19edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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>2011-07-~~19 18~~:14:34 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-20 00:30:23 UTC</tt>.<br>

: The original revision id was <tt>~~242006093~~</tt>.<br>

: The original revision id was <tt>242053421</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>

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The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for [[Meantone#|meantone]] temperament. It is also a suitable for [[Regular Temperaments#magic|magic/muggles]] temperament, because five of its major thirds are equivalent to one of its //twelfths.// For both of these there are more optimal tunings: the fifth of 19-et is flatter than the usual for meantone, and a more accurate approximation is [[31edo|31 equal temperament]]. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; [[41edo|41 equal temperament]] more closely matches it. It does make for a good tuning for muggles, which in 19et is the same as magic.

However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with [[Harmonic Limit|5-limit]] music in a tolerable manner, and is the fifth (after 12) [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]]. It is less successful with [[7-limit]] (but still better than 12-et), as it eliminates the distinction between a septimal minor third ([[7_6|7/6]]), and a septimal whole tone ([[8_7|8/7]]). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, muggles and triton, and fairly decent for sensi and liese. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. The [[Graham complexity]] of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone/flattone, 12 for magic/muggles and liese and 13 for sensi.

However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with [[Harmonic Limit|5-limit]] music in a tolerable manner, and is the fifth (after 12) [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]]. It is less successful with [[7-limit]] (but still better than 12-et), as it eliminates the distinction between a septimal minor third ([[7_6|7/6]]), and a septimal whole tone ([[8_7|8/7]]). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, muggles and triton, and fairly decent for sensi and liese. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. The [[Graham complexity]] of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone/flattone, 11 for triton, 12 for magic/muggles and liese and 13 for sensi.

==Intervals==

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The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for [[Meantone#|meantone]] temperament. It is also a suitable for <a class="wiki_link" href="/Regular%20Temperaments#magic">magic/muggles</a> temperament, because five of its major thirds are equivalent to one of its <em>twelfths.</em> For both of these there are more optimal tunings: the fifth of 19-et is flatter than the usual for meantone, and a more accurate approximation is <a class="wiki_link" href="/31edo">31 equal temperament</a>. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; <a class="wiki_link" href="/41edo">41 equal temperament</a> more closely matches it. It does make for a good tuning for muggles, which in 19et is the same as magic.<br />

<br />

However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a> music in a tolerable manner, and is the fifth (after 12) <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">zeta integral edo</a>. It is less successful with <a class="wiki_link" href="/7-limit">7-limit</a> (but still better than 12-et), as it eliminates the distinction between a septimal minor third (<a class="wiki_link" href="/7_6">7/6</a>), and a septimal whole tone (<a class="wiki_link" href="/8_7">8/7</a>). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, muggles and triton, and fairly decent for sensi and liese. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. The <a class="wiki_link" href="/Graham%20complexity">Graham complexity</a> of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone/flattone, 12 for magic/muggles and liese and 13 for sensi.<br />

However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a> music in a tolerable manner, and is the fifth (after 12) <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">zeta integral edo</a>. It is less successful with <a class="wiki_link" href="/7-limit">7-limit</a> (but still better than 12-et), as it eliminates the distinction between a septimal minor third (<a class="wiki_link" href="/7_6">7/6</a>), and a septimal whole tone (<a class="wiki_link" href="/8_7">8/7</a>). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, muggles and triton, and fairly decent for sensi and liese. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. The <a class="wiki_link" href="/Graham%20complexity">Graham complexity</a> of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone/flattone, 11 for triton, 12 for magic/muggles and liese and 13 for sensi.<br />

<br />

<h2 id="toc2"><a name="Theory-Intervals"></a>Intervals</h2>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2011-07-19 18:14:34 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-20 00:30:23 UTC</tt>.<br>
-: The original revision id was <tt>242006093</tt>.<br>
+: The original revision id was <tt>242053421</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>
@@ Line 18: / Line 18: @@
 The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for [[Meantone#|meantone]] temperament. It is also a suitable for [[Regular Temperaments#magic|magic/muggles]] temperament, because five of its major thirds are equivalent to one of its //twelfths.// For both of these there are more optimal tunings: the fifth of 19-et is flatter than the usual for meantone, and a more accurate approximation is [[31edo|31 equal temperament]]. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; [[41edo|41 equal temperament]] more closely matches it. It does make for a good tuning for muggles, which in 19et is the same as magic.
-However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with [[Harmonic Limit|5-limit]] music in a tolerable manner, and is the fifth (after 12) [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]]. It is less successful with [[7-limit]] (but still better than 12-et), as it eliminates the distinction between a septimal minor third ([[7_6|7/6]]), and a septimal whole tone ([[8_7|8/7]]). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, muggles and triton, and fairly decent for sensi and liese. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. The [[Graham complexity]] of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone/flattone, 12 for magic/muggles and liese and 13 for sensi.
+However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with [[Harmonic Limit|5-limit]] music in a tolerable manner, and is the fifth (after 12) [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]]. It is less successful with [[7-limit]] (but still better than 12-et), as it eliminates the distinction between a septimal minor third ([[7_6|7/6]]), and a septimal whole tone ([[8_7|8/7]]). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, muggles and triton, and fairly decent for sensi and liese. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. The [[Graham complexity]] of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone/flattone, 11 for triton, 12 for magic/muggles and liese and 13 for sensi.
 ==Intervals==
@@ Line 132: / Line 132: @@
 The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for [[Meantone#|meantone]] temperament. It is also a suitable for &lt;a class="wiki_link" href="/Regular%20Temperaments#magic"&gt;magic/muggles&lt;/a&gt; temperament, because five of its major thirds are equivalent to one of its &lt;em&gt;twelfths.&lt;/em&gt; For both of these there are more optimal tunings: the fifth of 19-et is flatter than the usual for meantone, and a more accurate approximation is &lt;a class="wiki_link" href="/31edo"&gt;31 equal temperament&lt;/a&gt;. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; &lt;a class="wiki_link" href="/41edo"&gt;41 equal temperament&lt;/a&gt; more closely matches it. It does make for a good tuning for muggles, which in 19et is the same as magic.&lt;br /&gt;
 &lt;br /&gt;
-However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;5-limit&lt;/a&gt; music in a tolerable manner, and is the fifth (after 12) &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists"&gt;zeta integral edo&lt;/a&gt;. It is less successful with &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; (but still better than 12-et), as it eliminates the distinction between a septimal minor third (&lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;), and a septimal whole tone (&lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, muggles and triton, and fairly decent for sensi and liese. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. The &lt;a class="wiki_link" href="/Graham%20complexity"&gt;Graham complexity&lt;/a&gt; of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone/flattone, 12 for magic/muggles and liese and 13 for sensi.&lt;br /&gt;
+However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;5-limit&lt;/a&gt; music in a tolerable manner, and is the fifth (after 12) &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists"&gt;zeta integral edo&lt;/a&gt;. It is less successful with &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; (but still better than 12-et), as it eliminates the distinction between a septimal minor third (&lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;), and a septimal whole tone (&lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, muggles and triton, and fairly decent for sensi and liese. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. The &lt;a class="wiki_link" href="/Graham%20complexity"&gt;Graham complexity&lt;/a&gt; of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone/flattone, 11 for triton, 12 for magic/muggles and liese and 13 for sensi.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Theory-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;Intervals&lt;/h2&gt;