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Wikispaces>Andrew_Heathwaite **Imported revision 165734929 - Original comment: added table - incomplete as of now** |
Wikispaces>xenwolf **Imported revision 165746295 - Original comment: off-by-1-error fixed ;-)** |
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| Line 1: | Line 1: | ||
<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-09-27 13:38:09 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>165746295</tt>.<br> | ||
: The revision comment was: <tt> | : The revision comment was: <tt>off-by-1-error fixed ;-)</tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
| Line 21: | Line 21: | ||
||~ Degree ||~ 88cET ||~ 41edo ||~ 8th Root of 3:2 ||~ Some Nearby JI Intervals || | ||~ Degree ||~ 88cET ||~ 41edo ||~ 8th Root of 3:2 ||~ Some Nearby JI Intervals || | ||
|| | || 1 || 88 || 87.805 || || || | ||
|| | || 2 || 176 || 175.610 || || || | ||
|| | || 3 || 264 || 263.415 || || || | ||
|| | || 4 || 352 || 351.220 || || || | ||
|| | || 5 || 440 || 439.024 || || || | ||
|| | || 6 || 528 || 526.829 || || || | ||
|| | || 7 || 616 || 614.634 || || || | ||
|| | || 8 || 704 || 702.439 || 701.955 || || | ||
|| | || 9 || 792 || 790.244 || || || | ||
|| | || 10 || 880 || 878.049 || || || | ||
|| | || 11 || 968 || 965.854 || || || | ||
|| | || 12 || 1056 || 1053.659 || || || | ||
|| | || 13 || 1144 || 1141.463 || || || | ||
||||||||||~ second octave || | ||||||||||~ second octave || | ||
|| | || 14 || 32 || 29.268 || || || | ||
|| | || 15 || 120 || || || || | ||
|| | || 16 || 208 || || || || | ||
|| | || 17 || 296 || || || || | ||
|| | || 18 || 384 || || || || | ||
|| | || 19 || 472 || || || || | ||
|| | || 20 || 560 || || || || | ||
|| | || 21 || 648 || || || || | ||
|| | || 22 || 736 || || || || | ||
|| | || 23 || 824 || || || || | ||
|| | || 24 || 912 || || || || | ||
|| | || 25 || 1000 || || || || | ||
|| | || 26 || 1088 || || || || | ||
|| | || 27 || 1176 || || || || | ||
||||||||||~ third octave || | ||||||||||~ third octave || | ||
|| | || 28 || 64 || || || || | ||
|| | || 29 || 152 || || || || | ||
|| | || 30 || 240 || || || || | ||
|| | || 31 || 328 || || || || | ||
|| | || 32 || 416 || || || || | ||
|| | || 33 || 504 || || || || | ||
|| | || 34 || 592 || || || || | ||
|| | || 35 || 680 || || || || | ||
|| | || 36 || 768 || || || || | ||
|| | || 37 || 856 || || || || | ||
|| | || 38 || 944 || || || || | ||
|| | || 39 || 1032 || || || || | ||
|| | || 40 || 1120 || || || || | ||
||||||||||~ fourth octave (near match) || | ||||||||||~ fourth octave (near match) || | ||
|| | || 41 || 8 || || || || | ||
==Compositions== | ==Compositions== | ||
| Line 102: | Line 102: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>1<br /> | ||
</td> | </td> | ||
<td>88<br /> | <td>88<br /> | ||
| Line 114: | Line 114: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>2<br /> | ||
</td> | </td> | ||
<td>176<br /> | <td>176<br /> | ||
| Line 126: | Line 126: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>3<br /> | ||
</td> | </td> | ||
<td>264<br /> | <td>264<br /> | ||
| Line 138: | Line 138: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>4<br /> | ||
</td> | </td> | ||
<td>352<br /> | <td>352<br /> | ||
| Line 150: | Line 150: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>5<br /> | ||
</td> | </td> | ||
<td>440<br /> | <td>440<br /> | ||
| Line 162: | Line 162: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>6<br /> | ||
</td> | </td> | ||
<td>528<br /> | <td>528<br /> | ||
| Line 174: | Line 174: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>7<br /> | ||
</td> | </td> | ||
<td>616<br /> | <td>616<br /> | ||
| Line 186: | Line 186: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>8<br /> | ||
</td> | </td> | ||
<td>704<br /> | <td>704<br /> | ||
| Line 198: | Line 198: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>9<br /> | ||
</td> | </td> | ||
<td>792<br /> | <td>792<br /> | ||
| Line 210: | Line 210: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>10<br /> | ||
</td> | </td> | ||
<td>880<br /> | <td>880<br /> | ||
| Line 222: | Line 222: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>11<br /> | ||
</td> | </td> | ||
<td>968<br /> | <td>968<br /> | ||
| Line 234: | Line 234: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>12<br /> | ||
</td> | </td> | ||
<td>1056<br /> | <td>1056<br /> | ||
| Line 246: | Line 246: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>13<br /> | ||
</td> | </td> | ||
<td>1144<br /> | <td>1144<br /> | ||
| Line 262: | Line 262: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>14<br /> | ||
</td> | </td> | ||
<td>32<br /> | <td>32<br /> | ||
| Line 274: | Line 274: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>15<br /> | ||
</td> | </td> | ||
<td>120<br /> | <td>120<br /> | ||
| Line 286: | Line 286: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>16<br /> | ||
</td> | </td> | ||
<td>208<br /> | <td>208<br /> | ||
| Line 298: | Line 298: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>17<br /> | ||
</td> | </td> | ||
<td>296<br /> | <td>296<br /> | ||
| Line 310: | Line 310: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>18<br /> | ||
</td> | </td> | ||
<td>384<br /> | <td>384<br /> | ||
| Line 322: | Line 322: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>19<br /> | ||
</td> | </td> | ||
<td>472<br /> | <td>472<br /> | ||
| Line 334: | Line 334: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>20<br /> | ||
</td> | </td> | ||
<td>560<br /> | <td>560<br /> | ||
| Line 346: | Line 346: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>21<br /> | ||
</td> | </td> | ||
<td>648<br /> | <td>648<br /> | ||
| Line 358: | Line 358: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>22<br /> | ||
</td> | </td> | ||
<td>736<br /> | <td>736<br /> | ||
| Line 370: | Line 370: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>23<br /> | ||
</td> | </td> | ||
<td>824<br /> | <td>824<br /> | ||
| Line 382: | Line 382: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>24<br /> | ||
</td> | </td> | ||
<td>912<br /> | <td>912<br /> | ||
| Line 394: | Line 394: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>25<br /> | ||
</td> | </td> | ||
<td>1000<br /> | <td>1000<br /> | ||
| Line 406: | Line 406: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>26<br /> | ||
</td> | </td> | ||
<td>1088<br /> | <td>1088<br /> | ||
| Line 418: | Line 418: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>27<br /> | ||
</td> | </td> | ||
<td>1176<br /> | <td>1176<br /> | ||
| Line 434: | Line 434: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>28<br /> | ||
</td> | </td> | ||
<td>64<br /> | <td>64<br /> | ||
| Line 446: | Line 446: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>29<br /> | ||
</td> | </td> | ||
<td>152<br /> | <td>152<br /> | ||
| Line 458: | Line 458: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>30<br /> | ||
</td> | </td> | ||
<td>240<br /> | <td>240<br /> | ||
| Line 470: | Line 470: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>31<br /> | ||
</td> | </td> | ||
<td>328<br /> | <td>328<br /> | ||
| Line 482: | Line 482: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>32<br /> | ||
</td> | </td> | ||
<td>416<br /> | <td>416<br /> | ||
| Line 494: | Line 494: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>33<br /> | ||
</td> | </td> | ||
<td>504<br /> | <td>504<br /> | ||
| Line 506: | Line 506: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>34<br /> | ||
</td> | </td> | ||
<td>592<br /> | <td>592<br /> | ||
| Line 518: | Line 518: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>35<br /> | ||
</td> | </td> | ||
<td>680<br /> | <td>680<br /> | ||
| Line 530: | Line 530: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>36<br /> | ||
</td> | </td> | ||
<td>768<br /> | <td>768<br /> | ||
| Line 542: | Line 542: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>37<br /> | ||
</td> | </td> | ||
<td>856<br /> | <td>856<br /> | ||
| Line 554: | Line 554: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>38<br /> | ||
</td> | </td> | ||
<td>944<br /> | <td>944<br /> | ||
| Line 566: | Line 566: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>39<br /> | ||
</td> | </td> | ||
<td>1032<br /> | <td>1032<br /> | ||
| Line 578: | Line 578: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>40<br /> | ||
</td> | </td> | ||
<td>1120<br /> | <td>1120<br /> | ||
| Line 594: | Line 594: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>41<br /> | ||
</td> | </td> | ||
<td>8<br /> | <td>8<br /> | ||
Revision as of 13:38, 27 September 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 xenwolf and made on 2010-09-27 13:38:09 UTC.
- The original revision id was 165746295.
- The revision comment was: off-by-1-error fixed ;-)
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
=88cET= ==Theory== 88 cent equal temperament uses 88 cents, or 11/150 of an octave, to generate a nonoctave rank one scale. Since 88 cents is an excellent generator for [[Tetracot family|octacot temperament]], it can be viewed as the generator chain of octacot, stripped of octaves. However viewed, octacot and 88 cents equal temperament are very closely related. Eight steps of 88 cents gives 704 cents, two cents sharp of 3/2, and eighteen gives 1584 cents, two cents flat of 5/2. Taken together this tells us that (5/2)^4/(3/2)^9 = 20000/19683, the minimal diesis or tetracot comma, must be being tempered out. Eleven steps of 88 cents gives 968 cents, less than a cent flat of 7/4, and this tells us that (7/4)^8/(3/2)^11 = 5764801/5668704 must be tempered out also. Taking this, multiplying it by the tetracot comma and taking the fourth root yields 245/243, which therefore must be tempered out also. The tetracot comma and 245/243 taken together define 7-limit octacot. Continuing on, twenty steps of 88 cents gives 1760 cents, whioh we may compare to the 1751.3 cents of 11/4 and suggests 100/99 being tempered out, and four steps gives 352 cents, which may be compared to the 359.5 cents of 16/13, and suggestes 325/324 being tempered out. These would give an extended octacot, for which 88 cents would be an excellent generator tuning. ==Intervals== 88cET is considered a very consonant tuning, and you will find that many of its intervals fall very close to simple ratios in 7- and 11-limit just intonation. It is also extremely close to [[41edo]], which is itself extremely close to the 8th root of 3:2 (a perfect fifth divided into exactly 8 logarithmically equal steps). See chart: ||~ Degree ||~ 88cET ||~ 41edo ||~ 8th Root of 3:2 ||~ Some Nearby JI Intervals || || 1 || 88 || 87.805 || || || || 2 || 176 || 175.610 || || || || 3 || 264 || 263.415 || || || || 4 || 352 || 351.220 || || || || 5 || 440 || 439.024 || || || || 6 || 528 || 526.829 || || || || 7 || 616 || 614.634 || || || || 8 || 704 || 702.439 || 701.955 || || || 9 || 792 || 790.244 || || || || 10 || 880 || 878.049 || || || || 11 || 968 || 965.854 || || || || 12 || 1056 || 1053.659 || || || || 13 || 1144 || 1141.463 || || || ||||||||||~ second octave || || 14 || 32 || 29.268 || || || || 15 || 120 || || || || || 16 || 208 || || || || || 17 || 296 || || || || || 18 || 384 || || || || || 19 || 472 || || || || || 20 || 560 || || || || || 21 || 648 || || || || || 22 || 736 || || || || || 23 || 824 || || || || || 24 || 912 || || || || || 25 || 1000 || || || || || 26 || 1088 || || || || || 27 || 1176 || || || || ||||||||||~ third octave || || 28 || 64 || || || || || 29 || 152 || || || || || 30 || 240 || || || || || 31 || 328 || || || || || 32 || 416 || || || || || 33 || 504 || || || || || 34 || 592 || || || || || 35 || 680 || || || || || 36 || 768 || || || || || 37 || 856 || || || || || 38 || 944 || || || || || 39 || 1032 || || || || || 40 || 1120 || || || || ||||||||||~ fourth octave (near match) || || 41 || 8 || || || || ==Compositions== [[http://www.seraph.it/dep/det/88east.mp3|88 East]] by [[Carlo Serafini]] [[http://www.seraph.it/dep/det/88vocoeast.mp3|88 VocoEast]] by [[Carlo Serafini]] [[http://www.seraph.it/dep/det/88Bulgarians.mp3|88 Bulgarians]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/9660ca3450a996ea8b55713cbf36151f-15.html|blog entry]]) [[http://www.seraph.it/dep/int/88jinglebells.mp3|88 Jingle Bells]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/495ec175ce56cf38cb399d1cd24db164-17.html|blog entry]])
Original HTML content:
<html><head><title>88cET</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x88cET"></a><!-- ws:end:WikiTextHeadingRule:0 -->88cET</h1>
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x88cET-Theory"></a><!-- ws:end:WikiTextHeadingRule:2 -->Theory</h2>
<br />
88 cent equal temperament uses 88 cents, or 11/150 of an octave, to generate a nonoctave rank one scale. Since 88 cents is an excellent generator for <a class="wiki_link" href="/Tetracot%20family">octacot temperament</a>, it can be viewed as the generator chain of octacot, stripped of octaves. However viewed, octacot and 88 cents equal temperament are very closely related.<br />
<br />
Eight steps of 88 cents gives 704 cents, two cents sharp of 3/2, and eighteen gives 1584 cents, two cents flat of 5/2. Taken together this tells us that (5/2)^4/(3/2)^9 = 20000/19683, the minimal diesis or tetracot comma, must be being tempered out. Eleven steps of 88 cents gives 968 cents, less than a cent flat of 7/4, and this tells us that (7/4)^8/(3/2)^11 = 5764801/5668704 must be tempered out also. Taking this, multiplying it by the tetracot comma and taking the fourth root yields 245/243, which therefore must be tempered out also. The tetracot comma and 245/243 taken together define 7-limit octacot. <br />
<br />
Continuing on, twenty steps of 88 cents gives 1760 cents, whioh we may compare to the 1751.3 cents of 11/4 and suggests 100/99 being tempered out, and four steps gives 352 cents, which may be compared to the 359.5 cents of 16/13, and suggestes 325/324 being tempered out. These would give an extended octacot, for which 88 cents would be an excellent generator tuning.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x88cET-Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h2>
<br />
88cET is considered a very consonant tuning, and you will find that many of its intervals fall very close to simple ratios in 7- and 11-limit just intonation. It is also extremely close to <a class="wiki_link" href="/41edo">41edo</a>, which is itself extremely close to the 8th root of 3:2 (a perfect fifth divided into exactly 8 logarithmically equal steps). See chart:<br />
<br />
<table class="wiki_table">
<tr>
<th>Degree<br />
</th>
<th>88cET<br />
</th>
<th>41edo<br />
</th>
<th>8th Root of 3:2<br />
</th>
<th>Some Nearby JI Intervals<br />
</th>
</tr>
<tr>
<td>1<br />
</td>
<td>88<br />
</td>
<td>87.805<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>176<br />
</td>
<td>175.610<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>264<br />
</td>
<td>263.415<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>352<br />
</td>
<td>351.220<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>440<br />
</td>
<td>439.024<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>528<br />
</td>
<td>526.829<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>616<br />
</td>
<td>614.634<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>704<br />
</td>
<td>702.439<br />
</td>
<td>701.955<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>792<br />
</td>
<td>790.244<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>880<br />
</td>
<td>878.049<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>968<br />
</td>
<td>965.854<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>1056<br />
</td>
<td>1053.659<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>1144<br />
</td>
<td>1141.463<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<th colspan="5">second octave<br />
</th>
</tr>
<tr>
<td>14<br />
</td>
<td>32<br />
</td>
<td>29.268<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>120<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>208<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>296<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>384<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>472<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>560<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>648<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>736<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>824<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>912<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>1000<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>1088<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>1176<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<th colspan="5">third octave<br />
</th>
</tr>
<tr>
<td>28<br />
</td>
<td>64<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>152<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>240<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>328<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>416<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>504<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>592<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>680<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>768<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>856<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>944<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>1032<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>1120<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<th colspan="5">fourth octave (near match)<br />
</th>
</tr>
<tr>
<td>41<br />
</td>
<td>8<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x88cET-Compositions"></a><!-- ws:end:WikiTextHeadingRule:6 -->Compositions</h2>
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