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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-06-28 02:42:41 UTC</tt>.<br>
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| : The original revision id was <tt>239085981</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <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;white-space: pre-wrap ! important" class="old-revision-html">The //1200 division// divides the octave in 1200 equal parts of exactly 1 [[cent]] each. It is notable mostly because it is the equal division corresponding to cents.
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| 1200edo is uniquely [[consistent]] through the [[11-limit]], which means the intervals of the 11-limit[[tonality diamond| tonality diamond]], and hence their size in cents rounded to the nearest integer, can be found by applying the 11-limit patent val <1200 1902 2786 3369 4141|. It is [[contorted]] in the [[5-limit]], having the same mapping as 600edo. In the [[7-limit]], it tempers out 2460375/2458624 and 95703125/95551488, leading to a temperament it supports with a period of 1/3 octave and a generator which is an approximate 225/224 of 7\1200, also supported by [[171edo]]. In the 11-limit, it tempers out 9801/9800, 234375/234256 and 825000/823543, leading to a temperament with a half-octave period and an approximate 99/98 generator of 17\1200, also supported by [[494edo]].</pre></div> | | 1200edo is notable for being the equal division of the octave whose step size corresponds to exactly 1 [[cent]]. |
| <h4>Original HTML content:</h4>
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| <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"><html><head><title>1200edo</title></head><body>The <em>1200 division</em> divides the octave in 1200 equal parts of exactly 1 <a class="wiki_link" href="/cent">cent</a> each. It is notable mostly because it is the equal division corresponding to cents.<br />
| | == Theory == |
| <br />
| | 1200edo is [[consistency|distinctly consistent]] through the [[11-odd-limit]]. This means that whole-cent approximations of the 11-odd-limit [[tonality diamond]] intervals are conveniently represented through the 11-limit [[patent val]] {{val| 1200 1902 2786 3369 4151 }}. It is [[enfactoring|enfactored]] in the [[5-limit]], having the same tuning as [[600edo]]. |
| 1200edo is uniquely <a class="wiki_link" href="/consistent">consistent</a> through the <a class="wiki_link" href="/11-limit">11-limit</a>, which means the intervals of the 11-limit<a class="wiki_link" href="/tonality%20diamond"> tonality diamond</a>, and hence their size in cents rounded to the nearest integer, can be found by applying the 11-limit patent val &lt;1200 1902 2786 3369 4141|. It is <a class="wiki_link" href="/contorted">contorted</a> in the <a class="wiki_link" href="/5-limit">5-limit</a>, having the same mapping as 600edo. In the <a class="wiki_link" href="/7-limit">7-limit</a>, it tempers out 2460375/2458624 and 95703125/95551488, leading to a temperament it supports with a period of 1/3 octave and a generator which is an approximate 225/224 of 7\1200, also supported by <a class="wiki_link" href="/171edo">171edo</a>. In the 11-limit, it tempers out 9801/9800, 234375/234256 and 825000/823543, leading to a temperament with a half-octave period and an approximate 99/98 generator of 17\1200, also supported by <a class="wiki_link" href="/494edo">494edo</a>.</body></html></pre></div>
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| | The equal temperament [[tempering out|tempers out]] 2460375/2458624 and 95703125/95551488 in the [[7-limit]], supporting the 171 & 1029 temperament, with a period of 1/3 octave and a generator which is an approximate [[225/224]] of 7\1200. It tempers out [[9801/9800]], 234375/234256 and 825000/823543 in the 11-limit, supporting the 494 & 706 temperament, with a half-octave period and an approximate 99/98 generator of 17\1200. |
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| | It also provides a 7-limit val, 1200ccd, which is extremely closely close to the 7-limit [[POTE tuning]] of [[quadritikleismic temperament]]: {{val| 1200 1902 2785 3368 }}. It also provides the optimal patent val for the 224 & 976 temperament tempering out [[2200/2197]], [[4096/4095]], 9801/9800 and 35750/35721. |
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| | Upwards to the 47-limit, 1200edo offers relatively accurate approximations for 2, 3, 7, 17, 31, 41, and 47, and in the 2.3.7.17.31.41.47 [[subgroup]] it tempers out 2304/2303, 3808/3807, 6273/6272, 506447/506268, 632056/632043, 10218313/10214416. The 47th harmonic is 6666 steps and 666 steps reduced – a mathematical coincidence in our decimal system. |
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| | === Prime harmonics === |
| | {{Harmonics in equal|1200}} |
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| | === Subsets and supersets === |
| | The nontrivial divisors of 1200 are {{EDOs| 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, and 600 }}. These are all the edos whose step size is an integer amount of cents, and thus can be played exactly on any digital audio workstation that offers detuning by cents. |
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| | == Regular temperament properties == |
| | {| class="wikitable center-4 center-5 center-6" |
| | ! rowspan="2" | [[Subgroup]] |
| | ! rowspan="2" | [[Comma list]] |
| | ! rowspan="2" | [[Mapping]] |
| | ! rowspan="2" | Optimal<br>8ve Stretch (¢) |
| | ! colspan="2" | Tuning Error |
| | |- |
| | ! [[TE error|Absolute]] (¢) |
| | ! [[TE simple badness|Relative]] (%) |
| | |- |
| | | 2.3.5.7 |
| | | 2460375/2458624, 95703125/95551488, {{monzo| 36 -5 0 -10 }} |
| | | {{mapping| 1200 1902 2786 3369 }} |
| | | +0.0112 |
| | | 0.0748 |
| | | 7.48 |
| | |- |
| | | 2.3.5.7.11 |
| | | 9801/9800, 234375/234256, 825000/823543, 1771561/1769472 |
| | | {{mapping| 1200 1902 2786 3369 4151 }} |
| | | +0.0273 |
| | | 0.0743 |
| | | 7.43 |
| | |} |
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| | == Music == |
| | ; [[Hideya]] |
| | * [https://www.youtube.com/watch?v=FJhmgbuoRHA ''Like scattered blue light''] (2024) |
| | |
| | ; [[Sevish]] |
| | * [https://www.youtube.com/watch?v=lTT3QGTngIs ''Dream Up''] (2021, demo version) |
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| | [[Category:Listen]] |