Strictly proper 7-tone 31edo scales
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Below are listed scales which are [[http://en.wikipedia.org/wiki/Rothenberg_propriety|strictly proper]], in the sense the term is used by music theorist David Rothenberg. The "type" of a scale is defined by what linear temperament supported by 31et in which it has the least span. "Breed type" means it is a tie between miracle and hemiwuerschmidt.
===Meantone type===
||~ schema ||~ name ||~ example(s) ||
|| **{{5535553}}** || Meantone[7]; diatonic scale || ||
|| **{{5355553}}** || Melodic minor scale || ||
|| **{{5355373}}** || Harmonic minor scale; inverse harmonic major || ||
|| **{{5535373}}** || Harmonic major scale; inverse harmonic minor || ||
|| **{{5533555}}** || Major locrian scale || ||
|| **{{3717355}}** || Diminished diatonic scale || [[http://chrisvaisvil.com/?p=142|Strange Diatonic]] by [[Chris Vaisvil]] ||
|| **{{5535643}}** || Enharmonic major; inverse enharmonic minor || ||
|| **{{5346535}}** || Enharmonic minor; inverse enharmonic major || ||
|| **{{5535625}}** || Enharmonic mixolydian || ||
|| **{{5526535}}** || Inverse enharmonic mixolydian || ||
|| **{{5526355}}** || Enharmonic major-minor || ||
|| **{{5553625}}** || Inverse enharmonic major-minor || ||
|| **{{6435625}}** || Major doubleflat; inverse minor doubleflat || ||
|| **{{5346526}}** || Minor doubleflat; inverse major doubleflat || ||
|| **{{5553652}}** || Ping || ||
|| **{{3555256}}** || Inverse ping || ||
|| **{{3726355}}** || Alhijaz; inverse ambika || ||
|| **{{6273553}}** || Ambika; inverse alhijaz || ||
|| **{{6453652}}** || Kung; inverse ousak || ||
|| **{{3546256}}** || Ousak; inverse kung || ||
===Valentine===
|| **{{6446272}}** || Silver ||
|| **{{6444472}}** || Harmonia ||
|| **{{4446274}}** || Inverse harmonia ||
|| **{{6444562}}** || Pendragon ||
|| **{{4626544}}** || Inverse pendragon ||
|| **{{6264463}}** || Hipop ||
|| **{{4626364}}** || Inverse Hipop ||
|| **{{4626445}}** || Malakon ||
|| **{{4626454}}** || Inverse malakon ||
|| **{{4464526}}** || Bagpipe ||
|| **{{4644625}}** || Inverse bagpipe ||
|| **{{6444625}}** || Pitu ||
|| **{{6444652}}** || Inverse pitu ||
|| **{{6444445}}** || Porch ||
|| **{{4446544}}** || Inverse porch ||
===Miracle type===
|| **{{5436346}}** || Subdom scale; inverse superton ||
|| **{{5643634}}** || Superton scale; inverse subdom ||
|| **{{5436364}}** || Nudia; neutral diatonic ||
|| **{{5463634}}** || Inverse nudia ||
|| **{{3636346}}** || Nurow; Neutral triads in row ||
|| **{{6363643}}** || Inverse nurow ||
===Mohajira type===
|| **{{4554454}}** || Sikah; Rast; Neutral Diatonic Hypolydian ||
|| **{{4444555}}** || Sheimanic ||
|| **{{4554445}}** || Thaiic ||
|| **{{4544455}}** || Inverse thaiic ||
|| **{{4545454}}** || Mohajira; Neutral Dorian ||
===Hemiwuerschmidt type===
|| **{{5555515}}** || Hemiwuerschmidt/Hemithirds[7] ||
|| **{{5544652}}** || Hemaj; inverse hemin ||
|| **{{4455256}}** || Hemin; inverse hemaj ||
|| **{{4525546}}** || Gypsi; 11/9-10/7-7/4 chord on tonic ||
|| **{{4552546}}** || Inverse gypsi; 11/9-10/7-7/4 chord on tonic ||
|| **{{5555542}}** || Leadhole ||
|| **{{5555524}}** || Inverse leadhole ||
===Mothra type===
|| **{{5553643}}** || Lydic ||
|| **{{5553463}}** || Inverse lydic ||
|| **{{5535463}}** || Ionic ||
|| **{{5364535}}** || Aeolic; inverse ionic ||
|| **{{4644463}}** || Quahog ||
|| **{{6444643}}** || Inverse quahog ||
|| **{{6453643}}** || Higasi ||
|| **{{4635463}}** || Inverse higasi ||
===Orwell type===
|| **{{5364463}}** || Orminor ||
|| **{{4644643}}** || Ormed ||
|| **{{4644364}}** || Augton ||
|| **{{4644634}}** || Inverse augton ||
===Breed type===
|| **{{3456265}}** || Hemisub ||
|| **{{4356265}}** || Inverse hemisub ||
|| **{{6354535}}** || Heminewt ||
|| **{{4536535}}** || Inverse heminewt ||
|| {{ }} || ||Original HTML content:
<html><head><title>Strictly proper 7-note 31edo scales</title></head><body>Below are listed scales which are <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Rothenberg_propriety" rel="nofollow">strictly proper</a>, in the sense the term is used by music theorist David Rothenberg. The "type" of a scale is defined by what linear temperament supported by 31et in which it has the least span. "Breed type" means it is a tie between miracle and hemiwuerschmidt.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h3> --><h3 id="toc0"><a name="x--Meantone type"></a><!-- ws:end:WikiTextHeadingRule:0 -->Meantone type</h3>
<table class="wiki_table">
<tr>
<th>schema<br />
</th>
<th>name<br />
</th>
<th>example(s)<br />
</th>
</tr>
<tr>
<td><strong><tt>5535553</tt></strong><br />
</td>
<td>Meantone[7]; diatonic scale<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><strong><tt>5355553</tt></strong><br />
</td>
<td>Melodic minor scale<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><strong><tt>5355373</tt></strong><br />
</td>
<td>Harmonic minor scale; inverse harmonic major<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><strong><tt>5535373</tt></strong><br />
</td>
<td>Harmonic major scale; inverse harmonic minor<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><strong><tt>5533555</tt></strong><br />
</td>
<td>Major locrian scale<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><strong><tt>3717355</tt></strong><br />
</td>
<td>Diminished diatonic scale<br />
</td>
<td><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=142" rel="nofollow">Strange Diatonic</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br />
</td>
</tr>
<tr>
<td><strong><tt>5535643</tt></strong><br />
</td>
<td>Enharmonic major; inverse enharmonic minor<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><strong><tt>5346535</tt></strong><br />
</td>
<td>Enharmonic minor; inverse enharmonic major<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><strong><tt>5535625</tt></strong><br />
</td>
<td>Enharmonic mixolydian<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><strong><tt>5526535</tt></strong><br />
</td>
<td>Inverse enharmonic mixolydian<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><strong><tt>5526355</tt></strong><br />
</td>
<td>Enharmonic major-minor<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><strong><tt>5553625</tt></strong><br />
</td>
<td>Inverse enharmonic major-minor<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><strong><tt>6435625</tt></strong><br />
</td>
<td>Major doubleflat; inverse minor doubleflat<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><strong><tt>5346526</tt></strong><br />
</td>
<td>Minor doubleflat; inverse major doubleflat<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><strong><tt>5553652</tt></strong><br />
</td>
<td>Ping<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><strong><tt>3555256</tt></strong><br />
</td>
<td>Inverse ping<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><strong><tt>3726355</tt></strong><br />
</td>
<td>Alhijaz; inverse ambika<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><strong><tt>6273553</tt></strong><br />
</td>
<td>Ambika; inverse alhijaz<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><strong><tt>6453652</tt></strong><br />
</td>
<td>Kung; inverse ousak<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><strong><tt>3546256</tt></strong><br />
</td>
<td>Ousak; inverse kung<br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x--Valentine"></a><!-- ws:end:WikiTextHeadingRule:2 -->Valentine</h3>
<table class="wiki_table">
<tr>
<td><strong><tt>6446272</tt></strong><br />
</td>
<td>Silver<br />
</td>
</tr>
<tr>
<td><strong><tt>6444472</tt></strong><br />
</td>
<td>Harmonia<br />
</td>
</tr>
<tr>
<td><strong><tt>4446274</tt></strong><br />
</td>
<td>Inverse harmonia<br />
</td>
</tr>
<tr>
<td><strong><tt>6444562</tt></strong><br />
</td>
<td>Pendragon<br />
</td>
</tr>
<tr>
<td><strong><tt>4626544</tt></strong><br />
</td>
<td>Inverse pendragon<br />
</td>
</tr>
<tr>
<td><strong><tt>6264463</tt></strong><br />
</td>
<td>Hipop<br />
</td>
</tr>
<tr>
<td><strong><tt>4626364</tt></strong><br />
</td>
<td>Inverse Hipop<br />
</td>
</tr>
<tr>
<td><strong><tt>4626445</tt></strong><br />
</td>
<td>Malakon<br />
</td>
</tr>
<tr>
<td><strong><tt>4626454</tt></strong><br />
</td>
<td>Inverse malakon<br />
</td>
</tr>
<tr>
<td><strong><tt>4464526</tt></strong><br />
</td>
<td>Bagpipe<br />
</td>
</tr>
<tr>
<td><strong><tt>4644625</tt></strong><br />
</td>
<td>Inverse bagpipe<br />
</td>
</tr>
<tr>
<td><strong><tt>6444625</tt></strong><br />
</td>
<td>Pitu<br />
</td>
</tr>
<tr>
<td><strong><tt>6444652</tt></strong><br />
</td>
<td>Inverse pitu<br />
</td>
</tr>
<tr>
<td><strong><tt>6444445</tt></strong><br />
</td>
<td>Porch<br />
</td>
</tr>
<tr>
<td><strong><tt>4446544</tt></strong><br />
</td>
<td>Inverse porch<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="x--Miracle type"></a><!-- ws:end:WikiTextHeadingRule:4 -->Miracle type</h3>
<table class="wiki_table">
<tr>
<td><strong><tt>5436346</tt></strong><br />
</td>
<td>Subdom scale; inverse superton<br />
</td>
</tr>
<tr>
<td><strong><tt>5643634</tt></strong><br />
</td>
<td>Superton scale; inverse subdom<br />
</td>
</tr>
<tr>
<td><strong><tt>5436364</tt></strong><br />
</td>
<td>Nudia; neutral diatonic<br />
</td>
</tr>
<tr>
<td><strong><tt>5463634</tt></strong><br />
</td>
<td>Inverse nudia<br />
</td>
</tr>
<tr>
<td><strong><tt>3636346</tt></strong><br />
</td>
<td>Nurow; Neutral triads in row<br />
</td>
</tr>
<tr>
<td><strong><tt>6363643</tt></strong><br />
</td>
<td>Inverse nurow<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc3"><a name="x--Mohajira type"></a><!-- ws:end:WikiTextHeadingRule:6 -->Mohajira type</h3>
<table class="wiki_table">
<tr>
<td><strong><tt>4554454</tt></strong><br />
</td>
<td>Sikah; Rast; Neutral Diatonic Hypolydian<br />
</td>
</tr>
<tr>
<td><strong><tt>4444555</tt></strong><br />
</td>
<td>Sheimanic<br />
</td>
</tr>
<tr>
<td><strong><tt>4554445</tt></strong><br />
</td>
<td>Thaiic<br />
</td>
</tr>
<tr>
<td><strong><tt>4544455</tt></strong><br />
</td>
<td>Inverse thaiic<br />
</td>
</tr>
<tr>
<td><strong><tt>4545454</tt></strong><br />
</td>
<td>Mohajira; Neutral Dorian<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:8:<h3> --><h3 id="toc4"><a name="x--Hemiwuerschmidt type"></a><!-- ws:end:WikiTextHeadingRule:8 -->Hemiwuerschmidt type</h3>
<table class="wiki_table">
<tr>
<td><strong><tt>5555515</tt></strong><br />
</td>
<td>Hemiwuerschmidt/Hemithirds[7]<br />
</td>
</tr>
<tr>
<td><strong><tt>5544652</tt></strong><br />
</td>
<td>Hemaj; inverse hemin<br />
</td>
</tr>
<tr>
<td><strong><tt>4455256</tt></strong><br />
</td>
<td>Hemin; inverse hemaj<br />
</td>
</tr>
<tr>
<td><strong><tt>4525546</tt></strong><br />
</td>
<td>Gypsi; 11/9-10/7-7/4 chord on tonic<br />
</td>
</tr>
<tr>
<td><strong><tt>4552546</tt></strong><br />
</td>
<td>Inverse gypsi; 11/9-10/7-7/4 chord on tonic<br />
</td>
</tr>
<tr>
<td><strong><tt>5555542</tt></strong><br />
</td>
<td>Leadhole<br />
</td>
</tr>
<tr>
<td><strong><tt>5555524</tt></strong><br />
</td>
<td>Inverse leadhole<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:10:<h3> --><h3 id="toc5"><a name="x--Mothra type"></a><!-- ws:end:WikiTextHeadingRule:10 -->Mothra type</h3>
<table class="wiki_table">
<tr>
<td><strong><tt>5553643</tt></strong><br />
</td>
<td>Lydic<br />
</td>
</tr>
<tr>
<td><strong><tt>5553463</tt></strong><br />
</td>
<td>Inverse lydic<br />
</td>
</tr>
<tr>
<td><strong><tt>5535463</tt></strong><br />
</td>
<td>Ionic<br />
</td>
</tr>
<tr>
<td><strong><tt>5364535</tt></strong><br />
</td>
<td>Aeolic; inverse ionic<br />
</td>
</tr>
<tr>
<td><strong><tt>4644463</tt></strong><br />
</td>
<td>Quahog<br />
</td>
</tr>
<tr>
<td><strong><tt>6444643</tt></strong><br />
</td>
<td>Inverse quahog<br />
</td>
</tr>
<tr>
<td><strong><tt>6453643</tt></strong><br />
</td>
<td>Higasi<br />
</td>
</tr>
<tr>
<td><strong><tt>4635463</tt></strong><br />
</td>
<td>Inverse higasi<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:12:<h3> --><h3 id="toc6"><a name="x--Orwell type"></a><!-- ws:end:WikiTextHeadingRule:12 -->Orwell type</h3>
<table class="wiki_table">
<tr>
<td><strong><tt>5364463</tt></strong><br />
</td>
<td>Orminor<br />
</td>
</tr>
<tr>
<td><strong><tt>4644643</tt></strong><br />
</td>
<td>Ormed<br />
</td>
</tr>
<tr>
<td><strong><tt>4644364</tt></strong><br />
</td>
<td>Augton<br />
</td>
</tr>
<tr>
<td><strong><tt>4644634</tt></strong><br />
</td>
<td>Inverse augton<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:14:<h3> --><h3 id="toc7"><a name="x--Breed type"></a><!-- ws:end:WikiTextHeadingRule:14 -->Breed type</h3>
<table class="wiki_table">
<tr>
<td><strong><tt>3456265</tt></strong><br />
</td>
<td>Hemisub<br />
</td>
</tr>
<tr>
<td><strong><tt>4356265</tt></strong><br />
</td>
<td>Inverse hemisub<br />
</td>
</tr>
<tr>
<td><strong><tt>6354535</tt></strong><br />
</td>
<td>Heminewt<br />
</td>
</tr>
<tr>
<td><strong><tt>4536535</tt></strong><br />
</td>
<td>Inverse heminewt<br />
</td>
</tr>
</table>
<br />
<br />
<table class="wiki_table">
<tr>
<td> <br />
</td>
<td><br />
</td>
</tr>
</table>
</body></html>