1ed88c
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 2011-09-09 21:59:09 UTC.
- The original revision id was 252536858.
- 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:
=[[media type="custom" key="9458032"]]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, which 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 suggests 325/324 being tempered out. These would give an extended octacot, for which 88 cents would be an excellent generator tuning. ==The 88cET family== Gary Morrison originally conceived of 88cET as composed of steps of exactly 88¢. Nonetheless, composers have recognized a kinship between strict 88cET and some other scales -- in particular, the 41st root of 8 (equivalent to taking three steps of [[41edo]] as a generator with no octaves), the 8th root of 3/2, and the 11th root of 7/4, the latter being a preferred variant of composer and software designer X. J. Scott. These three cousins of strict 88cET have single steps of approximately 87.805¢, 87.744¢, and 88.075¢, respectively. These small differences add up, as can be seen by examining the interval list below. ==Intervals== ||~ Degree ||~ 11th root of 7/4 ||~ 88cET ||~ 41st root of 8 (41ed8) ||~ 8th root of 3/2 ||~ Solfege ||~ Some Nearby || ||~ ||~ ||~ ||~ ||~ ||~ syllable ||~ JI Intervals || ||||||||||||~ **//first octave//** ||~ || || 0 || 0 || 0 || 0 || 0 || do || 1/1=0 || || 1 || 88.075 || 88 || 87.805 || 87.744 || rih || 22/21=80.537, 21/20=84.467, 20/19=88.801, 19/18=93.603 || || 2 || 176.15 || 176 || 175.610 || 175.489 || reh || [[11_10|11/10]]=165.004, 21/19=173.268, [[10_9|10/9]]=182.404 || || 3 || 264.225 || 264 || 263.415 || 263.233 || ma || [[7_6|7/6]]=266.871 || || 4 || 352.3 || 352 || 351.220 || 350.978 || mu || [[11_9|11/9]]= 347.408, 27/22=354.547, 16/13=359.472 || || 5 || 440.375 || 440 || 439.024 || 438.722 || mo || 32/25=427.373, [[9_7|9/7]]=435.084, 22/17 446.363 || || 6 || 528.45 || 528 || 526.829 || 526.466 || fih || 19/14=528.687, 49/36=533.742, [[15_11|15/11]]=536.95 || || 7 || 616.526 || 616 || 614.634 || 614.211 || se || [[10_7|10/7]]=617.488 || || 8 || 704.601 || 704 || 702.439 || 701.955 || sol || [[3_2|3/2]]=701.955 || || 9 || 792.676 || 792 || 790.244 || 789.699 || leh || [[11_7|11/7]]=782.492, 30/19=790.756, 128/81=792.180, 19/12=795.558, 27/17=800.910, [[8_5|8/5]]=813.686 || || 10 || 880.751 || 880 || 878.049 || 878.444 || la || [[5_3|5/3]]=884.359 || || 11 || 968.826 || 968 || 965.854 || 965.188 || ta || [[7_4|7/4]]=968.826 || || 12 || 1056.901 || 1056 || 1053.659 || 1052.933 || tu || [[11_6|11/6]]=1049.363, 35/19=1057.627, 24/13=1061.427 || || 13 || 1144.976 || 1144 || 1141.463 || 1140.677 || to || 27/14=1137.039, 31/16=1145.036 || ||||||||||||~ **//second octave//** ||~ || || 14 || 33.051 || 32 || 29.268 || 28.421 || di || 65/64=26.841, 64/63=27.264, 63/62=27.700, 58/57=30.109 || || 15 || 121.126 || 120 || 117.073 || 116.166 || ra || 16/15=111.731, 15/14=119.443, 14/13=128.298 || || 16 || 209.201 || 208 || 204.878 || 203.910 || re || 9/8=203.910 || || 17 || 297.276 || 296 || 292.683 || 291.654 || meh || 13/11=289.210, 32/27=294.135, 19/16=297.513 || || 18 || 385.351 || 384 || 380.488 || 379.399 || mi || 5/4=386.314 || || 19 || 473.427 || 472 || 468.293 || 467.143 || fe || 17/13=464.428, 21/16=470.781 || || 20 || 561.502 || 560 || 556.098 || 554.888 || fu || 11/8=551.318, 18/13=563.382 || || 21 || 649.577 || 648 || 643.902 || 642.632 || su || 16/11=648.682 || || 22 || 737.652 || 736 || 731.707 || 730.376 || si || 32/21=729.219, 26/17=735.572, 49/32=737.652 || || 23 || 825.727 || 824 || 819.512 || 818.121 || le || 8/5=813.686, 45/28=821.398, 21/13=830.253 || || 24 || 913.802 || 912 || 907.317 || 905.865 || laa || 42/25=898.153, 32/19=902.487, 27/16=905.865, 22/13=910.790, 17/10=918.642 || || 25 || 1001.877 || 1000 || 995.122 || 993.609 || teh || 39/22=991.165, 16/9=996.090, 25/14=1003.802, 34/19=1007.442 || || 26 || 1089.952 || 1088 || 1082.927 || 1081.354 || ti || 28/15=1080.557, 15/8=1088.269 || || 27 || 1178.027 || 1176 || 1170.732 || 1169.098 || da || 63/32=1172.736, 160/81=1178.494 || ||||||||||||~ **//third octave//** ||~ || || 28 || 66.102 || 64 || 58.537 || 56.843 || ro || 33/3253.273, 28/27=62.961, 80/77=66.170, 27/26=65.337 || || 29 || 154.177 || 152 || 146.341 || 144.587 || ru || 49/45=147.428, 12/11=150.637, 35/32=155.140 || || 30 || 242.252 || 240 || 234.146 || 232.331 || ri || 8/7=231.174, 23/20=241.961, 15/13=247.741 || || 31 || 330.328 || 328 || 321.951 || 320.076 || me || 6/5=315.641, 23/19=330.761 || || 32 || 418.403 || 416 || 409.756 || 407.820 || maa || 81/64=407.820, 33/26=412.745, 14/11=417.508 || || 33 || 506.478 || 504 || 497.561 || 495.564 || fa || 85/64=491.269, 4/3=498.045, 75/56=505.757 || || 34 || 594.553 || 592 || 585.366 || 583.309 || fi || 7/5=582.512, 45/32=590.224, 38/27=591.648 || || 35 || 682.628 || 680 || 673.171 || 671.053 || sih || 28/19=671.313, 40/27=680.449 || || 36 || 770.703 || 768 || 760.976 || 758.798 || lo || 17/11=753.637, 99/64=755.228, 14/9=764.916, 39/25=769.855, 25/16=772.627 || || 37 || 858.778 || 856 || 848.780 || 846.542 || lu || 13/8=840.528, 18/11=852.592 || || 38 || 946.853 || 944 || 936.585 || 934.286 || li || 12/7=933.129, 19/11=946.195 || || 39 || 1034.928 || 1032 || 1024.390 || 1022.031 || te || 9/5=1017.596, 49/27=1031.787, 20/11=1034.996 || || 40 || 1123.003 || 1120 || 1112.195 || 1109.775 || taa || 36/19=1106.397, 243/128=1109.775, 19/10=1111.199, 21/11=1119.463 || ||||||||||||~ **//fourth octave//** (near match) ||~ || || 41 || 11.078 || 8 || 0 || 1197.59 || do || 1/1=0, 2/1=1200 || ==Compositions== <span class="ymp-btn-page-play ymp-media-495785593852bb775b5c611348abe945">[[http://www.seraph.it/dep/det/88east.mp3|88 East]] </span> by [[Carlo Serafini]] <span class="ymp-btn-page-play ymp-media-0eec9409132570e087858a748b80b969">[[http://www.seraph.it/dep/det/88vocoeast.mp3|88 VocoEast]] </span> by [[Carlo Serafini]] <span class="ymp-btn-page-play ymp-media-a43b46e2ba54959d045772c4e452232c">[[http://www.seraph.it/dep/det/88Bulgarians.mp3|88 Bulgarians]] </span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/9660ca3450a996ea8b55713cbf36151f-15.html|blog entry]]) <span class="ymp-btn-page-play ymp-media-db5d569ced088a975707d1a1ba01c739">[[http://www.seraph.it/dep/int/88jinglebells.mp3|88 Jingle Bells]] </span> by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/495ec175ce56cf38cb399d1cd24db164-17.html|blog entry]]) <span class="ymp-btn-page-play ymp-media-e32c31e0585b669853d287adb8753ae8">[[http://micro.soonlabel.com/88cent_nonoctave/STE-004_88_cent_guitar.mp3|88 cent guitar improvisation]]</span> by [[@http://www.chrisvaisvil.com|Chris Vaisvil]] <span class="ymp-btn-page-play ymp-media-bb747291b4a026593ee10b7c928912e4">[[http://micro.soonlabel.com/88cent_nonoctave/Prelude_in_88_Cent_Tuning.mp3|A Simple Prelude for 88 Cent Piano]]</span> by [[http://chrisvaisvil.com/?p=951|Chris Vaisvil]] ([[http://micro.soonlabel.com/88cent_nonoctave/A_Simple_Prelude_in_88_Cent_Tuning.pdf|scordata]])
Original HTML content:
<html><head><title>88cET</title></head><body><!-- ws:start:WikiTextHeadingRule:1:<h1> --><h1 id="toc0"><a name="x88cET"></a><!-- ws:end:WikiTextHeadingRule:1 --><!-- ws:start:WikiTextMediaRule:0:<img src="http://www.wikispaces.com/site/embedthumbnail/custom/9458032?h=0&w=0" class="WikiMedia WikiMediaCustom" id="wikitext@@media@@type=&quot;custom&quot; key=&quot;9458032&quot;" title="Custom Media"/> --><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js">
</script><!-- ws:end:WikiTextMediaRule:0 -->88cET</h1>
<br />
<!-- ws:start:WikiTextHeadingRule:3:<h2> --><h2 id="toc1"><a name="x88cET-Theory"></a><!-- ws:end:WikiTextHeadingRule:3 -->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, which 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 suggests 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:5:<h2> --><h2 id="toc2"><a name="x88cET-The 88cET family"></a><!-- ws:end:WikiTextHeadingRule:5 -->The 88cET family</h2>
<br />
Gary Morrison originally conceived of 88cET as composed of steps of exactly 88¢. Nonetheless, composers have recognized a kinship between strict 88cET and some other scales -- in particular, the 41st root of 8 (equivalent to taking three steps of <a class="wiki_link" href="/41edo">41edo</a> as a generator with no octaves), the 8th root of 3/2, and the 11th root of 7/4, the latter being a preferred variant of composer and software designer X. J. Scott. These three cousins of strict 88cET have single steps of approximately 87.805¢, 87.744¢, and 88.075¢, respectively. These small differences add up, as can be seen by examining the interval list below.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:7:<h2> --><h2 id="toc3"><a name="x88cET-Intervals"></a><!-- ws:end:WikiTextHeadingRule:7 -->Intervals</h2>
<br />
<table class="wiki_table">
<tr>
<th>Degree<br />
</th>
<th>11th root<br />
of 7/4<br />
</th>
<th>88cET<br />
</th>
<th>41st root of 8<br />
(41ed8)<br />
</th>
<th>8th root<br />
of 3/2<br />
</th>
<th>Solfege<br />
</th>
<th>Some Nearby<br />
</th>
</tr>
<tr>
<th><br />
</th>
<th><br />
</th>
<th><br />
</th>
<th><br />
</th>
<th><br />
</th>
<th>syllable<br />
</th>
<th>JI Intervals<br />
</th>
</tr>
<tr>
<th colspan="6"><strong><em>first octave</em></strong><br />
</th>
<th><br />
</th>
</tr>
<tr>
<td>0<br />
</td>
<td>0<br />
</td>
<td>0<br />
</td>
<td>0<br />
</td>
<td>0<br />
</td>
<td>do<br />
</td>
<td>1/1=0<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>88.075<br />
</td>
<td>88<br />
</td>
<td>87.805<br />
</td>
<td>87.744<br />
</td>
<td>rih<br />
</td>
<td>22/21=80.537, 21/20=84.467, 20/19=88.801, 19/18=93.603<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>176.15<br />
</td>
<td>176<br />
</td>
<td>175.610<br />
</td>
<td>175.489<br />
</td>
<td>reh<br />
</td>
<td><a class="wiki_link" href="/11_10">11/10</a>=165.004, 21/19=173.268, <a class="wiki_link" href="/10_9">10/9</a>=182.404<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>264.225<br />
</td>
<td>264<br />
</td>
<td>263.415<br />
</td>
<td>263.233<br />
</td>
<td>ma<br />
</td>
<td><a class="wiki_link" href="/7_6">7/6</a>=266.871<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>352.3<br />
</td>
<td>352<br />
</td>
<td>351.220<br />
</td>
<td>350.978<br />
</td>
<td>mu<br />
</td>
<td><a class="wiki_link" href="/11_9">11/9</a>= 347.408, 27/22=354.547, 16/13=359.472<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>440.375<br />
</td>
<td>440<br />
</td>
<td>439.024<br />
</td>
<td>438.722<br />
</td>
<td>mo<br />
</td>
<td>32/25=427.373, <a class="wiki_link" href="/9_7">9/7</a>=435.084, 22/17 446.363<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>528.45<br />
</td>
<td>528<br />
</td>
<td>526.829<br />
</td>
<td>526.466<br />
</td>
<td>fih<br />
</td>
<td>19/14=528.687, 49/36=533.742, <a class="wiki_link" href="/15_11">15/11</a>=536.95<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>616.526<br />
</td>
<td>616<br />
</td>
<td>614.634<br />
</td>
<td>614.211<br />
</td>
<td>se<br />
</td>
<td><a class="wiki_link" href="/10_7">10/7</a>=617.488<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>704.601<br />
</td>
<td>704<br />
</td>
<td>702.439<br />
</td>
<td>701.955<br />
</td>
<td>sol<br />
</td>
<td><a class="wiki_link" href="/3_2">3/2</a>=701.955<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>792.676<br />
</td>
<td>792<br />
</td>
<td>790.244<br />
</td>
<td>789.699<br />
</td>
<td>leh<br />
</td>
<td><a class="wiki_link" href="/11_7">11/7</a>=782.492, 30/19=790.756, 128/81=792.180, 19/12=795.558, 27/17=800.910, <a class="wiki_link" href="/8_5">8/5</a>=813.686<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>880.751<br />
</td>
<td>880<br />
</td>
<td>878.049<br />
</td>
<td>878.444<br />
</td>
<td>la<br />
</td>
<td><a class="wiki_link" href="/5_3">5/3</a>=884.359<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>968.826<br />
</td>
<td>968<br />
</td>
<td>965.854<br />
</td>
<td>965.188<br />
</td>
<td>ta<br />
</td>
<td><a class="wiki_link" href="/7_4">7/4</a>=968.826<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>1056.901<br />
</td>
<td>1056<br />
</td>
<td>1053.659<br />
</td>
<td>1052.933<br />
</td>
<td>tu<br />
</td>
<td><a class="wiki_link" href="/11_6">11/6</a>=1049.363, 35/19=1057.627, 24/13=1061.427<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>1144.976<br />
</td>
<td>1144<br />
</td>
<td>1141.463<br />
</td>
<td>1140.677<br />
</td>
<td>to<br />
</td>
<td>27/14=1137.039, 31/16=1145.036<br />
</td>
</tr>
<tr>
<th colspan="6"><strong><em>second octave</em></strong><br />
</th>
<th><br />
</th>
</tr>
<tr>
<td>14<br />
</td>
<td>33.051<br />
</td>
<td>32<br />
</td>
<td>29.268<br />
</td>
<td>28.421<br />
</td>
<td>di<br />
</td>
<td>65/64=26.841, 64/63=27.264, 63/62=27.700, 58/57=30.109<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>121.126<br />
</td>
<td>120<br />
</td>
<td>117.073<br />
</td>
<td>116.166<br />
</td>
<td>ra<br />
</td>
<td>16/15=111.731, 15/14=119.443, 14/13=128.298<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>209.201<br />
</td>
<td>208<br />
</td>
<td>204.878<br />
</td>
<td>203.910<br />
</td>
<td>re<br />
</td>
<td>9/8=203.910<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>297.276<br />
</td>
<td>296<br />
</td>
<td>292.683<br />
</td>
<td>291.654<br />
</td>
<td>meh<br />
</td>
<td>13/11=289.210, 32/27=294.135, 19/16=297.513<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>385.351<br />
</td>
<td>384<br />
</td>
<td>380.488<br />
</td>
<td>379.399<br />
</td>
<td>mi<br />
</td>
<td>5/4=386.314<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>473.427<br />
</td>
<td>472<br />
</td>
<td>468.293<br />
</td>
<td>467.143<br />
</td>
<td>fe<br />
</td>
<td>17/13=464.428, 21/16=470.781<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>561.502<br />
</td>
<td>560<br />
</td>
<td>556.098<br />
</td>
<td>554.888<br />
</td>
<td>fu<br />
</td>
<td>11/8=551.318, 18/13=563.382<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>649.577<br />
</td>
<td>648<br />
</td>
<td>643.902<br />
</td>
<td>642.632<br />
</td>
<td>su<br />
</td>
<td>16/11=648.682<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>737.652<br />
</td>
<td>736<br />
</td>
<td>731.707<br />
</td>
<td>730.376<br />
</td>
<td>si<br />
</td>
<td>32/21=729.219, 26/17=735.572, 49/32=737.652<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>825.727<br />
</td>
<td>824<br />
</td>
<td>819.512<br />
</td>
<td>818.121<br />
</td>
<td>le<br />
</td>
<td>8/5=813.686, 45/28=821.398, 21/13=830.253<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>913.802<br />
</td>
<td>912<br />
</td>
<td>907.317<br />
</td>
<td>905.865<br />
</td>
<td>laa<br />
</td>
<td>42/25=898.153, 32/19=902.487, 27/16=905.865, 22/13=910.790, 17/10=918.642<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>1001.877<br />
</td>
<td>1000<br />
</td>
<td>995.122<br />
</td>
<td>993.609<br />
</td>
<td>teh<br />
</td>
<td>39/22=991.165, 16/9=996.090, 25/14=1003.802, 34/19=1007.442<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>1089.952<br />
</td>
<td>1088<br />
</td>
<td>1082.927<br />
</td>
<td>1081.354<br />
</td>
<td>ti<br />
</td>
<td>28/15=1080.557, 15/8=1088.269<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>1178.027<br />
</td>
<td>1176<br />
</td>
<td>1170.732<br />
</td>
<td>1169.098<br />
</td>
<td>da<br />
</td>
<td>63/32=1172.736, 160/81=1178.494<br />
</td>
</tr>
<tr>
<th colspan="6"><strong><em>third octave</em></strong><br />
</th>
<th><br />
</th>
</tr>
<tr>
<td>28<br />
</td>
<td>66.102<br />
</td>
<td>64<br />
</td>
<td>58.537<br />
</td>
<td>56.843<br />
</td>
<td>ro<br />
</td>
<td>33/3253.273, 28/27=62.961, 80/77=66.170, 27/26=65.337<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>154.177<br />
</td>
<td>152<br />
</td>
<td>146.341<br />
</td>
<td>144.587<br />
</td>
<td>ru<br />
</td>
<td>49/45=147.428, 12/11=150.637, 35/32=155.140<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>242.252<br />
</td>
<td>240<br />
</td>
<td>234.146<br />
</td>
<td>232.331<br />
</td>
<td>ri<br />
</td>
<td>8/7=231.174, 23/20=241.961, 15/13=247.741<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>330.328<br />
</td>
<td>328<br />
</td>
<td>321.951<br />
</td>
<td>320.076<br />
</td>
<td>me<br />
</td>
<td>6/5=315.641, 23/19=330.761<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>418.403<br />
</td>
<td>416<br />
</td>
<td>409.756<br />
</td>
<td>407.820<br />
</td>
<td>maa<br />
</td>
<td>81/64=407.820, 33/26=412.745, 14/11=417.508<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>506.478<br />
</td>
<td>504<br />
</td>
<td>497.561<br />
</td>
<td>495.564<br />
</td>
<td>fa<br />
</td>
<td>85/64=491.269, 4/3=498.045, 75/56=505.757<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>594.553<br />
</td>
<td>592<br />
</td>
<td>585.366<br />
</td>
<td>583.309<br />
</td>
<td>fi<br />
</td>
<td>7/5=582.512, 45/32=590.224, 38/27=591.648<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>682.628<br />
</td>
<td>680<br />
</td>
<td>673.171<br />
</td>
<td>671.053<br />
</td>
<td>sih<br />
</td>
<td>28/19=671.313, 40/27=680.449<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>770.703<br />
</td>
<td>768<br />
</td>
<td>760.976<br />
</td>
<td>758.798<br />
</td>
<td>lo<br />
</td>
<td>17/11=753.637, 99/64=755.228, 14/9=764.916, 39/25=769.855, 25/16=772.627<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>858.778<br />
</td>
<td>856<br />
</td>
<td>848.780<br />
</td>
<td>846.542<br />
</td>
<td>lu<br />
</td>
<td>13/8=840.528, 18/11=852.592<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>946.853<br />
</td>
<td>944<br />
</td>
<td>936.585<br />
</td>
<td>934.286<br />
</td>
<td>li<br />
</td>
<td>12/7=933.129, 19/11=946.195<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>1034.928<br />
</td>
<td>1032<br />
</td>
<td>1024.390<br />
</td>
<td>1022.031<br />
</td>
<td>te<br />
</td>
<td>9/5=1017.596, 49/27=1031.787, 20/11=1034.996<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>1123.003<br />
</td>
<td>1120<br />
</td>
<td>1112.195<br />
</td>
<td>1109.775<br />
</td>
<td>taa<br />
</td>
<td>36/19=1106.397, 243/128=1109.775, 19/10=1111.199, 21/11=1119.463<br />
</td>
</tr>
<tr>
<th colspan="6"><strong><em>fourth octave</em></strong> (near match)<br />
</th>
<th><br />
</th>
</tr>
<tr>
<td>41<br />
</td>
<td>11.078<br />
</td>
<td>8<br />
</td>
<td>0<br />
</td>
<td>1197.59<br />
</td>
<td>do<br />
</td>
<td>1/1=0, 2/1=1200<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:9:<h2> --><h2 id="toc4"><a name="x88cET-Compositions"></a><!-- ws:end:WikiTextHeadingRule:9 -->Compositions</h2>
<span class="ymp-btn-page-play ymp-media-495785593852bb775b5c611348abe945"><a class="wiki_link_ext" href="http://www.seraph.it/dep/det/88east.mp3" rel="nofollow">88 East</a> </span> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a><br />
<span class="ymp-btn-page-play ymp-media-0eec9409132570e087858a748b80b969"><a class="wiki_link_ext" href="http://www.seraph.it/dep/det/88vocoeast.mp3" rel="nofollow">88 VocoEast</a> </span> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a><br />
<span class="ymp-btn-page-play ymp-media-a43b46e2ba54959d045772c4e452232c"><a class="wiki_link_ext" href="http://www.seraph.it/dep/det/88Bulgarians.mp3" rel="nofollow">88 Bulgarians</a> </span> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/9660ca3450a996ea8b55713cbf36151f-15.html" rel="nofollow">blog entry</a>)<br />
<span class="ymp-btn-page-play ymp-media-db5d569ced088a975707d1a1ba01c739"><a class="wiki_link_ext" href="http://www.seraph.it/dep/int/88jinglebells.mp3" rel="nofollow">88 Jingle Bells</a> </span> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/495ec175ce56cf38cb399d1cd24db164-17.html" rel="nofollow">blog entry</a>)<br />
<span class="ymp-btn-page-play ymp-media-e32c31e0585b669853d287adb8753ae8"><a class="wiki_link_ext" href="http://micro.soonlabel.com/88cent_nonoctave/STE-004_88_cent_guitar.mp3" rel="nofollow">88 cent guitar improvisation</a></span> by <a class="wiki_link_ext" href="http://www.chrisvaisvil.com" rel="nofollow" target="_blank">Chris Vaisvil</a><br />
<span class="ymp-btn-page-play ymp-media-bb747291b4a026593ee10b7c928912e4"><a class="wiki_link_ext" href="http://micro.soonlabel.com/88cent_nonoctave/Prelude_in_88_Cent_Tuning.mp3" rel="nofollow">A Simple Prelude for 88 Cent Piano</a></span> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=951" rel="nofollow">Chris Vaisvil</a> (<a class="wiki_link_ext" href="http://micro.soonlabel.com/88cent_nonoctave/A_Simple_Prelude_in_88_Cent_Tuning.pdf" rel="nofollow">scordata</a>)</body></html>