https://en.xen.wiki/index.php?action=history&feed=atom&title=User%3AVectorGraphics%2FVector%27s_introduction_to_15edo%2FTemperaments 2026-07-08T06:01:22Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=User:VectorGraphics/Vector%27s_introduction_to_15edo/Temperaments&diff=189350&oldid=prev 2025-04-01T06:16:41Z

<p>Created page with &quot;The &quot;intervals&quot; section describes the intervals that 15edo uses. This section describes the relationships between intervals. All descriptions here will be &quot;octave-reduced&quot; - t...&quot;</p> <p><b>New page</b></p><div>The &quot;intervals&quot; section describes the intervals that 15edo uses. This section describes the relationships between intervals. All descriptions here will be &quot;octave-reduced&quot; - that is, &quot;returns you to the root&quot; may mean &quot;returns you to a note some number of octaves above the root&quot;. Each tuning has a different combination of temperaments, and the ones here are different from the ones you get when using 12edo. <br /> <br /> A note about nomenclature: several of the equivalences described here come from the same underlying &quot;regular temperament&quot;, which is why the same name is listed twice in some cases, but for transparency I&#039;ve listed them separately.<br /> <br /> == The fundamentals ==<br /> <br /> * &#039;&#039;&#039;Blackwood&#039;&#039;&#039;: Stacking 5 fifths returns you to the root.<br /> * &#039;&#039;&#039;Augmented&#039;&#039;&#039;: Stacking 3 major thirds returns you to the root.<br /> * &#039;&#039;&#039;Porcupine&#039;&#039;&#039;: The intervals between the wolf and minor thirds, and between the minor and major thirds, are the same interval. In other words, you only need 1 set of accidentals to notate 15edo&#039;s diatonic scale, while in other tunings like 34edo you&#039;d need two.<br /> <br /> == Other curiosities ==<br /> <br /> * &#039;&#039;&#039;Valentine:&#039;&#039;&#039; The large whole-tone is found at 3 chromatic scale steps, the major third at 5, and the perfect fifth at 9.<br /> * &#039;&#039;&#039;Porcupine:&#039;&#039;&#039; The minor third can be split into two equal intervals, while the major third cannot.<br /> * &#039;&#039;&#039;Semaphore:&#039;&#039;&#039; Stacking two large whole-tones gives you a perfect fourth.<br /> * &#039;&#039;&#039;Slendric:&#039;&#039;&#039; Stacking three large whole-tones gives you a perfect fifth.<br /> ** &#039;&#039;&#039;Blackwood:&#039;&#039;&#039; The perfect fourth is, consequently, 2/3 of a perfect fifth.<br /> * &#039;&#039;&#039;Blackwood:&#039;&#039;&#039; The octave is split into five parts; the perfect fifth is found at the third.<br /> ** &#039;&#039;&#039;Cloudy:&#039;&#039;&#039; Each of the five parts is also a large whole tone; large whole tones close the octave.<br /> * &#039;&#039;&#039;Kleismic:&#039;&#039;&#039; By stacking six minor thirds, you reach the perfect fifth.<br /> * &#039;&#039;&#039;Augmented:&#039;&#039;&#039; By stacking two major thirds, you get a minor sixth.<br /> * &#039;&#039;&#039;Augmented:&#039;&#039;&#039; The diatonic and chromatic semitones are the same size.<br /> * &#039;&#039;&#039;Archy:&#039;&#039;&#039; By stacking two perfect fourths, you get a harmonic seventh. <br /> * &#039;&#039;&#039;Keegic:&#039;&#039;&#039; By stacking three large tritones, you get a perfect fifth.<br /> * &#039;&#039;&#039;Paralimmic:&#039;&#039;&#039; By stacking three large tritones, you get a perfect fifth.<br /> ** Trust me, the RTT gods say these are different things for some reason</div>

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