Ragismic microtemperaments: 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>2012-02-~~16 13~~:32:31 UTC</tt>.<br>

: This revision was by author [[User:guest|guest]] and made on <tt>2012-03-04 20:52:15 UTC</tt>.<br>

: The original revision id was <tt>~~302464576~~</tt>.<br>

: The original revision id was <tt>307689046</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">[[toc]]

The ragisma is 4375/4374 with a monzo of |-1 -7 4 1>, the smallest 7-limit superparticular ratio. Since (10/9)^4 4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word "relatively" should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low complexity, with the same caveat about "relatively"; however 27/25 is the period for ennealimmal.

The ragisma is 4375/4374 with a monzo of |-1 -7 4 1>, the smallest 7-limit superparticular ratio. Since (10/9)^4=4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word "relatively" should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low complexity, with the same caveat about "relatively"; however 27/25 is the period for ennealimmal.

=Ennealimmal=

Line 88:

Badness: 0.0146

===Ennealimnic===

Commas: 169/168, 243/242, 325/324, 441/440

POTE generator: ~36/35 = 49.708

Line 97:

Badness: 0.0207

==Ennealiminal==

Commas: 385/384, 1375/1372, 4375/4374

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Badness: 0.0108

==Semisupermajor==

Commas: 3025/3024, 4375/4374, 35156250/35153041

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Badness: 0.00886

=Semidimi=

Commas: 4375/4374, 3955078125/3954653486

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Badness: 0.0151

=Brahmagupta=

Commas: 4375/4374, 70368744177664/70338939985125

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Badness: 0.0291

==11-limit==

Commas: 4000/3993, 4375/4374, 131072/130977

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Badness: 0.0522

=Neusec=

Commas: 3025/3024, 4375/4374, 235298/234375

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Badness: 0.0591

==13-limit==

Commas: 847/845, 1001/1000, 3025/3024, 4375/4374

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Badness: 0.0309

=Quasithird=

Commas: 4375/4374, 1153470752371588581/1152921504606846976

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Badness: 0.0618

==11-limit==

Commas: 3025/3024, 4375/4374, 4296700485/4294967296

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Badness: 0.0211

==13-limit==

Commas: 2200/2197, 3025/3024, 4375/4374, 468512/468195

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Badness: 0.0295

=Semidimfourth=

Commas: 4375/4374, 235298/234375

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Badness: 0.0552

=Acrokleismic=

Commas: 4375/4374, 2202927104/2197265625

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Badness: 0.0562

==11-limit==

Commas: 4375/4374, 41503/41472, 172032/171875

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Badness: 0.0369

==13-limit==

Commas: 676/675, 1001/1000, 4375/4374, 10985/10976

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Badness: 0.0268

==Counteracro==

Commas: 4375/4374, 5632/5625, 117649/117612

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Badness: 0.0426

===13-limit===

Commas: 676/675, 1716/1715, 4225/4224, 4375/4374

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Badness: 0.0153

==Music==

http://www.archive.org/details/Dreyfus

[[http://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3|play]]

==Octopus==

Commas: 169/168, 325/324, 364/363, 540/539

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Badness: 0.0236

==11-limit==

Commas: 540/539, 4375/4374, 5120/5103

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Badness: 0.0497

==Parkleismic==

Commas: 176/175, 1375/1372, 2200/2187

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Badness: 0.0559

===13-limit===

Commas: 169/168, 176/175, 325/324, 1375/1372

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Badness: 0.0366

==Paradigmic==

Commas: 540/539, 896/891, 3136/3125

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Badness: 0.0417

===13-limit===

Commas: 169/168, 325/324, 540/539, 832/825

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Badness: 0.0358

=Semiparakleismic=

Commas: 3025/3024, 3136/3125, 4375/4374

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Map: [<1 2 2 3 4 5 5 4|, <0 -30 -49 -14 -39 -94 -66 18|]

EDOs: 72, 145, 217

Badness: 0.0152

Badness: 0.0152</pre></div>

</pre></div>

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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>Ragismic microtemperaments</title></head><body><div id="toc"><h1 class="nopad">Table of Contents</h1><div style="margin-left: 1em;"><a href="#Ennealimmal">Ennealimmal</a></div>

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<div style="margin-left: 2em;"><a href="#Quincy-19-limit">19-limit</a></div>

</div>

The ragisma is 4375/4374 with a monzo of |-1 -7 4 1&gt;, the smallest 7-limit superparticular ratio. Since (10/9)^4 4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word &quot;relatively&quot; should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low complexity, with the same caveat about &quot;relatively&quot;; however 27/25 is the period for ennealimmal.<br />

The ragisma is 4375/4374 with a monzo of |-1 -7 4 1&gt;, the smallest 7-limit superparticular ratio. Since (10/9)^4=4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word &quot;relatively&quot; should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low complexity, with the same caveat about &quot;relatively&quot;; however 27/25 is the period for ennealimmal.<br />

<br />

<h1 id="toc0"><a name="Ennealimmal"></a>Ennealimmal</h1>

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<br />

<h3 id="toc8"><a name="Ennealimmal-Ennealimmic-Ennealimnic"></a>Ennealimnic</h3>

Commas: 169/168, 243/242, 325/324, 441/440<br />

<br />

POTE generator: ~36/35 = 49.708<br />

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<br />

<h2 id="toc9"><a name="Ennealimmal-Ennealiminal"></a>Ennealiminal</h2>

Commas: 385/384, 1375/1372, 4375/4374<br />

<br />

POTE generator: ~36/35 = 49.504<br />

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<br />

<h2 id="toc13"><a name="Supermajor-Semisupermajor"></a>Semisupermajor</h2>

Commas: 3025/3024, 4375/4374, 35156250/35153041<br />

<br />

POTE generator: ~9/7 = 435.082<br />

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<br />

<h1 id="toc22"><a name="Semidimi"></a>Semidimi</h1>

Commas: 4375/4374, 3955078125/3954653486<br />

<br />

POTE generator: ~35/27 = 449.127<br />

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<br />

<h1 id="toc23"><a name="Brahmagupta"></a>Brahmagupta</h1>

Commas: 4375/4374, 70368744177664/70338939985125<br />

<br />

POTE generator: ~27/20 = 519.716<br />

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<br />

<h2 id="toc24"><a name="Brahmagupta-11-limit"></a>11-limit</h2>

Commas: 4000/3993, 4375/4374, 131072/130977<br />

<br />

POTE generator: ~27/20 = 519.704<br />

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<br />

<h1 id="toc25"><a name="Neusec"></a>Neusec</h1>

Commas: 3025/3024, 4375/4374, 235298/234375<br />

<br />

POTE generator: ~12/11 = 151.547<br />

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<br />

<h2 id="toc26"><a name="Neusec-13-limit"></a>13-limit</h2>

Commas: 847/845, 1001/1000, 3025/3024, 4375/4374<br />

<br />

POTE generator: ~12/11 = 151.545<br />

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<br />

<h1 id="toc27"><a name="Quasithird"></a>Quasithird</h1>

Commas: 4375/4374, 1153470752371588581/1152921504606846976<br />

<br />

POTE generator: ~5103/4096 = 380.388<br />

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<br />

<h2 id="toc28"><a name="Quasithird-11-limit"></a>11-limit</h2>

Commas: 3025/3024, 4375/4374, 4296700485/4294967296<br />

<br />

POTE generator: ~5103/4096 = 380.387<br />

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<br />

<h2 id="toc29"><a name="Quasithird-13-limit"></a>13-limit</h2>

Commas: 2200/2197, 3025/3024, 4375/4374, 468512/468195<br />

<br />

POTE generator: ~5103/4096 = 380.385<br />

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<br />

<h1 id="toc30"><a name="Semidimfourth"></a>Semidimfourth</h1>

Commas: 4375/4374, 235298/234375<br />

<br />

POTE generator: ~35/27 = 448.457<br />

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<br />

<h1 id="toc31"><a name="Acrokleismic"></a>Acrokleismic</h1>

Commas: 4375/4374, 2202927104/2197265625<br />

<br />

POTE generator: ~6/5 = 315.557<br />

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<br />

<h2 id="toc32"><a name="Acrokleismic-11-limit"></a>11-limit</h2>

Commas: 4375/4374, 41503/41472, 172032/171875<br />

<br />

POTE generator: ~6/5 = 315.558<br />

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<br />

<h2 id="toc33"><a name="Acrokleismic-13-limit"></a>13-limit</h2>

Commas: 676/675, 1001/1000, 4375/4374, 10985/10976<br />

<br />

POTE generator: ~6/5 = 315.557<br />

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<br />

<h2 id="toc34"><a name="Acrokleismic-Counteracro"></a>Counteracro</h2>

Commas: 4375/4374, 5632/5625, 117649/117612<br />

<br />

POTE generator: ~6/5 = 315.553<br />

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<br />

<h3 id="toc35"><a name="Acrokleismic-Counteracro-13-limit"></a>13-limit</h3>

Commas: 676/675, 1716/1715, 4225/4224, 4375/4374<br />

<br />

POTE generator: ~6/5 = 315.554<br />

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<br />

<h2 id="toc40"><a name="Octoid-Music"></a>Music</h2>

<a class="wiki_link_ext" href="http://www.archive.org/details/Dreyfus" rel="nofollow">http://www.archive.org/details/Dreyfus</a><br />

<br />

<h2 id="toc41"><a name="Octoid-Octopus"></a>Octopus</h2>

Commas: 169/168, 325/324, 364/363, 540/539<br />

<br />

POTE generator: ~7/5 = 583.892<br />

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<br />

<h2 id="toc45"><a name="Amity-11-limit"></a>11-limit</h2>

Commas: 540/539, 4375/4374, 5120/5103<br />

<br />

POTE generator: ~243/200 = 339.464<br />

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<br />

<h2 id="toc51"><a name="Parakleismic-Parkleismic"></a>Parkleismic</h2>

Commas: 176/175, 1375/1372, 2200/2187<br />

<br />

POTE generator: ~6/5 = 315.060<br />

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<br />

<h3 id="toc52"><a name="Parakleismic-Parkleismic-13-limit"></a>13-limit</h3>

Commas: 169/168, 176/175, 325/324, 1375/1372<br />

<br />

POTE generator: ~6/5 = 315.075<br />

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<br />

<h2 id="toc53"><a name="Parakleismic-Paradigmic"></a>Paradigmic</h2>

Commas: 540/539, 896/891, 3136/3125<br />

<br />

POTE generator: ~6/5 = 315.096<br />

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<br />

<h3 id="toc54"><a name="Parakleismic-Paradigmic-13-limit"></a>13-limit</h3>

Commas: 169/168, 325/324, 540/539, 832/825<br />

<br />

POTE generator: ~6/5 = 315.080<br />

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<br />

<h1 id="toc55"><a name="Semiparakleismic"></a>Semiparakleismic</h1>

Commas: 3025/3024, 3136/3125, 4375/4374<br />

<br />

POTE generator: 315.181<br />

@@ 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>2012-02-16 13:32:31 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2012-03-04 20:52:15 UTC</tt>.<br>
-: The original revision id was <tt>302464576</tt>.<br>
+: The original revision id was <tt>307689046</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">[[toc]]
-The ragisma is 4375/4374 with a monzo of |-1 -7 4 1&gt;, the smallest 7-limit superparticular ratio. Since (10/9)^4 4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word "relatively" should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low complexity, with the same caveat about "relatively"; however 27/25 is the period for ennealimmal.
+The ragisma is 4375/4374 with a monzo of |-1 -7 4 1&gt;, the smallest 7-limit superparticular ratio. Since (10/9)^4=4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word "relatively" should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low complexity, with the same caveat about "relatively"; however 27/25 is the period for ennealimmal.
 =Ennealimmal=
@@ Line 88: / Line 88: @@
 Badness: 0.0146
 ===Ennealimnic===
-Commas:  169/168, 243/242, 325/324, 441/440
+Commas: 169/168, 243/242, 325/324, 441/440
 POTE generator: ~36/35 = 49.708
@@ Line 97: / Line 97: @@
 Badness: 0.0207
 ==Ennealiminal==
 Commas: 385/384, 1375/1372, 4375/4374
@@ Line 136: / Line 136: @@
 Badness: 0.0108
 ==Semisupermajor==
 Commas: 3025/3024, 4375/4374, 35156250/35153041
@@ Line 221: / Line 221: @@
 Badness: 0.00886
 =Semidimi=
 Commas: 4375/4374, 3955078125/3954653486
@@ Line 231: / Line 231: @@
 Badness: 0.0151
 =Brahmagupta=
 Commas: 4375/4374, 70368744177664/70338939985125
@@ Line 241: / Line 241: @@
 Badness: 0.0291
 ==11-limit==
 Commas: 4000/3993, 4375/4374, 131072/130977
@@ Line 250: / Line 250: @@
 Badness: 0.0522
 =Neusec=
 Commas: 3025/3024, 4375/4374, 235298/234375
@@ Line 259: / Line 259: @@
 Badness: 0.0591
 ==13-limit==
 Commas: 847/845, 1001/1000, 3025/3024, 4375/4374
@@ Line 268: / Line 268: @@
 Badness: 0.0309
 =Quasithird=
 Commas: 4375/4374, 1153470752371588581/1152921504606846976
@@ Line 278: / Line 278: @@
 Badness: 0.0618
 ==11-limit==
 Commas: 3025/3024, 4375/4374, 4296700485/4294967296
@@ Line 287: / Line 287: @@
 Badness: 0.0211
 ==13-limit==
 Commas: 2200/2197, 3025/3024, 4375/4374, 468512/468195
@@ Line 296: / Line 296: @@
 Badness: 0.0295
 =Semidimfourth=
 Commas: 4375/4374, 235298/234375
@@ Line 306: / Line 306: @@
 Badness: 0.0552
 =Acrokleismic=
 Commas: 4375/4374, 2202927104/2197265625
@@ Line 316: / Line 316: @@
 Badness: 0.0562
 ==11-limit==
 Commas: 4375/4374, 41503/41472, 172032/171875
@@ Line 325: / Line 325: @@
 Badness: 0.0369
 ==13-limit==
 Commas: 676/675, 1001/1000, 4375/4374, 10985/10976
@@ Line 334: / Line 334: @@
 Badness: 0.0268
 ==Counteracro==
 Commas: 4375/4374, 5632/5625, 117649/117612
@@ Line 343: / Line 343: @@
 Badness: 0.0426
 ===13-limit===
 Commas: 676/675, 1716/1715, 4225/4224, 4375/4374
@@ Line 383: / Line 383: @@
 Badness: 0.0153
 ==Music==
 http://www.archive.org/details/Dreyfus
 [[http://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3|play]]
 ==Octopus==
 Commas: 169/168, 325/324, 364/363, 540/539
@@ Line 420: / Line 420: @@
 Badness: 0.0236
 ==11-limit==
 Commas: 540/539, 4375/4374, 5120/5103
@@ Line 475: / Line 475: @@
 Badness: 0.0497
 ==Parkleismic==
 Commas: 176/175, 1375/1372, 2200/2187
@@ Line 484: / Line 484: @@
 Badness: 0.0559
 ===13-limit===
 Commas: 169/168, 176/175, 325/324, 1375/1372
@@ Line 493: / Line 493: @@
 Badness: 0.0366
 ==Paradigmic==
 Commas: 540/539, 896/891, 3136/3125
@@ Line 502: / Line 502: @@
 Badness: 0.0417
 ===13-limit===
 Commas: 169/168, 325/324, 540/539, 832/825
@@ Line 511: / Line 511: @@
 Badness: 0.0358
 =Semiparakleismic=
 Commas: 3025/3024, 3136/3125, 4375/4374
@@ Line 563: / Line 563: @@
 Map: [&lt;1 2 2 3 4 5 5 4|, &lt;0 -30 -49 -14 -39 -94 -66 18|]
 EDOs: 72, 145, 217
-Badness: 0.0152
+Badness: 0.0152</pre></div>
-</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Ragismic microtemperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:122:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:122 --&gt;&lt;!-- ws:start:WikiTextTocRule:123: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Ennealimmal"&gt;Ennealimmal&lt;/a&gt;&lt;/div&gt;
@@ Line 628: / Line 627: @@
 &lt;!-- ws:end:WikiTextTocRule:182 --&gt;&lt;!-- ws:start:WikiTextTocRule:183: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quincy-19-limit"&gt;19-limit&lt;/a&gt;&lt;/div&gt;
 &lt;!-- ws:end:WikiTextTocRule:183 --&gt;&lt;!-- ws:start:WikiTextTocRule:184: --&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:184 --&gt;The ragisma is 4375/4374 with a monzo of |-1 -7 4 1&amp;gt;, the smallest 7-limit superparticular ratio. Since (10/9)^4 4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word &amp;quot;relatively&amp;quot; should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low complexity, with the same caveat about &amp;quot;relatively&amp;quot;; however 27/25 is the period for ennealimmal.&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:184 --&gt;The ragisma is 4375/4374 with a monzo of |-1 -7 4 1&amp;gt;, the smallest 7-limit superparticular ratio. Since (10/9)^4=4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word &amp;quot;relatively&amp;quot; should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low complexity, with the same caveat about &amp;quot;relatively&amp;quot;; however 27/25 is the period for ennealimmal.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Ennealimmal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Ennealimmal&lt;/h1&gt;
@@ Line 710: / Line 709: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="Ennealimmal-Ennealimmic-Ennealimnic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Ennealimnic&lt;/h3&gt;
-Commas:  169/168, 243/242, 325/324, 441/440&lt;br /&gt;
+ Commas: 169/168, 243/242, 325/324, 441/440&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~36/35 = 49.708&lt;br /&gt;
@@ Line 719: / Line 718: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Ennealimmal-Ennealiminal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Ennealiminal&lt;/h2&gt;
-Commas: 385/384, 1375/1372, 4375/4374&lt;br /&gt;
+ Commas: 385/384, 1375/1372, 4375/4374&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~36/35 = 49.504&lt;br /&gt;
@@ Line 758: / Line 757: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Supermajor-Semisupermajor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Semisupermajor&lt;/h2&gt;
-Commas: 3025/3024, 4375/4374, 35156250/35153041&lt;br /&gt;
+ Commas: 3025/3024, 4375/4374, 35156250/35153041&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~9/7 = 435.082&lt;br /&gt;
@@ Line 843: / Line 842: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc22"&gt;&lt;a name="Semidimi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Semidimi&lt;/h1&gt;
-Commas: 4375/4374, 3955078125/3954653486&lt;br /&gt;
+ Commas: 4375/4374, 3955078125/3954653486&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~35/27 = 449.127&lt;br /&gt;
@@ Line 853: / Line 852: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc23"&gt;&lt;a name="Brahmagupta"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Brahmagupta&lt;/h1&gt;
-Commas: 4375/4374, 70368744177664/70338939985125&lt;br /&gt;
+ Commas: 4375/4374, 70368744177664/70338939985125&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~27/20 = 519.716&lt;br /&gt;
@@ Line 863: / Line 862: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Brahmagupta-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;11-limit&lt;/h2&gt;
-Commas: 4000/3993, 4375/4374, 131072/130977&lt;br /&gt;
+ Commas: 4000/3993, 4375/4374, 131072/130977&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~27/20 = 519.704&lt;br /&gt;
@@ Line 872: / Line 871: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc25"&gt;&lt;a name="Neusec"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Neusec&lt;/h1&gt;
-Commas: 3025/3024, 4375/4374, 235298/234375&lt;br /&gt;
+ Commas: 3025/3024, 4375/4374, 235298/234375&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~12/11 = 151.547&lt;br /&gt;
@@ Line 881: / Line 880: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Neusec-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;13-limit&lt;/h2&gt;
-Commas: 847/845, 1001/1000, 3025/3024, 4375/4374&lt;br /&gt;
+ Commas: 847/845, 1001/1000, 3025/3024, 4375/4374&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~12/11 = 151.545&lt;br /&gt;
@@ Line 890: / Line 889: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc27"&gt;&lt;a name="Quasithird"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;Quasithird&lt;/h1&gt;
-Commas: 4375/4374, 1153470752371588581/1152921504606846976&lt;br /&gt;
+ Commas: 4375/4374, 1153470752371588581/1152921504606846976&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~5103/4096 = 380.388&lt;br /&gt;
@@ Line 900: / Line 899: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Quasithird-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;11-limit&lt;/h2&gt;
-Commas: 3025/3024, 4375/4374, 4296700485/4294967296&lt;br /&gt;
+ Commas: 3025/3024, 4375/4374, 4296700485/4294967296&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~5103/4096 = 380.387&lt;br /&gt;
@@ Line 909: / Line 908: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc29"&gt;&lt;a name="Quasithird-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;13-limit&lt;/h2&gt;
-Commas: 2200/2197, 3025/3024, 4375/4374, 468512/468195&lt;br /&gt;
+ Commas: 2200/2197, 3025/3024, 4375/4374, 468512/468195&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~5103/4096 = 380.385&lt;br /&gt;
@@ Line 918: / Line 917: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc30"&gt;&lt;a name="Semidimfourth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;Semidimfourth&lt;/h1&gt;
-Commas: 4375/4374, 235298/234375&lt;br /&gt;
+ Commas: 4375/4374, 235298/234375&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~35/27 = 448.457&lt;br /&gt;
@@ Line 928: / Line 927: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc31"&gt;&lt;a name="Acrokleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;Acrokleismic&lt;/h1&gt;
-Commas: 4375/4374, 2202927104/2197265625&lt;br /&gt;
+ Commas: 4375/4374, 2202927104/2197265625&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 315.557&lt;br /&gt;
@@ Line 938: / Line 937: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc32"&gt;&lt;a name="Acrokleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;11-limit&lt;/h2&gt;
-Commas: 4375/4374, 41503/41472, 172032/171875&lt;br /&gt;
+ Commas: 4375/4374, 41503/41472, 172032/171875&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 315.558&lt;br /&gt;
@@ Line 947: / Line 946: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc33"&gt;&lt;a name="Acrokleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;13-limit&lt;/h2&gt;
-Commas: 676/675, 1001/1000, 4375/4374, 10985/10976&lt;br /&gt;
+ Commas: 676/675, 1001/1000, 4375/4374, 10985/10976&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 315.557&lt;br /&gt;
@@ Line 956: / Line 955: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc34"&gt;&lt;a name="Acrokleismic-Counteracro"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;Counteracro&lt;/h2&gt;
-Commas: 4375/4374, 5632/5625, 117649/117612&lt;br /&gt;
+ Commas: 4375/4374, 5632/5625, 117649/117612&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 315.553&lt;br /&gt;
@@ Line 965: / Line 964: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc35"&gt;&lt;a name="Acrokleismic-Counteracro-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;13-limit&lt;/h3&gt;
-Commas: 676/675, 1716/1715, 4225/4224, 4375/4374&lt;br /&gt;
+ Commas: 676/675, 1716/1715, 4225/4224, 4375/4374&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 315.554&lt;br /&gt;
@@ Line 1,005: / Line 1,004: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:80:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc40"&gt;&lt;a name="Octoid-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:80 --&gt;Music&lt;/h2&gt;
-&lt;!-- ws:start:WikiTextUrlRule:700:http://www.archive.org/details/Dreyfus --&gt;&lt;a class="wiki_link_ext" href="http://www.archive.org/details/Dreyfus" rel="nofollow"&gt;http://www.archive.org/details/Dreyfus&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:700 --&gt;&lt;br /&gt;
+ &lt;!-- ws:start:WikiTextUrlRule:700:http://www.archive.org/details/Dreyfus --&gt;&lt;a class="wiki_link_ext" href="http://www.archive.org/details/Dreyfus" rel="nofollow"&gt;http://www.archive.org/details/Dreyfus&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:700 --&gt;&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:82:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc41"&gt;&lt;a name="Octoid-Octopus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:82 --&gt;Octopus&lt;/h2&gt;
-Commas: 169/168, 325/324, 364/363, 540/539&lt;br /&gt;
+ Commas: 169/168, 325/324, 364/363, 540/539&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~7/5 = 583.892&lt;br /&gt;
@@ Line 1,042: / Line 1,041: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:90:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc45"&gt;&lt;a name="Amity-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:90 --&gt;11-limit&lt;/h2&gt;
-Commas: 540/539, 4375/4374, 5120/5103&lt;br /&gt;
+ Commas: 540/539, 4375/4374, 5120/5103&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~243/200 = 339.464&lt;br /&gt;
@@ Line 1,097: / Line 1,096: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:102:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc51"&gt;&lt;a name="Parakleismic-Parkleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:102 --&gt;Parkleismic&lt;/h2&gt;
-Commas: 176/175, 1375/1372, 2200/2187&lt;br /&gt;
+ Commas: 176/175, 1375/1372, 2200/2187&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 315.060&lt;br /&gt;
@@ Line 1,106: / Line 1,105: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:104:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc52"&gt;&lt;a name="Parakleismic-Parkleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:104 --&gt;13-limit&lt;/h3&gt;
-Commas: 169/168, 176/175, 325/324, 1375/1372&lt;br /&gt;
+ Commas: 169/168, 176/175, 325/324, 1375/1372&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 315.075&lt;br /&gt;
@@ Line 1,115: / Line 1,114: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:106:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc53"&gt;&lt;a name="Parakleismic-Paradigmic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:106 --&gt;Paradigmic&lt;/h2&gt;
-Commas: 540/539, 896/891, 3136/3125&lt;br /&gt;
+ Commas: 540/539, 896/891, 3136/3125&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 315.096&lt;br /&gt;
@@ Line 1,124: / Line 1,123: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:108:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc54"&gt;&lt;a name="Parakleismic-Paradigmic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:108 --&gt;13-limit&lt;/h3&gt;
-Commas: 169/168, 325/324, 540/539, 832/825&lt;br /&gt;
+ Commas: 169/168, 325/324, 540/539, 832/825&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 315.080&lt;br /&gt;
@@ Line 1,133: / Line 1,132: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:110:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc55"&gt;&lt;a name="Semiparakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:110 --&gt;Semiparakleismic&lt;/h1&gt;
-Commas: 3025/3024, 3136/3125, 4375/4374&lt;br /&gt;
+ Commas: 3025/3024, 3136/3125, 4375/4374&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: 315.181&lt;br /&gt;