Mina: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:hearneg|hearneg]] and made on <tt>2017-06-11 03:43:56 UTC</tt>.

: This revision was by author [[User:hearneg|hearneg]] and made on <tt>2017-06-11 04:20:54 UTC</tt>.

: The original revision id was <tt>~~614524037~~</tt>.

: The original revision id was <tt>614524401</tt>.

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

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

<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">The //mina// is a unit of interval size which has been proposed by [[George Secor]] and [[Dave Keenan]], and which is defined as 1/2460 of an [[octave]], the step size of [[2460edo]]. 2460 is divisible by both 12 and 41, two important systems, and it's been suggested that degrees and minutes can be used to express values in it, so that for instance 3/2, which is 1439 minas, could be denoted by 23°59', meaning very slightly flat of the 24\41 [[41edo]] fifths. This works out since 41 * 60 = 2460; an octave is therefore expressed as if it were an angle of 41 degrees.

Other popular systems that can be represented exactly in whole numbers of minas include [[10edo]] and [[15edo]]. Moreover a cent is exactly 2.05 [[xenharmonic/mina|mina]]s, and a mem, 1\205 octaves, is exactly 12 minas.

The following table lists some intervals which may be represented exactly in minas and in degrees and minutes, with the sizes listed in both [[cent]]s and minas and expressed as degrees and minutes.

||~ interval ||~ size in

cents ||~ size in

minas ||~ size as degrees

and minutes ||

|| 1\2460 || 0.488 || 1 || 1' ||

|| 1\205 || 5.835 || 12 || 12' ||

|| 1\41 || 29.268 || 60 || 1° ||

|| 1\15 || 80 || 164 || 2°44' ||

|| 1\12 || 100 || 205 || 3°25' ||

|| 1\10 || 120 || 246 || 4°6' ||

|| 1\6 || 200 || 410 || 6°50' ||

|| 1\5 || 240 || 492 || 8°12' ||

|| 1\4 || 300 || 615 || 10°15' ||

|| 1\3 || 400 || 820 || 13°40' ||

|| 2\5 || 480 || 984 || 16°24' ||

|| 5\12 || 500 || 1025 || 17°5' ||

|| 1\2 || 600 || 1230 || 20°30' ||

|| 7\12 || 700 || 1435 || 23°55' ||

|| 3\5 || 720 || 1476 || 24°36' ||

|| 2\3 || 800 || 1640 || 27°20' ||

|| 3\4 || 900 || 1845 || 30°45' ||

|| 4\5 || 960 || 1960 || 32°48' ||

|| 5\6 || 1000 || 2050 || 34°10 ||

|| 11\12 || 1100 || 2255 || 37°35 ||

|| 2/1 || 1200 || 2460 || 41° ||

Another helpful proponent of the mina is the accuracy and breadth of it's approximation to just intervals. Accordingly it is hardly necessary to express intervals in non-integer values of mina, something that arguably cannot be said of cents. [[2460edo]] It is uniquely [[xenharmonic/consistent|consistent]] through to the [[xenharmonic/27-limit|27-limit]], which is not very remarkable in itself ([[xenharmonic/388edo|388edo]] is the first such system), but what is remarkable is the degree of accuracy to which it represents the 27-limit intervals. It is also a [[xenharmonic/The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta peak edo]] and has a lower 19-limit [[xenharmonic/Tenney-Euclidean temperament measures#TE%20simple%20badness|relative error]] than any edo until [[xenharmonic/3395edo|3395]], and a lower 23-limit relative error than any until [[xenharmonic/8269edo|8269]]. Also it has a lower 23-limit [[xenharmonic/Tenney-Euclidean metrics#Logflat%20TE%20badness| TE loglfat badness]] than any smaller edo and less than any until [[xenharmonic/16808edo|16808]].

Below the intervals of the [[27-limit]] [[tonality diamond]] are tabulated, with the sizes listed in both [[cent]]s and minas and expressed as degrees and minutes (rounded to the nearest minute). The value in minas, rounded to the nearest integer, can be found by applying the [[23-limit]] [[patent val]] <2460 3899 5712 6906 8510 9103 10055 10450 11128| for 2460edo; this will not work for [[1200edo]] and cents.

Line 172:

Line 203:

<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>mina</title></head><body>The mina is a unit of interval size which has been proposed by <a class="wiki_link" href="/George%20Secor">George Secor</a> and <a class="wiki_link" href="/Dave%20Keenan">Dave Keenan</a>, and which is defined as 1/2460 of an <a class="wiki_link" href="/octave">octave</a>, the step size of <a class="wiki_link" href="/2460edo">2460edo</a>. 2460 is divisible by both 12 and 41, two important systems, and it's been suggested that degrees and minutes can be used to express values in it, so that for instance 3/2, which is 1439 minas, could be denoted by 23°59', meaning very slightly flat of the 24\41 <a class="wiki_link" href="/41edo">41edo</a> fifths. This works out since 41 * 60 = 2460; an octave is therefore expressed as if it were an angle of 41 degrees.

Other popular systems that can be represented exactly in whole numbers of minas include <a class="wiki_link" href="/10edo">10edo</a> and <a class="wiki_link" href="/15edo">15edo</a>. Moreover a cent is exactly 2.05 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mina">mina</a>s, and a mem, 1\205 octaves, is exactly 12 minas.

The following table lists some intervals which may be represented exactly in minas and in degrees and minutes, with the sizes listed in both <a class="wiki_link" href="/cent">cent</a>s and minas and expressed as degrees and minutes.

<tr>

<th>interval

</th>

<th>size in

cents

</th>

<th>size in

minas

</th>

<th>size as degrees

and minutes

</th>

</tr>

<tr>

<td>1\2460

</td>

<td>0.488

</td>

<td>1

</td>

<td>1'

</td>

</tr>

<tr>

<td>1\205

</td>

<td>5.835

</td>

<td>12

</td>

<td>12'

</td>

</tr>

<tr>

<td>1\41

</td>

<td>29.268

</td>

<td>60

</td>

<td>1°

</td>

</tr>

<tr>

<td>1\15

</td>

<td>80

</td>

<td>164

</td>

<td>2°44'

</td>

</tr>

<tr>

<td>1\12

</td>

<td>100

</td>

<td>205

</td>

<td>3°25'

</td>

</tr>

<tr>

<td>1\10

</td>

<td>120

</td>

<td>246

</td>

<td>4°6'

</td>

</tr>

<tr>

<td>1\6

</td>

<td>200

</td>

<td>410

</td>

<td>6°50'

</td>

</tr>

<tr>

<td>1\5

</td>

<td>240

</td>

<td>492

</td>

<td>8°12'

</td>

</tr>

<tr>

<td>1\4

</td>

<td>300

</td>

<td>615

</td>

<td>10°15'

</td>

</tr>

<tr>

<td>1\3

</td>

<td>400

</td>

<td>820

</td>

<td>13°40'

</td>

</tr>

<tr>

<td>2\5

</td>

<td>480

</td>

<td>984

</td>

<td>16°24'

</td>

</tr>

<tr>

<td>5\12

</td>

<td>500

</td>

<td>1025

</td>

<td>17°5'

</td>

</tr>

<tr>

<td>1\2

</td>

<td>600

</td>

<td>1230

</td>

<td>20°30'

</td>

</tr>

<tr>

<td>7\12

</td>

<td>700

</td>

<td>1435

</td>

<td>23°55'

</td>

</tr>

<tr>

<td>3\5

</td>

<td>720

</td>

<td>1476

</td>

<td>24°36'

</td>

</tr>

<tr>

<td>2\3

</td>

<td>800

</td>

<td>1640

</td>

<td>27°20'

</td>

</tr>

<tr>

<td>3\4

</td>

<td>900

</td>

<td>1845

</td>

<td>30°45'

</td>

</tr>

<tr>

<td>4\5

</td>

<td>960

</td>

<td>1960

</td>

<td>32°48'

</td>

</tr>

<tr>

<td>5\6

</td>

<td>1000

</td>

<td>2050

</td>

<td>34°10

</td>

</tr>

<tr>

<td>11\12

</td>

<td>1100

</td>

<td>2255

</td>

<td>37°35

</td>

</tr>

<tr>

<td>2/1

</td>

<td>1200

</td>

<td>2460

</td>

<td>41°

</td>

</tr>

</table>

Another helpful proponent of the mina is the accuracy and breadth of it's approximation to just intervals. Accordingly it is hardly necessary to express intervals in non-integer values of mina, something that arguably cannot be said of cents. <a class="wiki_link" href="/2460edo">2460edo</a> It is uniquely <a class="wiki_link" href="http://xenharmonic.wikispaces.com/consistent">consistent</a> through to the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/27-limit">27-limit</a>, which is not very remarkable in itself (<a class="wiki_link" href="http://xenharmonic.wikispaces.com/388edo">388edo</a> is the first such system), but what is remarkable is the degree of accuracy to which it represents the 27-limit intervals. It is also a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta peak edo</a> and has a lower 19-limit <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Tenney-Euclidean%20temperament%20measures#TE%20simple%20badness">relative error</a> than any edo until <a class="wiki_link" href="http://xenharmonic.wikispaces.com/3395edo">3395</a>, and a lower 23-limit relative error than any until <a class="wiki_link" href="http://xenharmonic.wikispaces.com/8269edo">8269</a>. Also it has a lower 23-limit <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Tenney-Euclidean%20metrics#Logflat%20TE%20badness"> TE loglfat badness</a> than any smaller edo and less than any until <a class="wiki_link" href="http://xenharmonic.wikispaces.com/16808edo">16808</a>.

Below the intervals of the <a class="wiki_link" href="/27-limit">27-limit</a> <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a> are tabulated, with the sizes listed in both <a class="wiki_link" href="/cent">cent</a>s and minas and expressed as degrees and minutes (rounded to the nearest minute). The value in minas, rounded to the nearest integer, can be found by applying the <a class="wiki_link" href="/23-limit">23-limit</a> <a class="wiki_link" href="/patent%20val">patent val</a> &lt;2460 3899 5712 6906 8510 9103 10055 10450 11128| for 2460edo; this will not work for <a class="wiki_link" href="/1200edo">1200edo</a> and cents.

@@ 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:hearneg|hearneg]] and made on <tt>2017-06-11 03:43:56 UTC</tt>.<br>
+: This revision was by author [[User:hearneg|hearneg]] and made on <tt>2017-06-11 04:20:54 UTC</tt>.<br>
-: The original revision id was <tt>614524037</tt>.<br>
+: The original revision id was <tt>614524401</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">The //mina// is a unit of interval size which has been proposed by [[George Secor]] and [[Dave Keenan]], and which is defined as 1/2460 of an [[octave]], the step size of [[2460edo]]. 2460 is divisible by both 12 and 41, two important systems, and it's been suggested that degrees and minutes can be used to express values in it, so that for instance 3/2, which is 1439 minas, could be denoted by 23°59', meaning very slightly flat of the 24\41 [[41edo]] fifths. This works out since 41 * 60 = 2460; an octave is therefore expressed as if it were an angle of 41 degrees.
+Other popular systems that can be represented exactly in whole numbers of minas include [[10edo]] and [[15edo]]. Moreover a cent is exactly 2.05 [[xenharmonic/mina|mina]]s, and a mem, 1\205 octaves, is exactly 12 minas.
+The following table lists some intervals which may be represented exactly in minas and in degrees and minutes, with the sizes listed in both [[cent]]s and minas and expressed as degrees and minutes.
+||~ interval ||~ size in
+cents ||~ size in
+minas ||~ size as degrees
+and minutes ||
+|| 1\2460 || 0.488 || 1 || 1' ||
+|| 1\205 || 5.835 || 12 || 12' ||
+|| 1\41 || 29.268 || 60 || 1° ||
+|| 1\15 || 80 || 164 || 2°44' ||
+|| 1\12 || 100 || 205 || 3°25' ||
+|| 1\10 || 120 || 246 || 4°6' ||
+|| 1\6 || 200 || 410 || 6°50' ||
+|| 1\5 || 240 || 492 || 8°12' ||
+|| 1\4 || 300 || 615 || 10°15' ||
+|| 1\3 || 400 || 820 || 13°40' ||
+|| 2\5 || 480 || 984 || 16°24' ||
+|| 5\12 || 500 || 1025 || 17°5' ||
+|| 1\2 || 600 || 1230 || 20°30' ||
+|| 7\12 || 700 || 1435 || 23°55' ||
+|| 3\5 || 720 || 1476 || 24°36' ||
+|| 2\3 || 800 || 1640 || 27°20' ||
+|| 3\4 || 900 || 1845 || 30°45' ||
+|| 4\5 || 960 || 1960 || 32°48' ||
+|| 5\6 || 1000 || 2050 || 34°10 ||
+|| 11\12 || 1100 || 2255 || 37°35 ||
+|| 2/1 || 1200 || 2460 || 41° ||
+Another helpful proponent of the mina is the accuracy and breadth of it's approximation to just intervals. Accordingly it is hardly necessary to express intervals in non-integer values of mina, something that arguably cannot be said of cents. [[2460edo]] It is uniquely [[xenharmonic/consistent|consistent]] through to the [[xenharmonic/27-limit|27-limit]], which is not very remarkable in itself ([[xenharmonic/388edo|388edo]] is the first such system), but what is remarkable is the degree of accuracy to which it represents the 27-limit intervals. It is also a [[xenharmonic/The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta peak edo]] and has a lower 19-limit [[xenharmonic/Tenney-Euclidean temperament measures#TE%20simple%20badness|relative error]] than any edo until [[xenharmonic/3395edo|3395]], and a lower 23-limit relative error than any until [[xenharmonic/8269edo|8269]]. Also it has a lower 23-limit [[xenharmonic/Tenney-Euclidean metrics#Logflat%20TE%20badness| TE loglfat badness]] than any smaller edo and less than any until [[xenharmonic/16808edo|16808]].
 Below the intervals of the [[27-limit]] [[tonality diamond]] are tabulated, with the sizes listed in both [[cent]]s and minas and expressed as degrees and minutes (rounded to the nearest minute). The value in minas, rounded to the nearest integer, can be found by applying the [[23-limit]] [[patent val]] &lt;2460 3899 5712 6906 8510 9103 10055 10450 11128| for 2460edo; this will not work for [[1200edo]] and cents.
@@ Line 172: / Line 203: @@
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;mina&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;mina&lt;/em&gt; is a unit of interval size which has been proposed by &lt;a class="wiki_link" href="/George%20Secor"&gt;George Secor&lt;/a&gt; and &lt;a class="wiki_link" href="/Dave%20Keenan"&gt;Dave Keenan&lt;/a&gt;, and which is defined as 1/2460 of an &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt;, the step size of &lt;a class="wiki_link" href="/2460edo"&gt;2460edo&lt;/a&gt;. 2460 is divisible by both 12 and 41, two important systems, and it's been suggested that degrees and minutes can be used to express values in it, so that for instance 3/2, which is 1439 minas, could be denoted by 23°59', meaning very slightly flat of the 24\41 &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt; fifths. This works out since 41 * 60 = 2460; an octave is therefore expressed as if it were an angle of 41 degrees.&lt;br /&gt;
+&lt;br /&gt;
+Other popular systems that can be represented exactly in whole numbers of minas include &lt;a class="wiki_link" href="/10edo"&gt;10edo&lt;/a&gt; and &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;. Moreover a cent is exactly 2.05 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/mina"&gt;mina&lt;/a&gt;s, and a mem, 1\205 octaves, is exactly 12 minas.&lt;br /&gt;
+&lt;br /&gt;
+The following table lists some intervals which may be represented exactly in minas and in degrees and minutes, with the sizes listed in both &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s and minas and expressed as degrees and minutes.&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;th&gt;interval&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;size in &lt;br /&gt;
+cents&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;size in &lt;br /&gt;
+minas&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;size as degrees &lt;br /&gt;
+and minutes&lt;br /&gt;
+&lt;/th&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1\2460&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0.488&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1'&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1\205&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5.835&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;12'&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1\41&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;29.268&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;60&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1°&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1\15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;80&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;164&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2°44'&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1\12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;100&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;205&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3°25'&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1\10&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;120&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;246&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4°6'&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1\6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;200&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;410&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6°50'&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1\5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;240&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;492&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8°12'&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1\4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;300&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;615&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;10°15'&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1\3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;400&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;820&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13°40'&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;2\5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;480&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;984&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;16°24'&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;5\12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;500&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1025&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;17°5'&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1\2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;600&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1230&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;20°30'&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;7\12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;700&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1435&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;23°55'&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;3\5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;720&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1476&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;24°36'&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;2\3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;800&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1640&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;27°20'&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;3\4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;900&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1845&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;30°45'&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;4\5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;960&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1960&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;32°48'&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;5\6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1000&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2050&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;34°10&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;11\12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1100&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2255&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;37°35&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;2/1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1200&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2460&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;41°&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;br /&gt;
+Another helpful proponent of the mina is the accuracy and breadth of it's approximation to just intervals. Accordingly it is hardly necessary to express intervals in non-integer values of mina, something that arguably cannot be said of cents. &lt;a class="wiki_link" href="/2460edo"&gt;2460edo&lt;/a&gt; It is uniquely &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/consistent"&gt;consistent&lt;/a&gt; through to the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/27-limit"&gt;27-limit&lt;/a&gt;, which is not very remarkable in itself (&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/388edo"&gt;388edo&lt;/a&gt; is the first such system), but what is remarkable is the degree of accuracy to which it represents the 27-limit intervals. It is also a &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta peak edo&lt;/a&gt; and has a lower 19-limit &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Tenney-Euclidean%20temperament%20measures#TE%20simple%20badness"&gt;relative error&lt;/a&gt; than any edo until &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/3395edo"&gt;3395&lt;/a&gt;, and a lower 23-limit relative error than any until &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/8269edo"&gt;8269&lt;/a&gt;. Also it has a lower 23-limit &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Tenney-Euclidean%20metrics#Logflat%20TE%20badness"&gt; TE loglfat badness&lt;/a&gt; than any smaller edo and less than any until &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/16808edo"&gt;16808&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 Below the intervals of the &lt;a class="wiki_link" href="/27-limit"&gt;27-limit&lt;/a&gt; &lt;a class="wiki_link" href="/tonality%20diamond"&gt;tonality diamond&lt;/a&gt; are tabulated, with the sizes listed in both &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s and minas and expressed as degrees and minutes (rounded to the nearest minute). The value in minas, rounded to the nearest integer, can be found by applying the &lt;a class="wiki_link" href="/23-limit"&gt;23-limit&lt;/a&gt; &lt;a class="wiki_link" href="/patent%20val"&gt;patent val&lt;/a&gt; &amp;lt;2460 3899 5712 6906 8510 9103 10055 10450 11128| for 2460edo; this will not work for &lt;a class="wiki_link" href="/1200edo"&gt;1200edo&lt;/a&gt; and cents.&lt;br /&gt;