Xenharmonic Wiki

41edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
Wikispaces>Andrew_Heathwaite
**Imported revision 288886877 - Original comment: **
Wikispaces>Andrew_Heathwaite
**Imported revision 288886919 - Original comment: **
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-31 01:58:17 UTC</tt>.<br>
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-31 01:59:10 UTC</tt>.<br>
: The original revision id was <tt>288886877</tt>.<br>
: The original revision id was <tt>288886919</tt>.<br>
: The revision comment was: <tt></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>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
Line 10: Line 10:
The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 [[cent]]s, an [[interval]] close in size to [[64_63|64/63]], the [[Septimal comma|septimal comma]]. 41-ET can be seen as a tuning of the //[[Schismatic family#Garibaldi|Garibaldi temperament]]// &lt;ref&gt;[[http://x31eq.com/schismic.htm|"Schismic Temperaments"]] at x31eq.com the websize of [[Graham Breed]]&lt;/ref&gt; , &lt;ref&gt;[[http://x31eq.com/decimal_lattice.htm|"Lattices with Decimal Notation"]] at x31eq.com&lt;/ref&gt; , &lt;ref&gt;[[http://en.wikipedia.org/wiki/Schismatic_temperament|Schismatic temperament]]&lt;/ref&gt; the //[[Magic family|Magic temperament]]// &lt;ref&gt;[[http://en.wikipedia.org/wiki/Magic_temperament|Magic temperament]]&lt;/ref&gt; and the superkleismic (41&amp;26) temperament. It is the second smallest equal temperament (after [[29edo]]) whose perfect fifth is closer to just intonation than that of [[12edo|12-ET]], and is the seventh [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]] after 31; it is not, however, a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta gap edo]]. This has to do with the fact that it can deal with the [[11-limit]] fairly well, and the [[13-limit]] perhaps close enough for government work, though its [[13_10|13/10]] is 14 cents sharp. 41-ET forms the foundation of the [[http://www.h-pi.com/theory/huntsystem1.html|H-System]], which uses the scale degrees of 41-ET as the basic [[13-limit]] intervals requiring fine tuning +/- 1 [[http://www.h-pi.com/theory/huntsystem2.html|average JND]] from the 41-ET circle in [[205edo]].
The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 [[cent]]s, an [[interval]] close in size to [[64_63|64/63]], the [[Septimal comma|septimal comma]]. 41-ET can be seen as a tuning of the //[[Schismatic family#Garibaldi|Garibaldi temperament]]// &lt;ref&gt;[[http://x31eq.com/schismic.htm|"Schismic Temperaments"]] at x31eq.com the websize of [[Graham Breed]]&lt;/ref&gt; , &lt;ref&gt;[[http://x31eq.com/decimal_lattice.htm|"Lattices with Decimal Notation"]] at x31eq.com&lt;/ref&gt; , &lt;ref&gt;[[http://en.wikipedia.org/wiki/Schismatic_temperament|Schismatic temperament]]&lt;/ref&gt; the //[[Magic family|Magic temperament]]// &lt;ref&gt;[[http://en.wikipedia.org/wiki/Magic_temperament|Magic temperament]]&lt;/ref&gt; and the superkleismic (41&amp;26) temperament. It is the second smallest equal temperament (after [[29edo]]) whose perfect fifth is closer to just intonation than that of [[12edo|12-ET]], and is the seventh [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]] after 31; it is not, however, a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta gap edo]]. This has to do with the fact that it can deal with the [[11-limit]] fairly well, and the [[13-limit]] perhaps close enough for government work, though its [[13_10|13/10]] is 14 cents sharp. 41-ET forms the foundation of the [[http://www.h-pi.com/theory/huntsystem1.html|H-System]], which uses the scale degrees of 41-ET as the basic [[13-limit]] intervals requiring fine tuning +/- 1 [[http://www.h-pi.com/theory/huntsystem2.html|average JND]] from the 41-ET circle in [[205edo]].


41edo is the 13th [[prime numbers|prime]] edo, following [[37edo]] and coming before [[47edo]].
41edo is the 13th [[prime numbers|prime]] edo, following [[37edo]] and coming before [[43edo]].


[[toc|flat]]
[[toc|flat]]
Line 159: Line 159:
The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s, an &lt;a class="wiki_link" href="/interval"&gt;interval&lt;/a&gt; close in size to &lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt;, the &lt;a class="wiki_link" href="/Septimal%20comma"&gt;septimal comma&lt;/a&gt;. 41-ET can be seen as a tuning of the &lt;em&gt;&lt;a class="wiki_link" href="/Schismatic%20family#Garibaldi"&gt;Garibaldi temperament&lt;/a&gt;&lt;/em&gt; &lt;!-- ws:start:WikiTextRefRule:2:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://x31eq.com/schismic.htm&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;amp;quot;Schismic Temperaments&amp;amp;quot;&amp;lt;/a&amp;gt; at x31eq.com the websize of &amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;/Graham%20Breed&amp;quot;&amp;gt;Graham Breed&amp;lt;/a&amp;gt;&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-1" class="reference"&gt;&lt;a href="#cite_note-1"&gt;[1]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:2 --&gt; , &lt;!-- ws:start:WikiTextRefRule:4:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://x31eq.com/decimal_lattice.htm&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;amp;quot;Lattices with Decimal Notation&amp;amp;quot;&amp;lt;/a&amp;gt; at x31eq.com&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-2" class="reference"&gt;&lt;a href="#cite_note-2"&gt;[2]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:4 --&gt; , &lt;!-- ws:start:WikiTextRefRule:6:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://en.wikipedia.org/wiki/Schismatic_temperament&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;Schismatic temperament&amp;lt;/a&amp;gt;&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-3" class="reference"&gt;&lt;a href="#cite_note-3"&gt;[3]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:6 --&gt; the &lt;em&gt;&lt;a class="wiki_link" href="/Magic%20family"&gt;Magic temperament&lt;/a&gt;&lt;/em&gt; &lt;!-- ws:start:WikiTextRefRule:8:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://en.wikipedia.org/wiki/Magic_temperament&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;Magic temperament&amp;lt;/a&amp;gt;&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-4" class="reference"&gt;&lt;a href="#cite_note-4"&gt;[4]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:8 --&gt; and the superkleismic (41&amp;amp;26) temperament. It is the second smallest equal temperament (after &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;) whose perfect fifth is closer to just intonation than that of &lt;a class="wiki_link" href="/12edo"&gt;12-ET&lt;/a&gt;, and is the seventh &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta integral edo&lt;/a&gt; after 31; it is not, however, a &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta gap edo&lt;/a&gt;. This has to do with the fact that it can deal with the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; fairly well, and the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; perhaps close enough for government work, though its &lt;a class="wiki_link" href="/13_10"&gt;13/10&lt;/a&gt; is 14 cents sharp. 41-ET forms the foundation of the &lt;a class="wiki_link_ext" href="http://www.h-pi.com/theory/huntsystem1.html" rel="nofollow"&gt;H-System&lt;/a&gt;, which uses the scale degrees of 41-ET as the basic &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; intervals requiring fine tuning +/- 1 &lt;a class="wiki_link_ext" href="http://www.h-pi.com/theory/huntsystem2.html" rel="nofollow"&gt;average JND&lt;/a&gt; from the 41-ET circle in &lt;a class="wiki_link" href="/205edo"&gt;205edo&lt;/a&gt;.&lt;br /&gt;
The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s, an &lt;a class="wiki_link" href="/interval"&gt;interval&lt;/a&gt; close in size to &lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt;, the &lt;a class="wiki_link" href="/Septimal%20comma"&gt;septimal comma&lt;/a&gt;. 41-ET can be seen as a tuning of the &lt;em&gt;&lt;a class="wiki_link" href="/Schismatic%20family#Garibaldi"&gt;Garibaldi temperament&lt;/a&gt;&lt;/em&gt; &lt;!-- ws:start:WikiTextRefRule:2:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://x31eq.com/schismic.htm&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;amp;quot;Schismic Temperaments&amp;amp;quot;&amp;lt;/a&amp;gt; at x31eq.com the websize of &amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;/Graham%20Breed&amp;quot;&amp;gt;Graham Breed&amp;lt;/a&amp;gt;&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-1" class="reference"&gt;&lt;a href="#cite_note-1"&gt;[1]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:2 --&gt; , &lt;!-- ws:start:WikiTextRefRule:4:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://x31eq.com/decimal_lattice.htm&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;amp;quot;Lattices with Decimal Notation&amp;amp;quot;&amp;lt;/a&amp;gt; at x31eq.com&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-2" class="reference"&gt;&lt;a href="#cite_note-2"&gt;[2]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:4 --&gt; , &lt;!-- ws:start:WikiTextRefRule:6:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://en.wikipedia.org/wiki/Schismatic_temperament&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;Schismatic temperament&amp;lt;/a&amp;gt;&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-3" class="reference"&gt;&lt;a href="#cite_note-3"&gt;[3]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:6 --&gt; the &lt;em&gt;&lt;a class="wiki_link" href="/Magic%20family"&gt;Magic temperament&lt;/a&gt;&lt;/em&gt; &lt;!-- ws:start:WikiTextRefRule:8:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://en.wikipedia.org/wiki/Magic_temperament&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;Magic temperament&amp;lt;/a&amp;gt;&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-4" class="reference"&gt;&lt;a href="#cite_note-4"&gt;[4]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:8 --&gt; and the superkleismic (41&amp;amp;26) temperament. It is the second smallest equal temperament (after &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;) whose perfect fifth is closer to just intonation than that of &lt;a class="wiki_link" href="/12edo"&gt;12-ET&lt;/a&gt;, and is the seventh &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta integral edo&lt;/a&gt; after 31; it is not, however, a &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta gap edo&lt;/a&gt;. This has to do with the fact that it can deal with the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; fairly well, and the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; perhaps close enough for government work, though its &lt;a class="wiki_link" href="/13_10"&gt;13/10&lt;/a&gt; is 14 cents sharp. 41-ET forms the foundation of the &lt;a class="wiki_link_ext" href="http://www.h-pi.com/theory/huntsystem1.html" rel="nofollow"&gt;H-System&lt;/a&gt;, which uses the scale degrees of 41-ET as the basic &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; intervals requiring fine tuning +/- 1 &lt;a class="wiki_link_ext" href="http://www.h-pi.com/theory/huntsystem2.html" rel="nofollow"&gt;average JND&lt;/a&gt; from the 41-ET circle in &lt;a class="wiki_link" href="/205edo"&gt;205edo&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
41edo is the 13th &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo, following &lt;a class="wiki_link" href="/37edo"&gt;37edo&lt;/a&gt; and coming before &lt;a class="wiki_link" href="/47edo"&gt;47edo&lt;/a&gt;.&lt;br /&gt;
41edo is the 13th &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo, following &lt;a class="wiki_link" href="/37edo"&gt;37edo&lt;/a&gt; and coming before &lt;a class="wiki_link" href="/43edo"&gt;43edo&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextTocRule:19:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt;&lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt; | &lt;a href="#Instruments"&gt;Instruments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt; | &lt;a href="#Harmonic Scale"&gt;Harmonic Scale&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt; | &lt;a href="#Nonoctave Temperaments"&gt;Nonoctave Temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt; | &lt;a href="#Links"&gt;Links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;
&lt;!-- ws:start:WikiTextTocRule:19:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt;&lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt; | &lt;a href="#Instruments"&gt;Instruments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt; | &lt;a href="#Harmonic Scale"&gt;Harmonic Scale&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt; | &lt;a href="#Nonoctave Temperaments"&gt;Nonoctave Temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt; | &lt;a href="#Links"&gt;Links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;
Retrieved from "https://en.xen.wiki/w/41edo"