https://en.xen.wiki/index.php?action=history&feed=atom&title=Lumatone_mapping_for_109edo 2026-10-21T03:20:41Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=Lumatone_mapping_for_109edo&diff=240088&oldid=prev 2026-10-19T07:06:52Z

<p>Create page, starting with the obligatory diatonic mapping and Bryan Deister&#039;s Leapweek mapping</p> <p><b>New page</b></p><div>{{Lumatone mapping intro}} <br /> <br /> == Diatonic ==<br /> Due to the size of this tuning system, nearly half of the notes are missing in the standard diatonic mapping.<br /> {{Lumatone EDO mapping|n=109|start=10|xstep=19|ystep=-12}}<br /> <br /> == Leapweek + Pentacircle ==<br /> It is possible to map [[109edo]] by the stacking of fifths ~[[3/2]] while getting all of the notes, but instead of the standard diatonic approach, it is necessary to make a mapping that spreads out the whole tone ~[[9/8]] (19\109, made from stacking two fifths) to two keys right plus one key down-right, as demonstrated in [[Bryan Deister]]&#039;s [https://www.youtube.com/watch?v=4p_aD8VAsA8 &#039;&#039;109edo improv&#039;&#039;] (2026). Since the fifth of 109edo is mildly sharp, the quasi-Pythagorean major third (38\109) maps to a near-just undecimal (pentacircle) major third ~[[14/11]], while the quasi-Pythagorean minor third (26\109) maps to a near-just (slightly flat) undecimal (pentacircle) minor third ~[[33/28]], making 109edo a [[leapweek]] tuning, which also supports [[pentacircle clan]] (rank-3) and [[pentacircle]] (rank-4) temperaments since the pentacircle comma [[896/891]] is tempered out. The range is just over two octaves, with a few repeated notes to mitigate wrarpounds, and the octaves have a barely noticeable downward slant.<br /> {{Lumatone EDO mapping|n=109|start=103|xstep=7|ystep=-2}}<br /> <br /> {{Navbox Lumatone}}</div>

Lucius Chiaraviglio