmonic chord: Difference between revisions

Revision as of 13:16, 22 April 2010

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author Andrew_Heathwaite and made on 2010-04-22 13:16:33 UTC.

The original revision id was 136399925.

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:

=isoharmonic chords= 

In [[JustIntonation|just intonation]], Isoharmonic chords are build by successive jumps up the [[OverToneSeries|harmonic series]] by some number of steps. Since the harmonic series is arranged such that each higher step is smaller than the one before it, all isoharmonic chords have this same shape -- with diminishing step size as one ascends. It happens that all isoharmonic chords are equal-hertz chords (but not all equal-hertz chords are isoharmonic chords). An isoharmonic "chord" may function more like a "scale" than a chord (depending on the composition of course), but I will use the word "chord" on this page for consistency.

===class i=== 
The simplest isoharmonic chords are built by stepping up the harmonic series by single steps (adjacent steps in the harmonic series). Take, for instance, 4:5:6:7, the harmonic seventh chord. I call these class i isoharmonic chords. There is one class i series (the harmonic series), which looks like this:

|| harmonic || 1 ||   || 2 ||   || 3 ||   || 4 ||   || 5 ||   || 6 ||   || 7 ||   || 8 ||   || 9 ||   || 10 ||   || 11 ||   || 12 ||   || 13 ||   || 14 ||   || 15 ||   || 16 ||
|| cents diff ||   || 1200 ||   || 702 ||   || 498 ||   || 386 ||   || 316 ||   || 267 ||   || 231 ||   || 204 ||   || 182 ||   || 165 ||   || 151 ||   || 139 ||   || 128 ||   || 119 ||   || 112 ||   ||

Some "scales" built this way: [[otones12-24]], [[otones20-40]]...

===class ii=== 
The next simplest isoharmonic chords are built by stepping up the harmonic series by two (skipping every other harmonic). This gives us chords such as 3:5:7:9 (the primary tetrad in the [[BP|Bohlen-Pierce]] tuning system) and 9:11:13:15. Note that if you start on an even number, your chord is equivalent to a class i harmonic chord: 4:6:8:10 = 2:3:4:5. Thus, there is one class ii series (the series of all odd harmonics):

|| harmonic || 1 ||   || 3 ||   || 5 ||   || 7 ||   || 9 ||   || 11 ||   || 13 ||   || 15 ||   || 17 ||   || 19 ||   || 21 ||   || 23 ||   || 25 ||   || 27 ||   || 29 ||   || 31 ||
|| cents diff ||   || 1904 ||   || 884 ||   || 583 ||   || 435 ||   || 347 ||   || 289 ||   || 248 ||   || 217 ||   || 193 ||   || 173 ||   || 157 ||   || 144 ||   || 133 ||   || 124 ||   || 115 ||   ||

===class iii=== 
Class iii isoharmonic chords are less common and more complex sounding. They include chords such as 7:10:13:16 and 14:17:20:23. Note that if you start on a number divisible by three, you'll again get a chord reducible to class i (eg. 9:12:15 = 3:4:5). There are two series for class iii:

|| harmonic || 1 ||   || 4 ||   || 7 ||   || 10 ||   || 13 ||   || 16 ||   || 19 ||   || 22 ||   || 25 ||   || 28 ||   || 31 ||   || 34 ||   || 37 ||   || 40 ||   || 43 ||   || 46 ||
|| cents diff ||   || 2400 ||   || 969 ||   || 617 ||   || 454 ||   || 359 ||   || 298 ||   || 254 ||   || 221 ||   || 196 ||   || 176 ||   || 160 ||   || 146 ||   || 135 ||   || 125 ||   || 117 ||   ||

|| harmonic || 2 ||   || 5 ||   || 8 ||   || 11 ||   || 14 ||   || 17 ||   || 20 ||   || 23 ||   || 26 ||   || 29 ||   || 32 ||   || 35 ||   || 38 ||   || 41 ||   || 44 ||   || 47 ||
|| cents diff ||   || 1586 ||   || 814 ||   || 551 ||   || 418 ||   || 336 ||   || 281 ||   || 242 ||   || 212 ||   || 189 ||   || 170 ||   || 155 ||   || 142 ||   || 132 ||   || 122 ||   || 114 ||   ||

===class iv=== 
|| harmonic || 1 ||   || 5 ||   || 9 ||   || 13 ||   || 17 ||   || 21 ||   || 25 ||   || 29 ||   || 33 ||   || 37 ||   || 41 ||   || 45 ||   || 49 ||   || 53 ||   || 57 ||   || 61 ||
|| cents diff ||   || 2786 ||   || 1018 ||   || 637 ||   || 464 ||   || 366 ||   || 302 ||   || 257 ||   || 224 ||   || 198 ||   || 178 ||   || 161 ||   || 147 ||   || 136 ||   || 126 ||   || 117 ||   ||

|| harmonic || 3 ||   || 7 ||   || 11 ||   || 15 ||   || 19 ||   || 23 ||   || 27 ||   || 31 ||   || 35 ||   || 39 ||   || 43 ||   || 47 ||   || 51 ||   || 55 ||   || 59 ||   || 63 ||
|| cents diff ||   || 1467 ||   || 782 ||   || 537 ||   || 409 ||   || 331 ||   || 278 ||   || 239 ||   || 210 ||   || 187 ||   || 169 ||   || 154 ||   || 141 ||   || 131 ||   || 122 ||   || 114 ||   ||

===class v=== 
|| harmonic || 1 ||   || 6 ||   || 11 ||   || 16 ||   || 21 ||   || 26 ||   || 31 ||   || 36 ||   || 41 ||   || 46 ||   || 51 ||   || 56 ||   || 61 ||   || 66 ||   || 71 ||   || 76 ||
|| cents diff ||   || 3102 ||   || 1049 ||   || 649 ||   || 471 ||   || 370 ||   || 306 ||   || 259 ||   || 225 ||   || 199 ||   || 179 ||   || 162 ||   || 148 ||   || 136 ||   || 126 ||   || 118 ||   ||

|| harmonic || 2 ||   || 7 ||   || 12 ||   || 17 ||   || 22 ||   || 27 ||   || 32 ||   || 37 ||   || 42 ||   || 47 ||   || 52 ||   || 57 ||   || 62 ||   || 67 ||   || 72 ||   || 77 ||
|| cents diff ||   || 2169 ||   || 933 ||   || 603 ||   || 446 ||   || 355 ||   || 294 ||   || 251 ||   || 219 ||   || 195 ||   || 175 ||   || 159 ||   || 146 ||   || 134 ||   || 125 ||   || 116 ||   ||

|| harmonic || 3 ||   || 8 ||   || 13 ||   || 18 ||   || 23 ||   || 28 ||   || 33 ||   || 38 ||   || 43 ||   || 48 ||   || 53 ||   || 58 ||   || 63 ||   || 68 ||   || 73 ||   || 78 ||
|| cents diff ||   || 1698 ||   || 841 ||   || 563 ||   || 424 ||   || 341 ||   || 284 ||   || 244 ||   || 214 ||   || 190 ||   || 172 ||   || 156 ||   || 143 ||   || 132 ||   || 123 ||   || 115 ||   ||

|| harmonic || 4 ||   || 9 ||   || 14 ||   || 19 ||   || 24 ||   || 29 ||   || 34 ||   || 39 ||   || 44 ||   || 49 ||   || 54 ||   || 59 ||   || 64 ||   || 69 ||   || 74 ||   || 79 ||
|| cents diff ||   || 1404 ||   || 765 ||   || 529 ||   || 404 ||   || 328 ||   || 275 ||   || 238 ||   || 209 ||   || 186 ||   || 168 ||   || 153 ||   || 141 ||   || 130 ||   || 121 ||   || 113 ||   ||

Original HTML content:

<html><head><title>isoharmonic chords</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="isoharmonic chords"></a><!-- ws:end:WikiTextHeadingRule:0 -->isoharmonic chords</h1>
 <br />
In <a class="wiki_link" href="/JustIntonation">just intonation</a>, Isoharmonic chords are build by successive jumps up the <a class="wiki_link" href="/OverToneSeries">harmonic series</a> by some number of steps. Since the harmonic series is arranged such that each higher step is smaller than the one before it, all isoharmonic chords have this same shape -- with diminishing step size as one ascends. It happens that all isoharmonic chords are equal-hertz chords (but not all equal-hertz chords are isoharmonic chords). An isoharmonic &quot;chord&quot; may function more like a &quot;scale&quot; than a chord (depending on the composition of course), but I will use the word &quot;chord&quot; on this page for consistency.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="isoharmonic chords--class i"></a><!-- ws:end:WikiTextHeadingRule:2 -->class i</h3>
 The simplest isoharmonic chords are built by stepping up the harmonic series by single steps (adjacent steps in the harmonic series). Take, for instance, 4:5:6:7, the harmonic seventh chord. I call these class i isoharmonic chords. There is one class i series (the harmonic series), which looks like this:<br />
<br />


<table class="wiki_table">
    <tr>
        <td>harmonic<br />
</td>
        <td>1<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td>8<br />
</td>
        <td><br />
</td>
        <td>9<br />
</td>
        <td><br />
</td>
        <td>10<br />
</td>
        <td><br />
</td>
        <td>11<br />
</td>
        <td><br />
</td>
        <td>12<br />
</td>
        <td><br />
</td>
        <td>13<br />
</td>
        <td><br />
</td>
        <td>14<br />
</td>
        <td><br />
</td>
        <td>15<br />
</td>
        <td><br />
</td>
        <td>16<br />
</td>
    </tr>
    <tr>
        <td>cents diff<br />
</td>
        <td><br />
</td>
        <td>1200<br />
</td>
        <td><br />
</td>
        <td>702<br />
</td>
        <td><br />
</td>
        <td>498<br />
</td>
        <td><br />
</td>
        <td>386<br />
</td>
        <td><br />
</td>
        <td>316<br />
</td>
        <td><br />
</td>
        <td>267<br />
</td>
        <td><br />
</td>
        <td>231<br />
</td>
        <td><br />
</td>
        <td>204<br />
</td>
        <td><br />
</td>
        <td>182<br />
</td>
        <td><br />
</td>
        <td>165<br />
</td>
        <td><br />
</td>
        <td>151<br />
</td>
        <td><br />
</td>
        <td>139<br />
</td>
        <td><br />
</td>
        <td>128<br />
</td>
        <td><br />
</td>
        <td>119<br />
</td>
        <td><br />
</td>
        <td>112<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
Some &quot;scales&quot; built this way: <a class="wiki_link" href="/otones12-24">otones12-24</a>, <a class="wiki_link" href="/otones20-40">otones20-40</a>...<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="isoharmonic chords--class ii"></a><!-- ws:end:WikiTextHeadingRule:4 -->class ii</h3>
 The next simplest isoharmonic chords are built by stepping up the harmonic series by two (skipping every other harmonic). This gives us chords such as 3:5:7:9 (the primary tetrad in the <a class="wiki_link" href="/BP">Bohlen-Pierce</a> tuning system) and 9:11:13:15. Note that if you start on an even number, your chord is equivalent to a class i harmonic chord: 4:6:8:10 = 2:3:4:5. Thus, there is one class ii series (the series of all odd harmonics):<br />
<br />


<table class="wiki_table">
    <tr>
        <td>harmonic<br />
</td>
        <td>1<br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td>9<br />
</td>
        <td><br />
</td>
        <td>11<br />
</td>
        <td><br />
</td>
        <td>13<br />
</td>
        <td><br />
</td>
        <td>15<br />
</td>
        <td><br />
</td>
        <td>17<br />
</td>
        <td><br />
</td>
        <td>19<br />
</td>
        <td><br />
</td>
        <td>21<br />
</td>
        <td><br />
</td>
        <td>23<br />
</td>
        <td><br />
</td>
        <td>25<br />
</td>
        <td><br />
</td>
        <td>27<br />
</td>
        <td><br />
</td>
        <td>29<br />
</td>
        <td><br />
</td>
        <td>31<br />
</td>
    </tr>
    <tr>
        <td>cents diff<br />
</td>
        <td><br />
</td>
        <td>1904<br />
</td>
        <td><br />
</td>
        <td>884<br />
</td>
        <td><br />
</td>
        <td>583<br />
</td>
        <td><br />
</td>
        <td>435<br />
</td>
        <td><br />
</td>
        <td>347<br />
</td>
        <td><br />
</td>
        <td>289<br />
</td>
        <td><br />
</td>
        <td>248<br />
</td>
        <td><br />
</td>
        <td>217<br />
</td>
        <td><br />
</td>
        <td>193<br />
</td>
        <td><br />
</td>
        <td>173<br />
</td>
        <td><br />
</td>
        <td>157<br />
</td>
        <td><br />
</td>
        <td>144<br />
</td>
        <td><br />
</td>
        <td>133<br />
</td>
        <td><br />
</td>
        <td>124<br />
</td>
        <td><br />
</td>
        <td>115<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="isoharmonic chords--class iii"></a><!-- ws:end:WikiTextHeadingRule:6 -->class iii</h3>
 Class iii isoharmonic chords are less common and more complex sounding. They include chords such as 7:10:13:16 and 14:17:20:23. Note that if you start on a number divisible by three, you'll again get a chord reducible to class i (eg. 9:12:15 = 3:4:5). There are two series for class iii:<br />
<br />


<table class="wiki_table">
    <tr>
        <td>harmonic<br />
</td>
        <td>1<br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td>10<br />
</td>
        <td><br />
</td>
        <td>13<br />
</td>
        <td><br />
</td>
        <td>16<br />
</td>
        <td><br />
</td>
        <td>19<br />
</td>
        <td><br />
</td>
        <td>22<br />
</td>
        <td><br />
</td>
        <td>25<br />
</td>
        <td><br />
</td>
        <td>28<br />
</td>
        <td><br />
</td>
        <td>31<br />
</td>
        <td><br />
</td>
        <td>34<br />
</td>
        <td><br />
</td>
        <td>37<br />
</td>
        <td><br />
</td>
        <td>40<br />
</td>
        <td><br />
</td>
        <td>43<br />
</td>
        <td><br />
</td>
        <td>46<br />
</td>
    </tr>
    <tr>
        <td>cents diff<br />
</td>
        <td><br />
</td>
        <td>2400<br />
</td>
        <td><br />
</td>
        <td>969<br />
</td>
        <td><br />
</td>
        <td>617<br />
</td>
        <td><br />
</td>
        <td>454<br />
</td>
        <td><br />
</td>
        <td>359<br />
</td>
        <td><br />
</td>
        <td>298<br />
</td>
        <td><br />
</td>
        <td>254<br />
</td>
        <td><br />
</td>
        <td>221<br />
</td>
        <td><br />
</td>
        <td>196<br />
</td>
        <td><br />
</td>
        <td>176<br />
</td>
        <td><br />
</td>
        <td>160<br />
</td>
        <td><br />
</td>
        <td>146<br />
</td>
        <td><br />
</td>
        <td>135<br />
</td>
        <td><br />
</td>
        <td>125<br />
</td>
        <td><br />
</td>
        <td>117<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />


<table class="wiki_table">
    <tr>
        <td>harmonic<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td>8<br />
</td>
        <td><br />
</td>
        <td>11<br />
</td>
        <td><br />
</td>
        <td>14<br />
</td>
        <td><br />
</td>
        <td>17<br />
</td>
        <td><br />
</td>
        <td>20<br />
</td>
        <td><br />
</td>
        <td>23<br />
</td>
        <td><br />
</td>
        <td>26<br />
</td>
        <td><br />
</td>
        <td>29<br />
</td>
        <td><br />
</td>
        <td>32<br />
</td>
        <td><br />
</td>
        <td>35<br />
</td>
        <td><br />
</td>
        <td>38<br />
</td>
        <td><br />
</td>
        <td>41<br />
</td>
        <td><br />
</td>
        <td>44<br />
</td>
        <td><br />
</td>
        <td>47<br />
</td>
    </tr>
    <tr>
        <td>cents diff<br />
</td>
        <td><br />
</td>
        <td>1586<br />
</td>
        <td><br />
</td>
        <td>814<br />
</td>
        <td><br />
</td>
        <td>551<br />
</td>
        <td><br />
</td>
        <td>418<br />
</td>
        <td><br />
</td>
        <td>336<br />
</td>
        <td><br />
</td>
        <td>281<br />
</td>
        <td><br />
</td>
        <td>242<br />
</td>
        <td><br />
</td>
        <td>212<br />
</td>
        <td><br />
</td>
        <td>189<br />
</td>
        <td><br />
</td>
        <td>170<br />
</td>
        <td><br />
</td>
        <td>155<br />
</td>
        <td><br />
</td>
        <td>142<br />
</td>
        <td><br />
</td>
        <td>132<br />
</td>
        <td><br />
</td>
        <td>122<br />
</td>
        <td><br />
</td>
        <td>114<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="isoharmonic chords--class iv"></a><!-- ws:end:WikiTextHeadingRule:8 -->class iv</h3>
 

<table class="wiki_table">
    <tr>
        <td>harmonic<br />
</td>
        <td>1<br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td>9<br />
</td>
        <td><br />
</td>
        <td>13<br />
</td>
        <td><br />
</td>
        <td>17<br />
</td>
        <td><br />
</td>
        <td>21<br />
</td>
        <td><br />
</td>
        <td>25<br />
</td>
        <td><br />
</td>
        <td>29<br />
</td>
        <td><br />
</td>
        <td>33<br />
</td>
        <td><br />
</td>
        <td>37<br />
</td>
        <td><br />
</td>
        <td>41<br />
</td>
        <td><br />
</td>
        <td>45<br />
</td>
        <td><br />
</td>
        <td>49<br />
</td>
        <td><br />
</td>
        <td>53<br />
</td>
        <td><br />
</td>
        <td>57<br />
</td>
        <td><br />
</td>
        <td>61<br />
</td>
    </tr>
    <tr>
        <td>cents diff<br />
</td>
        <td><br />
</td>
        <td>2786<br />
</td>
        <td><br />
</td>
        <td>1018<br />
</td>
        <td><br />
</td>
        <td>637<br />
</td>
        <td><br />
</td>
        <td>464<br />
</td>
        <td><br />
</td>
        <td>366<br />
</td>
        <td><br />
</td>
        <td>302<br />
</td>
        <td><br />
</td>
        <td>257<br />
</td>
        <td><br />
</td>
        <td>224<br />
</td>
        <td><br />
</td>
        <td>198<br />
</td>
        <td><br />
</td>
        <td>178<br />
</td>
        <td><br />
</td>
        <td>161<br />
</td>
        <td><br />
</td>
        <td>147<br />
</td>
        <td><br />
</td>
        <td>136<br />
</td>
        <td><br />
</td>
        <td>126<br />
</td>
        <td><br />
</td>
        <td>117<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />


<table class="wiki_table">
    <tr>
        <td>harmonic<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td>11<br />
</td>
        <td><br />
</td>
        <td>15<br />
</td>
        <td><br />
</td>
        <td>19<br />
</td>
        <td><br />
</td>
        <td>23<br />
</td>
        <td><br />
</td>
        <td>27<br />
</td>
        <td><br />
</td>
        <td>31<br />
</td>
        <td><br />
</td>
        <td>35<br />
</td>
        <td><br />
</td>
        <td>39<br />
</td>
        <td><br />
</td>
        <td>43<br />
</td>
        <td><br />
</td>
        <td>47<br />
</td>
        <td><br />
</td>
        <td>51<br />
</td>
        <td><br />
</td>
        <td>55<br />
</td>
        <td><br />
</td>
        <td>59<br />
</td>
        <td><br />
</td>
        <td>63<br />
</td>
    </tr>
    <tr>
        <td>cents diff<br />
</td>
        <td><br />
</td>
        <td>1467<br />
</td>
        <td><br />
</td>
        <td>782<br />
</td>
        <td><br />
</td>
        <td>537<br />
</td>
        <td><br />
</td>
        <td>409<br />
</td>
        <td><br />
</td>
        <td>331<br />
</td>
        <td><br />
</td>
        <td>278<br />
</td>
        <td><br />
</td>
        <td>239<br />
</td>
        <td><br />
</td>
        <td>210<br />
</td>
        <td><br />
</td>
        <td>187<br />
</td>
        <td><br />
</td>
        <td>169<br />
</td>
        <td><br />
</td>
        <td>154<br />
</td>
        <td><br />
</td>
        <td>141<br />
</td>
        <td><br />
</td>
        <td>131<br />
</td>
        <td><br />
</td>
        <td>122<br />
</td>
        <td><br />
</td>
        <td>114<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="isoharmonic chords--class v"></a><!-- ws:end:WikiTextHeadingRule:10 -->class v</h3>
 

<table class="wiki_table">
    <tr>
        <td>harmonic<br />
</td>
        <td>1<br />
</td>
        <td><br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td>11<br />
</td>
        <td><br />
</td>
        <td>16<br />
</td>
        <td><br />
</td>
        <td>21<br />
</td>
        <td><br />
</td>
        <td>26<br />
</td>
        <td><br />
</td>
        <td>31<br />
</td>
        <td><br />
</td>
        <td>36<br />
</td>
        <td><br />
</td>
        <td>41<br />
</td>
        <td><br />
</td>
        <td>46<br />
</td>
        <td><br />
</td>
        <td>51<br />
</td>
        <td><br />
</td>
        <td>56<br />
</td>
        <td><br />
</td>
        <td>61<br />
</td>
        <td><br />
</td>
        <td>66<br />
</td>
        <td><br />
</td>
        <td>71<br />
</td>
        <td><br />
</td>
        <td>76<br />
</td>
    </tr>
    <tr>
        <td>cents diff<br />
</td>
        <td><br />
</td>
        <td>3102<br />
</td>
        <td><br />
</td>
        <td>1049<br />
</td>
        <td><br />
</td>
        <td>649<br />
</td>
        <td><br />
</td>
        <td>471<br />
</td>
        <td><br />
</td>
        <td>370<br />
</td>
        <td><br />
</td>
        <td>306<br />
</td>
        <td><br />
</td>
        <td>259<br />
</td>
        <td><br />
</td>
        <td>225<br />
</td>
        <td><br />
</td>
        <td>199<br />
</td>
        <td><br />
</td>
        <td>179<br />
</td>
        <td><br />
</td>
        <td>162<br />
</td>
        <td><br />
</td>
        <td>148<br />
</td>
        <td><br />
</td>
        <td>136<br />
</td>
        <td><br />
</td>
        <td>126<br />
</td>
        <td><br />
</td>
        <td>118<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />


<table class="wiki_table">
    <tr>
        <td>harmonic<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td>12<br />
</td>
        <td><br />
</td>
        <td>17<br />
</td>
        <td><br />
</td>
        <td>22<br />
</td>
        <td><br />
</td>
        <td>27<br />
</td>
        <td><br />
</td>
        <td>32<br />
</td>
        <td><br />
</td>
        <td>37<br />
</td>
        <td><br />
</td>
        <td>42<br />
</td>
        <td><br />
</td>
        <td>47<br />
</td>
        <td><br />
</td>
        <td>52<br />
</td>
        <td><br />
</td>
        <td>57<br />
</td>
        <td><br />
</td>
        <td>62<br />
</td>
        <td><br />
</td>
        <td>67<br />
</td>
        <td><br />
</td>
        <td>72<br />
</td>
        <td><br />
</td>
        <td>77<br />
</td>
    </tr>
    <tr>
        <td>cents diff<br />
</td>
        <td><br />
</td>
        <td>2169<br />
</td>
        <td><br />
</td>
        <td>933<br />
</td>
        <td><br />
</td>
        <td>603<br />
</td>
        <td><br />
</td>
        <td>446<br />
</td>
        <td><br />
</td>
        <td>355<br />
</td>
        <td><br />
</td>
        <td>294<br />
</td>
        <td><br />
</td>
        <td>251<br />
</td>
        <td><br />
</td>
        <td>219<br />
</td>
        <td><br />
</td>
        <td>195<br />
</td>
        <td><br />
</td>
        <td>175<br />
</td>
        <td><br />
</td>
        <td>159<br />
</td>
        <td><br />
</td>
        <td>146<br />
</td>
        <td><br />
</td>
        <td>134<br />
</td>
        <td><br />
</td>
        <td>125<br />
</td>
        <td><br />
</td>
        <td>116<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />


<table class="wiki_table">
    <tr>
        <td>harmonic<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td>8<br />
</td>
        <td><br />
</td>
        <td>13<br />
</td>
        <td><br />
</td>
        <td>18<br />
</td>
        <td><br />
</td>
        <td>23<br />
</td>
        <td><br />
</td>
        <td>28<br />
</td>
        <td><br />
</td>
        <td>33<br />
</td>
        <td><br />
</td>
        <td>38<br />
</td>
        <td><br />
</td>
        <td>43<br />
</td>
        <td><br />
</td>
        <td>48<br />
</td>
        <td><br />
</td>
        <td>53<br />
</td>
        <td><br />
</td>
        <td>58<br />
</td>
        <td><br />
</td>
        <td>63<br />
</td>
        <td><br />
</td>
        <td>68<br />
</td>
        <td><br />
</td>
        <td>73<br />
</td>
        <td><br />
</td>
        <td>78<br />
</td>
    </tr>
    <tr>
        <td>cents diff<br />
</td>
        <td><br />
</td>
        <td>1698<br />
</td>
        <td><br />
</td>
        <td>841<br />
</td>
        <td><br />
</td>
        <td>563<br />
</td>
        <td><br />
</td>
        <td>424<br />
</td>
        <td><br />
</td>
        <td>341<br />
</td>
        <td><br />
</td>
        <td>284<br />
</td>
        <td><br />
</td>
        <td>244<br />
</td>
        <td><br />
</td>
        <td>214<br />
</td>
        <td><br />
</td>
        <td>190<br />
</td>
        <td><br />
</td>
        <td>172<br />
</td>
        <td><br />
</td>
        <td>156<br />
</td>
        <td><br />
</td>
        <td>143<br />
</td>
        <td><br />
</td>
        <td>132<br />
</td>
        <td><br />
</td>
        <td>123<br />
</td>
        <td><br />
</td>
        <td>115<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />


<table class="wiki_table">
    <tr>
        <td>harmonic<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td>9<br />
</td>
        <td><br />
</td>
        <td>14<br />
</td>
        <td><br />
</td>
        <td>19<br />
</td>
        <td><br />
</td>
        <td>24<br />
</td>
        <td><br />
</td>
        <td>29<br />
</td>
        <td><br />
</td>
        <td>34<br />
</td>
        <td><br />
</td>
        <td>39<br />
</td>
        <td><br />
</td>
        <td>44<br />
</td>
        <td><br />
</td>
        <td>49<br />
</td>
        <td><br />
</td>
        <td>54<br />
</td>
        <td><br />
</td>
        <td>59<br />
</td>
        <td><br />
</td>
        <td>64<br />
</td>
        <td><br />
</td>
        <td>69<br />
</td>
        <td><br />
</td>
        <td>74<br />
</td>
        <td><br />
</td>
        <td>79<br />
</td>
    </tr>
    <tr>
        <td>cents diff<br />
</td>
        <td><br />
</td>
        <td>1404<br />
</td>
        <td><br />
</td>
        <td>765<br />
</td>
        <td><br />
</td>
        <td>529<br />
</td>
        <td><br />
</td>
        <td>404<br />
</td>
        <td><br />
</td>
        <td>328<br />
</td>
        <td><br />
</td>
        <td>275<br />
</td>
        <td><br />
</td>
        <td>238<br />
</td>
        <td><br />
</td>
        <td>209<br />
</td>
        <td><br />
</td>
        <td>186<br />
</td>
        <td><br />
</td>
        <td>168<br />
</td>
        <td><br />
</td>
        <td>153<br />
</td>
        <td><br />
</td>
        <td>141<br />
</td>
        <td><br />
</td>
        <td>130<br />
</td>
        <td><br />
</td>
        <td>121<br />
</td>
        <td><br />
</td>
        <td>113<br />
</td>
        <td><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:guest|guest]] and made on <tt>2010-03-30 13:27:54 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2010-04-22 13:16:33 UTC</tt>.<br>
-: The original revision id was <tt>131380685</tt>.<br>
+: The original revision id was <tt>136399925</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 33: / Line 33: @@
 || cents diff ||   || 1586 ||   || 814 ||   || 551 ||   || 418 ||   || 336 ||   || 281 ||   || 242 ||   || 212 ||   || 189 ||   || 170 ||   || 155 ||   || 142 ||   || 132 ||   || 122 ||   || 114 ||   ||
+===class iv===
+|| harmonic || 1 ||   || 5 ||   || 9 ||   || 13 ||   || 17 ||   || 21 ||   || 25 ||   || 29 ||   || 33 ||   || 37 ||   || 41 ||   || 45 ||   || 49 ||   || 53 ||   || 57 ||   || 61 ||
+|| cents diff ||   || 2786 ||   || 1018 ||   || 637 ||   || 464 ||   || 366 ||   || 302 ||   || 257 ||   || 224 ||   || 198 ||   || 178 ||   || 161 ||   || 147 ||   || 136 ||   || 126 ||   || 117 ||   ||
-===class iv and beyond===
+|| harmonic || 3 ||   || 7 ||   || 11 ||   || 15 ||   || 19 ||   || 23 ||   || 27 ||   || 31 ||   || 35 ||   || 39 ||   || 43 ||   || 47 ||   || 51 ||   || 55 ||   || 59 ||   || 63 ||
-...explore for yourself!</pre></div>
+|| cents diff ||   || 1467 ||   || 782 ||   || 537 ||   || 409 ||   || 331 ||   || 278 ||   || 239 ||   || 210 ||   || 187 ||   || 169 ||   || 154 ||   || 141 ||   || 131 ||   || 122 ||   || 114 ||   ||
+===class v===
+|| harmonic || 1 ||   || 6 ||   || 11 ||   || 16 ||   || 21 ||   || 26 ||   || 31 ||   || 36 ||   || 41 ||   || 46 ||   || 51 ||   || 56 ||   || 61 ||   || 66 ||   || 71 ||   || 76 ||
+|| cents diff ||   || 3102 ||   || 1049 ||   || 649 ||   || 471 ||   || 370 ||   || 306 ||   || 259 ||   || 225 ||   || 199 ||   || 179 ||   || 162 ||   || 148 ||   || 136 ||   || 126 ||   || 118 ||   ||
+|| harmonic || 2 ||   || 7 ||   || 12 ||   || 17 ||   || 22 ||   || 27 ||   || 32 ||   || 37 ||   || 42 ||   || 47 ||   || 52 ||   || 57 ||   || 62 ||   || 67 ||   || 72 ||   || 77 ||
+|| cents diff ||   || 2169 ||   || 933 ||   || 603 ||   || 446 ||   || 355 ||   || 294 ||   || 251 ||   || 219 ||   || 195 ||   || 175 ||   || 159 ||   || 146 ||   || 134 ||   || 125 ||   || 116 ||   ||
+|| harmonic || 3 ||   || 8 ||   || 13 ||   || 18 ||   || 23 ||   || 28 ||   || 33 ||   || 38 ||   || 43 ||   || 48 ||   || 53 ||   || 58 ||   || 63 ||   || 68 ||   || 73 ||   || 78 ||
+|| cents diff ||   || 1698 ||   || 841 ||   || 563 ||   || 424 ||   || 341 ||   || 284 ||   || 244 ||   || 214 ||   || 190 ||   || 172 ||   || 156 ||   || 143 ||   || 132 ||   || 123 ||   || 115 ||   ||
+|| harmonic || 4 ||   || 9 ||   || 14 ||   || 19 ||   || 24 ||   || 29 ||   || 34 ||   || 39 ||   || 44 ||   || 49 ||   || 54 ||   || 59 ||   || 64 ||   || 69 ||   || 74 ||   || 79 ||
+|| cents diff ||   || 1404 ||   || 765 ||   || 529 ||   || 404 ||   || 328 ||   || 275 ||   || 238 ||   || 209 ||   || 186 ||   || 168 ||   || 153 ||   || 141 ||   || 130 ||   || 121 ||   || 113 ||   ||</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;isoharmonic chords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="isoharmonic chords"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;isoharmonic chords&lt;/h1&gt;
@@ Line 604: / Line 620: @@
 &lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="isoharmonic chords--class iv"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;class iv&lt;/h3&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;td&gt;harmonic&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;17&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;25&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;29&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;33&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;37&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;41&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;45&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;49&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;53&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;57&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;61&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;cents diff&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2786&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1018&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;637&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;464&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;366&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;302&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;257&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;224&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;198&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;178&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;161&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;147&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;136&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;126&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;117&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;td&gt;harmonic&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;19&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;23&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;27&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;31&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;35&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;39&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;43&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;47&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;51&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;55&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;59&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;63&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;cents diff&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1467&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;782&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;537&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;409&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;331&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;278&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;239&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;210&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;187&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;169&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;154&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;141&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;131&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;122&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;114&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="isoharmonic chords--class v"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;class v&lt;/h3&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;td&gt;harmonic&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;16&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;26&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;31&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;36&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;41&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;46&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;51&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;56&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;61&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;66&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;71&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;76&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;cents diff&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3102&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1049&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;649&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;471&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;370&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;306&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;259&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;225&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;199&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;179&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;162&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;148&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;136&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;126&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;118&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;td&gt;harmonic&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;17&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;22&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;27&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;32&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;37&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;42&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;47&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;52&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;57&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;62&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;67&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;77&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;cents diff&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2169&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;933&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;603&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;446&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;355&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;294&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;251&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;219&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;195&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;175&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;159&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;146&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;134&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;125&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;116&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="isoharmonic chords--class iv and beyond"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;class iv and beyond&lt;/h3&gt;
- ...explore for yourself!&lt;/body&gt;&lt;/html&gt;</pre></div>
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;td&gt;harmonic&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;18&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;23&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;28&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;33&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;38&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;43&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;48&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;53&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;58&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;63&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;68&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;73&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;78&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;cents diff&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1698&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;841&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;563&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;424&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;341&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;284&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;244&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;214&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;190&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;172&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;156&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;143&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;132&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;123&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;115&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;td&gt;harmonic&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;19&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;24&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;29&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;34&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;39&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;44&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;49&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;54&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;59&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;69&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;74&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;79&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;cents diff&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1404&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;765&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;529&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;404&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;328&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;275&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;238&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;209&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;186&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;168&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;153&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;141&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;130&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;121&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;113&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;/body&gt;&lt;/html&gt;</pre></div>

Isoharmonic chord: Difference between revisions

Revision as of 13:16, 22 April 2010

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

Navigation menu

Search