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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:Kosmorsky|Kosmorsky]] and made on <tt>2011-11-20 10:03:35 UTC</tt>.<br>
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| : The original revision id was <tt>277362058</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">8EDT
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| As the double of [[4edt]], harmonically, it is analogous to 10edo in that the harmonic chain is doubled. However, doing so does not make it a schismatic temperament like 10edo, because the full 3:5:7 triad is already present in 4edt. In any case, as a multiple of 4edt, I will say it is the widest variety of "Black-Extraterrestrial-Tree" temperament. | | == Theory == |
| | As the double of [[4edt]], it is the analog of [[10edo]] being the double of [[5edo]]. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in [[5edo]]. More precisely, 8edt is [[enfactoring|enfactored]] in the 3.5.7 subgroup. |
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| What it does introduce are flat pseudooctaves and sharp 3:2's, making it related to 5edo melodically. | | What it does introduce are flat [[2/1]] pseudo-octaves and sharp [[3/2]] perfect fifths, making it related to 5edo melodically. It is equivalent to 5edo with the [[3/1]] made just, by compressing the octave by 11.3 cents, which has the side effect of bringing the step size slightly closer to [[8/7]]. |
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| 0: 1/1 0.000 unison, perfect prime
| | === Harmonics === |
| 1: 237.744 cents 237.744
| | {{Harmonics in equal|8|3|1|}} |
| 2: 475.489 cents 4/3
| | {{Harmonics in equal|8|3|1|intervals=prime}} |
| 3: 713.233 cents 713.233
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| 4: 950.978 cents 5/3
| | == Interval table == |
| 5: 1188.722 cents 1188.722
| | {{Interval table}} |
| 6: 1426.466 cents 1426.466
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| 7: 1664.211 cents 1664.211
| | [[Category:Macrotonal]] |
| 8: 3/1 1901.955 perfect 12th</pre></div>
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| <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>8edt</title></head><body>8EDT<br />
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| As the double of <a class="wiki_link" href="/4edt">4edt</a>, harmonically, it is analogous to 10edo in that the harmonic chain is doubled. However, doing so does not make it a schismatic temperament like 10edo, because the full 3:5:7 triad is already present in 4edt. In any case, as a multiple of 4edt, I will say it is the widest variety of &quot;Black-Extraterrestrial-Tree&quot; temperament.<br />
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| <br />
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| What it does introduce are flat pseudooctaves and sharp 3:2's, making it related to 5edo melodically.<br />
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| <br />
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| 0: 1/1 0.000 unison, perfect prime<br />
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| 1: 237.744 cents 237.744<br />
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| 2: 475.489 cents 4/3<br />
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| 3: 713.233 cents 713.233<br />
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| 4: 950.978 cents 5/3<br />
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| 5: 1188.722 cents 1188.722<br />
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| 6: 1426.466 cents 1426.466<br />
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| 7: 1664.211 cents 1664.211<br />
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| 8: 3/1 1901.955 perfect 12th</body></html></pre></div>
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