https://en.xen.wiki/index.php?action=history&feed=atom&title=34th-octave_temperaments 2026-06-11T05:39:16Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=34th-octave_temperaments&diff=229236&oldid=prev 2026-05-01T10:47:11Z

<p>Created page with &quot;{{Technical data page}} {{Infobox fractional-octave|34}} This page collects rank-2 temperaments with a period that is 1/34 of an octave. <a href="/w/34edo" title="34edo">34edo</a> is a good tuning for harmonics 3, 5, 13 and 17, so giving an independent generator with 1/34-octave period makes sense. This approach leads to the hemigoth temperament. == Hemigoth == Hemigoth is identical to 34et in the no-7 subgroups, but has an independent generator for prime 7. <a href="/w/Subgroup" class="mw-redirect" title="Subgroup">Subgroup</a>: 2.3.5.7 <a href="/w/Comma_list" class="mw-redirect" title="Comma list">Comma list</a>: 204...&quot;</p> <p><b>New page</b></p><div>{{Technical data page}}<br /> {{Infobox fractional-octave|34}}<br /> This page collects rank-2 temperaments with a period that is 1/34 of an octave.<br /> <br /> [[34edo]] is a good tuning for harmonics 3, 5, 13 and 17, so giving an independent generator with 1/34-octave period makes sense. This approach leads to the hemigoth temperament.<br /> <br /> == Hemigoth ==<br /> Hemigoth is identical to 34et in the no-7 subgroups, but has an independent generator for prime 7.<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 2048/2025, 15625/15552<br /> <br /> {{Mapping|legend=1| 34 54 79 0 | 0 0 0 1 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[CTE]]: ~81/80 = 35.294{{c}} (1 ⧵ 34), ~7/4 = 968.826{{c}}<br /> * [[CWE]]: ~81/80 = 35.294{{c}} (1 ⧵ 34), ~7/4 = 971.146{{c}}<br /> <br /> {{Optimal ET sequence|legend=1| 34d, 68 }}<br /> <br /> [[Badness]] (Sintel): 3.383<br /> <br /> {{Navbox fractional-octave}}</div>

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