Trachytonic

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**Screamapillar** is a 7-note MODMOS in [[17edo]] (or its close cousins like [[27edt]] or [[44ed6]]), or the temperament which characterizes this scale. Screamapillar has three different step sizes and is described as a LLmmLLs scale (i. e., 3322331). As such, it is not a maximally even scale (since seconds, thirds, sixths, and sevenths all come in three rather than two sizes). However, screamapillar is notable for being [[Rothenberg propriety|strictly proper]], whereas the 17edo diatonic scale is not proper at all, and the 12edo diatonic scale is proper but not strictly so.

Screamapillar can be obtained by a single chromatic modification of the diatonic scale; if we take 17edo's diatonic major (Ionian) mode, and raise the fourth by one step, we get screamapillar (specifically, the Springfieldian mode). Screamapillar is also one modification away from the [[Mohajira|rast]] scale, so it has resemblance to both Western and Middle-Eastern scales. In fact, melodically, it corresponds to the [[http://www.maqamworld.com/maqamat/bayati.html|bayati]] maqam.

Screamapillar is named by analogy with [[scorp]] (as both are arthropod creatures starting with "sc"), and also because the major fourth of 17edo (which functions as 11:8, among others) has a very bright sound as though it is "screaming"'; ambulance sirens often use similar intervals. Timbres where the eleventh harmonic is strong tend to take on a similar character.

The sharpened fourth could also be called a "red note" (opposite of a blue note) due to the mood it creates. Also, the //[[https://en.wikipedia.org/wiki/The_Simpsons_Theme|Simpsons theme]]// uses a scale which, although not exactly screamapillar, does contain a sharpened fourth.

[[image:http://38.media.tumblr.com/7826da01fcce799fc36142847120597e/tumblr_mhg2qvcEiY1qe9qrbo4_250.gif]]

Because screamapillar is so similar to the diatonic scale, it's not as xen as one might expect a no-fives 13-limit system to be, and as a result it makes a good starting point for someone who wants to explore these higher harmonies without sounding too foreign.

Screamapillar contains five types of tertian (root-third-fifth) triads. These include 2 supermajor, 2 subminor, 1 neutral, 1 neutral-diminished, and 1 subminor-diminished. Of these, the neutral triad is harmonically somewhat rough and so it might be a good idea to modify it, fortunately, there are several options for doing this, such as changing it to a sus2, sus4, or even sus4add2. On the other hand, the neutral-diminished triad is actually very nice sounding since it very closely approximates 9:11:13, and its fifth is still clearly a fifth (albeit a narrow one) rather than being ambiguous like the 12edo tritone.

The subminor and supermajor chords can be harmonically stabilized by adding, respectively, the 4th [[https://en.wikipedia.org/wiki/Mu_chord|or the 2nd]]. This especially makes a difference in the latter case because supermajor triads sound somewhat unstable on their own.

Other high-limit chords and tone clusters can also be realized in screamapillar, including the approximations of 8:9:11:12 (which is like a sus chord but with more tension) and 12:13:14:16:18.

The modes of screamapillar could be given Simpsonsesque names as follows:

**Springfieldian**: Modified Ionian (major). 3 3 2 2 3 3 1

**Swartzwelderean****:** Modified Dorian. 3 2 2 3 3 1 3

**Capitalcitian:** Modified Phrygian: 2 2 3 3 1 3 3

**Northhaverbrookian:** Modified Lydian: 2 3 3 1 3 3 2

**Shelbyvillean:** Modified Mixolydian: 3 3 1 3 3 2 2

**Ogdenvillean****:** Modified Aeolian: 3 1 3 3 2 2 3

**Spittlean**: Mo**<span style="line-height: 1.5;">e</span>**<span style="line-height: 1.5;">dified Locrian: 1 3 3 2 2 3 3</span>


----

=<span style="line-height: 1.5;">As a temperament</span>= 

<span style="line-height: 1.5;">What is the temperament that provides the harmonic equivalencies featured in the screamapillar scale? Quite a few commas are tempered out including 64:63, 78:77, 99:98, 144:143, 243:242, etc.</span>

While 17edo itself is an excellent choice for such a temperament, there are other options, notably [[61edo]], whose version of the screamapillar scale has step pattern [[tel:11 11 7 7 11 11 3|11 11 7 7 11 11 3]]. [[78edo]] works as well (with step pattern [[tel:14 14 9 9 14 14 4|14 14 9 9 14 14 4]]); both of these improve the 7th and 13th harmonics at the expense of<span style="line-height: 1.5;"> the 3rd and 11th.</span>

Other options include [[44edo]] and [[27edo]], although the latter is a borderline case because it doesn't have a very good 11 (it maps 11:8 to 577.78 cents).

Original HTML content:

<html><head><title>Screamapillar</title></head><body><strong>Screamapillar</strong> is a 7-note MODMOS in <a class="wiki_link" href="/17edo">17edo</a> (or its close cousins like <a class="wiki_link" href="/27edt">27edt</a> or <a class="wiki_link" href="/44ed6">44ed6</a>), or the temperament which characterizes this scale. Screamapillar has three different step sizes and is described as a LLmmLLs scale (i. e., 3322331). As such, it is not a maximally even scale (since seconds, thirds, sixths, and sevenths all come in three rather than two sizes). However, screamapillar is notable for being <a class="wiki_link" href="/Rothenberg%20propriety">strictly proper</a>, whereas the 17edo diatonic scale is not proper at all, and the 12edo diatonic scale is proper but not strictly so.<br />
<br />
Screamapillar can be obtained by a single chromatic modification of the diatonic scale; if we take 17edo's diatonic major (Ionian) mode, and raise the fourth by one step, we get screamapillar (specifically, the Springfieldian mode). Screamapillar is also one modification away from the <a class="wiki_link" href="/Mohajira">rast</a> scale, so it has resemblance to both Western and Middle-Eastern scales. In fact, melodically, it corresponds to the <a class="wiki_link_ext" href="http://www.maqamworld.com/maqamat/bayati.html" rel="nofollow">bayati</a> maqam.<br />
<br />
Screamapillar is named by analogy with <a class="wiki_link" href="/scorp">scorp</a> (as both are arthropod creatures starting with &quot;sc&quot;), and also because the major fourth of 17edo (which functions as 11:8, among others) has a very bright sound as though it is &quot;screaming&quot;'; ambulance sirens often use similar intervals. Timbres where the eleventh harmonic is strong tend to take on a similar character.<br />
<br />
The sharpened fourth could also be called a &quot;red note&quot; (opposite of a blue note) due to the mood it creates. Also, the <em><a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/The_Simpsons_Theme" rel="nofollow">Simpsons theme</a></em> uses a scale which, although not exactly screamapillar, does contain a sharpened fourth.<br />
<br />
<!-- ws:start:WikiTextRemoteImageRule:3:&lt;img src=&quot;http://38.media.tumblr.com/7826da01fcce799fc36142847120597e/tumblr_mhg2qvcEiY1qe9qrbo4_250.gif&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="http://38.media.tumblr.com/7826da01fcce799fc36142847120597e/tumblr_mhg2qvcEiY1qe9qrbo4_250.gif" alt="external image tumblr_mhg2qvcEiY1qe9qrbo4_250.gif" title="external image tumblr_mhg2qvcEiY1qe9qrbo4_250.gif" /><!-- ws:end:WikiTextRemoteImageRule:3 --><br />
<br />
Because screamapillar is so similar to the diatonic scale, it's not as xen as one might expect a no-fives 13-limit system to be, and as a result it makes a good starting point for someone who wants to explore these higher harmonies without sounding too foreign.<br />
<br />
Screamapillar contains five types of tertian (root-third-fifth) triads. These include 2 supermajor, 2 subminor, 1 neutral, 1 neutral-diminished, and 1 subminor-diminished. Of these, the neutral triad is harmonically somewhat rough and so it might be a good idea to modify it, fortunately, there are several options for doing this, such as changing it to a sus2, sus4, or even sus4add2. On the other hand, the neutral-diminished triad is actually very nice sounding since it very closely approximates 9:11:13, and its fifth is still clearly a fifth (albeit a narrow one) rather than being ambiguous like the 12edo tritone.<br />
<br />
The subminor and supermajor chords can be harmonically stabilized by adding, respectively, the 4th <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Mu_chord" rel="nofollow">or the 2nd</a>. This especially makes a difference in the latter case because supermajor triads sound somewhat unstable on their own.<br />
<br />
Other high-limit chords and tone clusters can also be realized in screamapillar, including the approximations of 8:9:11:12 (which is like a sus chord but with more tension) and 12:13:14:16:18.<br />
<br />
The modes of screamapillar could be given Simpsonsesque names as follows:<br />
<br />
<strong>Springfieldian</strong>: Modified Ionian (major). 3 3 2 2 3 3 1<br />
<br />
<strong>Swartzwelderean</strong><strong>:</strong> Modified Dorian. 3 2 2 3 3 1 3<br />
<br />
<strong>Capitalcitian:</strong> Modified Phrygian: 2 2 3 3 1 3 3<br />
<br />
<strong>Northhaverbrookian:</strong> Modified Lydian: 2 3 3 1 3 3 2<br />
<br />
<strong>Shelbyvillean:</strong> Modified Mixolydian: 3 3 1 3 3 2 2<br />
<br />
<strong>Ogdenvillean</strong><strong>:</strong> Modified Aeolian: 3 1 3 3 2 2 3<br />
<br />
<strong>Spittlean</strong>: Mo<strong><span style="line-height: 1.5;">e</span></strong><span style="line-height: 1.5;">dified Locrian: 1 3 3 2 2 3 3</span><br />
<br />
<br />
<hr />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="As a temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="line-height: 1.5;">As a temperament</span></h1>
 <br />
<span style="line-height: 1.5;">What is the temperament that provides the harmonic equivalencies featured in the screamapillar scale? Quite a few commas are tempered out including 64:63, 78:77, 99:98, 144:143, 243:242, etc.</span><br />
<br />
While 17edo itself is an excellent choice for such a temperament, there are other options, notably <a class="wiki_link" href="/61edo">61edo</a>, whose version of the screamapillar scale has step pattern <a class="wiki_link" href="http://tel.wikispaces.com/11%2011%207%207%2011%2011%203">11 11 7 7 11 11 3</a>. <a class="wiki_link" href="/78edo">78edo</a> works as well (with step pattern <a class="wiki_link" href="http://tel.wikispaces.com/14%2014%209%209%2014%2014%204">14 14 9 9 14 14 4</a>); both of these improve the 7th and 13th harmonics at the expense of<span style="line-height: 1.5;"> the 3rd and 11th.</span><br />
<br />
Other options include <a class="wiki_link" href="/44edo">44edo</a> and <a class="wiki_link" href="/27edo">27edo</a>, although the latter is a borderline case because it doesn't have a very good 11 (it maps 11:8 to 577.78 cents).</body></html>