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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | '''Marvel woo''' is a particular tuning of [[marvel|undecimal marvel]] which is optimized for synchronized [[beat]]ing, and which also happens to be very close to the [[TE tuning]] for marvel. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-12-24 00:41:10 UTC</tt>.<br>
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| : The original revision id was <tt>479222878</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">[[Marvel]] is the 11-limit planar temperament tempering out 225/224 and 385/384. Marvel woo is the marvel tuning with 10/3, 7/2 and 11 as eigenmonzos. This gives three monzos with eigenvalue 1, and two with eigenvalue 0, allowing us to construct a projection matrix whose columns (or rows if you prefer) are fractional monzos, which defines the tuning. This matrix is [|0 -4 4 4 4>, |-21 6 -6 15 8>, |7 -18 18 11 4>, |-28 -4 4 32 4>, |0 0 0 0 28>]/28. It leads to a tuning where the octave is sharp by |-7 -1 1 1 1>/7 = (385/384)^(1/7), about 0.643 cents. In this tuning, 9/5 is sharp by only |-49 -26 -2 19 12>/28 = (385/384)^(3/7)/(225/224)^(1/4), about 0.0018 cents. Putting 10/3, 7/2, 11 and 9/5 together with 2 leads to the full 11-limit. This means every interval in the 11-limit tonality diamond is either pure, ±0.0018 cents from pure, or a certain number of octaves away from an interval which is within 0.0018 cents of pure. Because of this, the beat ratios of everything in the 11-limit diamond are closely approximated by small integer ratios. For instance, for every eight beats of the octave in the chord 1-5/4-3/2-7/4-2, the approximate 5/4 beats approximately 20 times, 3/2 12 times, and 7/4 7 times; the actual numbers being 19.968, 11.977, 6.997 and 8 respectively. Aside from these facts about beats, it should be noted that marvel woo tuning is very close to the TE tuning for marvel.
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| =12 notes= | | The marvel woo [[tuning map]] is {{val| 1200.643223 1901.313567 2785.029055 3369.469129 4151.317943 }}. |
| [[genus1125marvwoo]] | | __TOC__ |
| [[duohexmarvwoo]] | | == Math == |
| [[bluesmarvwoo]] | | Marvel woo is the marvel tuning with 10/3, 7/2 and 11 as [[eigenmonzo|eigenmonzos (unchanged-intervals)]]. This gives three monzos with eigenvalue 1, and two with eigenvalue 0, allowing us to construct a projection matrix whose columns (or rows if you prefer) are fractional monzos, which defines the tuning. This matrix is [{{monzo| 0 -4 4 4 4 }}, {{monzo| -21 6 -6 15 8 }}, {{monzo| 7 -18 18 11 4 }}, {{monzo| -28 -4 4 32 4 }}, {{monzo| 0 0 0 0 28 }}]/28. It leads to a tuning where the octave is sharp by {{nowrap|{{monzo| -7 -1 1 1 1 }}/7 = (385/384)<sup>1/7</sup>}}, about 0.643 [[cent]]s. In this tuning, 9/5 and 12/7 are sharp by only {{nowrap|{{monzo| -49 -26 -2 19 12 }}/28 = (385/384)<sup>3/7</sup>/(225/224)<sup>1/4</sup>}}, about 0.0018 cents. Putting 10/3, 7/2, 11, and 9/5 together with 2 leads to the full 11-limit. This means every interval in the [[11-odd-limit]] [[tonality diamond]] is either pure, ±0.0018 cents from pure, or a certain number of octaves away from an interval which is within 0.0018 cents of pure. Because of this, the [[beat ratio]]s of everything in the 11-odd-limit diamond are closely approximated by small integer ratios. For instance, for every eight beats of the [[octave]] in the chord 4:5:6:7:8, the approximate [[5/4]] beats approximately 20 times, [[3/2]] 12 times, and [[7/4]] 7 times; the actual numbers being 8, 19.968, 11.977 and 6.997 respectively. |
| [[dwarf12_11marvwoo]] | |
| [[glummamarvwoo]] | |
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| =14 notes= | | == Scales == |
| [[pum14marvwoo]] | | {| class="sortable wikitable" |
| | |- |
| | ! Size |
| | ! Name |
| | |- |
| | | 7 notes |
| | | [[max7amarvwoo]] |
| | |- |
| | | rowspan="7" | 12 notes |
| | | [[genus1125marvwoo]] |
| | |- |
| | | [[duohexmarvwoo]] |
| | |- |
| | | [[bluesmarvwoo]] |
| | |- |
| | | [[dwarf12_11marvwoo]] |
| | |- |
| | | [[glummamarvwoo]] |
| | |- |
| | | [[tertiadie3marvwoo]] |
| | |- |
| | | [[sixtetwoo|sixtetwoo]] |
| | |- |
| | | 14 notes |
| | | [[pum14marvwoo]] |
| | |- |
| | | rowspan="4" | 15 notes |
| | | [[pummelmarvwoo]] |
| | |- |
| | | [[dwarf15marvwoo]] |
| | |- |
| | | [[dekanymarvwoo]] |
| | |- |
| | | [[genus5625marvwoo]] |
| | |- |
| | | 16 notes |
| | | [[stellarhexmarvwoo]] |
| | |- |
| | | rowspan="7" | 17 notes |
| | | [[diam7plusmarvwoo]] |
| | |- |
| | | [[dwarf17marvwoo]] |
| | |- |
| | | [[elf17marvwoo]] |
| | |- |
| | | [[diamond_chess11marvwoo]] |
| | |- |
| | | [[rectsp6amarvwoo]] |
| | |- |
| | | [[chalmers_17marvwoo]] |
| | |- |
| | | [[genus3375plusmarvwoo]] |
| | |- |
| | | 18 notes |
| | | [[genus28125marvwoo]] |
| | |- |
| | | 19 notes |
| | | [[marvel19woo]] |
| | |- |
| | | 20 notes |
| | | [[genus16875marvwoo]] |
| | |- |
| | | rowspan="2" | 21 notes |
| | | [[dcon9marvwoo]] |
| | |- |
| | | [[blackwoo]] |
| | |- |
| | | rowspan="2" | 22 notes |
| | | [[marvel22woo]] |
| | |- |
| | | [[marvel22_11woo]] |
| | |- |
| | | 24 notes |
| | | [[bimarveldenewoo]] |
| | |} |
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| =15 notes= | | == Music == |
| [[pummelmarvwoo]] | | * [http://chrisvaisvil.com/the-mysteries-of-motivation-piano-tuned-to-marvel-woo/ The Mysteries of Motivation] ([http://micro.soonlabel.com/marvel/20140425_diam7_plus_woo.mp3 play MP3]) in [[diam7plusmarvwoo]] by [[Chris Vaisvil]] |
| [[dwarf15marvwoo]] | |
| [[dekanymarvwoo]] | |
| [[genus5625marvwoo]] | |
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| =16 notes=
| | * [https://soundcloud.com/morphosyntax-1/cave-of-marvels Cave of Marvels] by [[Herman Miller]] (2017) |
| [[stellarhexmarvwoo]] | |
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| =17 notes=
| | {{Navbox scale gallery}} |
| [[diam7plusmarvwoo]]
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| [[dwarf17marvwoo]]
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| [[elf17marvwoo]]
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| =18 notes=
| | [[Category:Marvel]] |
| [[genus28125marvwoo]] | | [[Category:Listen]] |
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| =19 notes=
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| [[marvel19woo]] | |
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| =20 notes=
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| [[genus16875marvwoo]]
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| =21 notes=
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| [[dcon9marvwoo]]
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| =22 notes=
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| [[marvel22woo]]
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| [[marvel22_11woo]]
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| =24 notes=
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| [[bimarveldenewoo]]</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>Marvel woo</title></head><body><a class="wiki_link" href="/Marvel">Marvel</a> is the 11-limit planar temperament tempering out 225/224 and 385/384. Marvel woo is the marvel tuning with 10/3, 7/2 and 11 as eigenmonzos. This gives three monzos with eigenvalue 1, and two with eigenvalue 0, allowing us to construct a projection matrix whose columns (or rows if you prefer) are fractional monzos, which defines the tuning. This matrix is [|0 -4 4 4 4&gt;, |-21 6 -6 15 8&gt;, |7 -18 18 11 4&gt;, |-28 -4 4 32 4&gt;, |0 0 0 0 28&gt;]/28. It leads to a tuning where the octave is sharp by |-7 -1 1 1 1&gt;/7 = (385/384)^(1/7), about 0.643 cents. In this tuning, 9/5 is sharp by only |-49 -26 -2 19 12&gt;/28 = (385/384)^(3/7)/(225/224)^(1/4), about 0.0018 cents. Putting 10/3, 7/2, 11 and 9/5 together with 2 leads to the full 11-limit. This means every interval in the 11-limit tonality diamond is either pure, ±0.0018 cents from pure, or a certain number of octaves away from an interval which is within 0.0018 cents of pure. Because of this, the beat ratios of everything in the 11-limit diamond are closely approximated by small integer ratios. For instance, for every eight beats of the octave in the chord 1-5/4-3/2-7/4-2, the approximate 5/4 beats approximately 20 times, 3/2 12 times, and 7/4 7 times; the actual numbers being 19.968, 11.977, 6.997 and 8 respectively. Aside from these facts about beats, it should be noted that marvel woo tuning is very close to the TE tuning for marvel.<br />
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| <a class="wiki_link" href="/genus1125marvwoo">genus1125marvwoo</a><br />
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| <a class="wiki_link" href="/duohexmarvwoo">duohexmarvwoo</a><br />
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| <a class="wiki_link" href="/bluesmarvwoo">bluesmarvwoo</a><br />
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| <a class="wiki_link" href="/dwarf12_11marvwoo">dwarf12_11marvwoo</a><br />
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| <a class="wiki_link" href="/glummamarvwoo">glummamarvwoo</a><br />
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| <a class="wiki_link" href="/pum14marvwoo">pum14marvwoo</a><br />
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| <a class="wiki_link" href="/pummelmarvwoo">pummelmarvwoo</a><br />
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| <a class="wiki_link" href="/dwarf15marvwoo">dwarf15marvwoo</a><br />
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| <a class="wiki_link" href="/dekanymarvwoo">dekanymarvwoo</a><br />
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| <a class="wiki_link" href="/genus5625marvwoo">genus5625marvwoo</a><br />
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| <a class="wiki_link" href="/stellarhexmarvwoo">stellarhexmarvwoo</a><br />
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| <a class="wiki_link" href="/diam7plusmarvwoo">diam7plusmarvwoo</a><br />
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| <a class="wiki_link" href="/dwarf17marvwoo">dwarf17marvwoo</a><br />
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| <a class="wiki_link" href="/elf17marvwoo">elf17marvwoo</a><br />
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| <a class="wiki_link" href="/genus28125marvwoo">genus28125marvwoo</a><br />
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| <a class="wiki_link" href="/marvel19woo">marvel19woo</a><br />
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| <a class="wiki_link" href="/genus16875marvwoo">genus16875marvwoo</a><br />
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| <a class="wiki_link" href="/dcon9marvwoo">dcon9marvwoo</a><br />
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| <a class="wiki_link" href="/marvel22woo">marvel22woo</a><br />
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| <a class="wiki_link" href="/marvel22_11woo">marvel22_11woo</a><br />
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| <a class="wiki_link" href="/bimarveldenewoo">bimarveldenewoo</a></body></html></pre></div>
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Marvel woo is a particular tuning of undecimal marvel which is optimized for synchronized beating, and which also happens to be very close to the TE tuning for marvel.
The marvel woo tuning map is ⟨1200.643223 1901.313567 2785.029055 3369.469129 4151.317943].
Math
Marvel woo is the marvel tuning with 10/3, 7/2 and 11 as eigenmonzos (unchanged-intervals). This gives three monzos with eigenvalue 1, and two with eigenvalue 0, allowing us to construct a projection matrix whose columns (or rows if you prefer) are fractional monzos, which defines the tuning. This matrix is [[0 -4 4 4 4⟩, [-21 6 -6 15 8⟩, [7 -18 18 11 4⟩, [-28 -4 4 32 4⟩, [0 0 0 0 28⟩]/28. It leads to a tuning where the octave is sharp by (385/384)1/7, about 0.643 cents. In this tuning, 9/5 and 12/7 are sharp by only (385/384)3/7/(225/224)1/4, about 0.0018 cents. Putting 10/3, 7/2, 11, and 9/5 together with 2 leads to the full 11-limit. This means every interval in the 11-odd-limit tonality diamond is either pure, ±0.0018 cents from pure, or a certain number of octaves away from an interval which is within 0.0018 cents of pure. Because of this, the beat ratios of everything in the 11-odd-limit diamond are closely approximated by small integer ratios. For instance, for every eight beats of the octave in the chord 4:5:6:7:8, the approximate 5/4 beats approximately 20 times, 3/2 12 times, and 7/4 7 times; the actual numbers being 8, 19.968, 11.977 and 6.997 respectively.
Scales
Music