Marvel woo: Difference between revisions

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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>~~

~~: This revision was by author~~ [[~~User:genewardsmith~~|~~genewardsmith~~]] ~~and made on <tt>2013-12-22 18:31:01 UTC</tt>.<br>~~

~~: The original revision id was <tt>479065820</tt>.<br>~~

~~: The revision comment was: <tt></tt><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>~~

<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 rows are fractional vals,~~ 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.

=~~14 notes~~=

The marvel woo [[tuning map]] is {{val| 1200.643223 1901.313567 2785.029055 3369.469129 4151.317943 }}.

[[~~pum14marvwoo~~]]

__TOC__

== Math ==

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.

=15 notes=

== Scales ==

[[pummelmarvwoo]]

{| class="sortable wikitable"

[[dwarf15marvwoo]]

|-

[[dekanymarvwoo]]

! 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]]

|}

=~~17 notes~~=

== Music ==

[[diam7plusmarvwoo]]

* [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]]

[[~~dwarf17marvwoo~~]]

~~=21 notes=~~

* [https://soundcloud.com/morphosyntax-1/cave-of-marvels Cave of Marvels] by [[Herman Miller]] (2017)

[[~~dcon9marvwoo]]</pre></div>~~

~~<h4>Original HTML content~~:</~~h4>~~

<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 rows are fractional vals, which defines the tuning. This matrix is [&lt;0 -~~4 4 4 4|, &lt;~~-~~21 6 -6 15 8|, &lt;7 -18 18 11 4|, &lt;-28 -4 4 32 4|, &lt;0 0 0 0 28|~~]~~/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 />

~~<br />~~

[[Category:Marvel]]

~~<h1 id="toc0"><a name="x14 notes"></a>14 notes</h1>~~

[[Category:Listen]]

~~<a class="wiki_link" href="/pum14marvwoo">pum14marvwoo</a><br />~~

~~<br />~~

~~<h1 id="toc1"><a name="x15 notes"></a>15 notes</h1>~~

~~<a class="wiki_link" href="/pummelmarvwoo">pummelmarvwoo</a><br />~~

~~<a class="wiki_link" href="/dwarf15marvwoo">dwarf15marvwoo</a><br />~~

~~<a class="wiki_link" href="/dekanymarvwoo">dekanymarvwoo</a><br />~~

~~<br />~~

~~<h1 id="toc2"><a name="x17 notes"></a>17 notes</h1>~~

~~<a class="wiki_link" href="/diam7plusmarvwoo">diam7plusmarvwoo</a><br />~~

~~<a class="wiki_link" href="/dwarf17marvwoo">dwarf17marvwoo</a><br />~~

~~<br />~~

~~<h1 id="toc3"><a name="x21 notes"></a>21 notes</h1>~~

~~<a class="wiki_link" href="/dcon9marvwoo">dcon9marvwoo</a></body></html></pre></div>~~

@@ Line 1: / Line 1: @@
-<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>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-12-22 18:31:01 UTC</tt>.<br>
-: The original revision id was <tt>479065820</tt>.<br>
-: The revision comment was: <tt></tt><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>
-<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 rows are fractional vals, which defines the tuning. This matrix is [&lt;0 -4 4 4 4|, &lt;-21 6 -6 15 8|, &lt;7 -18 18 11 4|, &lt;-28 -4 4 32 4|, &lt;0 0 0 0 28|]/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.
-=14 notes=
+The marvel woo [[tuning map]] is {{val| 1200.643223 1901.313567 2785.029055 3369.469129 4151.317943 }}.
-[[pum14marvwoo]]
+__TOC__
+== Math ==
+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.
-=15 notes=
+== Scales ==
-[[pummelmarvwoo]]
+{| class="sortable wikitable"
-[[dwarf15marvwoo]]
+|-
-[[dekanymarvwoo]]
+! 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]]
+|}
-=17 notes=
+== Music ==
-[[diam7plusmarvwoo]]
+* [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]]
-[[dwarf17marvwoo]]
-=21 notes=
+* [https://soundcloud.com/morphosyntax-1/cave-of-marvels Cave of Marvels] by [[Herman Miller]] (2017)
-[[dcon9marvwoo]]</pre></div>
-<h4>Original HTML content:</h4>
+{{Navbox scale gallery}}
-<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Marvel woo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;a class="wiki_link" href="/Marvel"&gt;Marvel&lt;/a&gt; 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 rows are fractional vals, which defines the tuning. This matrix is [&amp;lt;0 -4 4 4 4|, &amp;lt;-21 6 -6 15 8|, &amp;lt;7 -18 18 11 4|, &amp;lt;-28 -4 4 32 4|, &amp;lt;0 0 0 0 28|]/28. It leads to a tuning where the octave is sharp by |-7 -1 1 1 1&amp;gt;/7 = (385/384)^(1/7), about 0.643 cents. In this tuning, 9/5 is sharp by only |-49 -26 -2 19 12&amp;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.&lt;br /&gt;
-&lt;br /&gt;
+[[Category:Marvel]]
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x14 notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;14 notes&lt;/h1&gt;
+[[Category:Listen]]
-&lt;a class="wiki_link" href="/pum14marvwoo"&gt;pum14marvwoo&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="x15 notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;15 notes&lt;/h1&gt;
-&lt;a class="wiki_link" href="/pummelmarvwoo"&gt;pummelmarvwoo&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/dwarf15marvwoo"&gt;dwarf15marvwoo&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/dekanymarvwoo"&gt;dekanymarvwoo&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="x17 notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;17 notes&lt;/h1&gt;
-&lt;a class="wiki_link" href="/diam7plusmarvwoo"&gt;diam7plusmarvwoo&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/dwarf17marvwoo"&gt;dwarf17marvwoo&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="x21 notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;21 notes&lt;/h1&gt;
-&lt;a class="wiki_link" href="/dcon9marvwoo"&gt;dcon9marvwoo&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>