https://en.xen.wiki/index.php?action=history&feed=atom&title=User%3AFrostburn%2FHemiptol 2026-06-11T22:52:10Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=User:Frostburn/Hemiptol&diff=149346&oldid=prev 2024-08-02T11:49:45Z

<p>Whatever</p> <p><b>New page</b></p><div>Oops! Misguided article. The name is technically correct, but I have no clue why this would be more interesting than √2.√3.5.<br /> <br /> Hemiptol is to [[hemipyth]] what 5-limit (i.e. Ptolemaic tuning) is to 3-limit (i.e. Pythagorean tuning). It is the √2.√3.√5 [[subgroup]] i.e. the set of intervals that can be constructed by multiplying half-integer powers of 2, 3 and 5.<br /> <br /> == Supporting edos ==<br /> To support hemiptol an equal temperament must map all 2, 3 and 5 to even numbers of edosteps.<br /> <br /> Edos (patent vals) under 100 that achieve this are: 6, 20, 24, 30, 38, 44, 62, 68, 76, 82, 86, 92 (and 100 itself).<br /> <br /> Of these, 82 being the double of [[41edo]] is arguably the most convincing/accurate tuning for hemiptol.<br /> <br /> == Higher prime fudging ==<br /> Motivation for the system can be found from temperaments that are accurate enough to [[fudge|fudging]] most of the higher primes with the simple action of squashing the 5-limit to 50% of its size in cents.<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ Prime fudges<br /> |-<br /> ! Prime !! Hemiptol interval !! Associated comma<br /> |-<br /> | 7 || √(4000/81) || [[4000/3969|octagar comma]]<br /> |-<br /> | 11 || √(243/2) || [[rastma]]<br /> |-<br /> | 13 || √(675/4) || [[676/675|island comma]]<br /> |-<br /> | 17 || √288 || [[semitonisma]]<br /> |-<br /> | 19 || √(729/2) || [[729/722]]<br /> |-<br /> | 23 || √(1600/3) || [[1600/1587]]<br /> |-<br /> | 29 || √(3375/4) || [[3375/3364]]<br /> |-<br /> | 31 || √960 || [[961/960]]<br /> |}<br /> <br /> Most of these don&#039;t even need the square root of 5, smh.</div>

Frostburn