22edo: Difference between revisions
Wikispaces>hearneg **Imported revision 591425126 - Original comment: ** |
Wikispaces>PiotrGrochowski **Imported revision 592102176 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
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==Properties of 22 equal temperament== | ==Properties of 22 equal temperament== | ||
Possibly the most striking characteristic of 22-et to those not used to it is that it does **not** "temper out" the syntonic comma of 81/80, and therefore is not a system of [[Regular Temperaments#meantone|meantone]] temperament. This means that 22 distinguishes a number of Pythagorean and 5-limit intervals that 12-EDO | Possibly the most striking characteristic of 22-et to those not used to it is that it does **not** "temper out" the syntonic comma of 81/80, and therefore is not a system of [[Regular Temperaments#meantone|meantone]] temperament. This means that 22 distinguishes a number of Pythagorean and 5-limit intervals that 12-EDO, 19-EDO, 31-EDO, ... do not distinguish, such as the two whole tones 9/8 and 10/9. Indeed, these distinctions are exaggerated in comparison to 5-limit JI and many more accurate temperaments such as [[34edo]], [[41edo]] and [[53edo]]. | ||
The diatonic scale it produces is instead derived from [[superpyth]] temperament, which despite having the same melodic structure as meantone's diatonic scale (LLsLLLs or, [[5L 2s]]), has thirds approximating 9/7 and 7/6, rather than 5/4 and 6/5. This means that the septimal comma of 64/63 vanishes, rather than the syntonic comma of 81/80, which is one of the core features of 22-EDO. Superpyth is melodically interesting for having a quasi-equal pentatonic scale (as the large whole tone and subminor third are rather close in size) and a more uneven heptatonic scale, as compared with 12-equal and meantone systems: step patterns 4 4 5 4 5 and 4 4 1 4 4 4 1, respectively. | The diatonic scale it produces is instead derived from [[superpyth]] temperament, which despite having the same melodic structure as meantone's diatonic scale (LLsLLLs or, [[5L 2s]]), has thirds approximating 9/7 and 7/6, rather than 5/4 and 6/5. This means that the septimal comma of 64/63 vanishes, rather than the syntonic comma of 81/80, which is one of the core features of 22-EDO. Superpyth is melodically interesting for having a quasi-equal pentatonic scale (as the large whole tone and subminor third are rather close in size) and a more uneven heptatonic scale, as compared with 12-equal and meantone systems: step patterns 4 4 5 4 5 and 4 4 1 4 4 4 1, respectively. | ||
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<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc8"><a name="Theory-Properties of 22 equal temperament"></a><!-- ws:end:WikiTextHeadingRule:18 -->Properties of 22 equal temperament</h2> | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc8"><a name="Theory-Properties of 22 equal temperament"></a><!-- ws:end:WikiTextHeadingRule:18 -->Properties of 22 equal temperament</h2> | ||
<br /> | <br /> | ||
Possibly the most striking characteristic of 22-et to those not used to it is that it does <strong>not</strong> &quot;temper out&quot; the syntonic comma of 81/80, and therefore is not a system of <a class="wiki_link" href="/Regular%20Temperaments#meantone">meantone</a> temperament. This means that 22 distinguishes a number of Pythagorean and 5-limit intervals that 12-EDO | Possibly the most striking characteristic of 22-et to those not used to it is that it does <strong>not</strong> &quot;temper out&quot; the syntonic comma of 81/80, and therefore is not a system of <a class="wiki_link" href="/Regular%20Temperaments#meantone">meantone</a> temperament. This means that 22 distinguishes a number of Pythagorean and 5-limit intervals that 12-EDO, 19-EDO, 31-EDO, ... do not distinguish, such as the two whole tones 9/8 and 10/9. Indeed, these distinctions are exaggerated in comparison to 5-limit JI and many more accurate temperaments such as <a class="wiki_link" href="/34edo">34edo</a>, <a class="wiki_link" href="/41edo">41edo</a> and <a class="wiki_link" href="/53edo">53edo</a>.<br /> | ||
<br /> | <br /> | ||
The diatonic scale it produces is instead derived from <a class="wiki_link" href="/superpyth">superpyth</a> temperament, which despite having the same melodic structure as meantone's diatonic scale (LLsLLLs or, <a class="wiki_link" href="/5L%202s">5L 2s</a>), has thirds approximating 9/7 and 7/6, rather than 5/4 and 6/5. This means that the septimal comma of 64/63 vanishes, rather than the syntonic comma of 81/80, which is one of the core features of 22-EDO. Superpyth is melodically interesting for having a quasi-equal pentatonic scale (as the large whole tone and subminor third are rather close in size) and a more uneven heptatonic scale, as compared with 12-equal and meantone systems: step patterns 4 4 5 4 5 and 4 4 1 4 4 4 1, respectively.<br /> | The diatonic scale it produces is instead derived from <a class="wiki_link" href="/superpyth">superpyth</a> temperament, which despite having the same melodic structure as meantone's diatonic scale (LLsLLLs or, <a class="wiki_link" href="/5L%202s">5L 2s</a>), has thirds approximating 9/7 and 7/6, rather than 5/4 and 6/5. This means that the septimal comma of 64/63 vanishes, rather than the syntonic comma of 81/80, which is one of the core features of 22-EDO. Superpyth is melodically interesting for having a quasi-equal pentatonic scale (as the large whole tone and subminor third are rather close in size) and a more uneven heptatonic scale, as compared with 12-equal and meantone systems: step patterns 4 4 5 4 5 and 4 4 1 4 4 4 1, respectively.<br /> | ||