https://xenreference.com/wiki/index.php?action=history&feed=atom&title=Intergan
Intergan - Revision history
2026-08-31T10:59:53Z
Revision history for this page on the wiki
MediaWiki 1.44.2
https://xenreference.com/wiki/index.php?title=Intergan&diff=7895&oldid=prev
Ground at 05:56, 27 July 2026
2026-07-27T05:56:34Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 05:56, 27 July 2026</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Semiquartal ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Semiquartal ==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The default realization of Intergan is generated by semifourths.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* The most basic version is 2.3.11.13/5.17.19 5&24. 4/3 is split into two semifourths most simply represented by 15/13, and 22/17 is equated to 13/10 and 22/19 is equated to 15/13. It features the remarkably simple 10:13:15 ultramajor triad and its retroversion found in Island temperaments, along with the 16:19:22 +1+1 sub-diminished triad and 16:19:24:27 +3+5+3 minor add6 tetrad. 11:12:17:19 is present, although this adding 13, 14, or 15 to the subgroup will significantly improve its usefulness.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* The most basic version is 2.3.11.13/5.17.19 5&24. 4/3 is split into two semifourths most simply represented by 15/13, and 22/17 is equated to 13/10 and 22/19 is equated to 15/13. It features the remarkably simple 10:13:15 ultramajor triad and its retroversion found in Island temperaments, along with the 16:19:22 +1+1 sub-diminished triad and 16:19:24:27 +3+5+3 minor add6 tetrad. 11:12:17:19 is present, although this adding 13, 14, or 15 to the subgroup will significantly improve its usefulness.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Tempering out 81/80 is somewhat obvious, resulting in 2.3.5.11.13.17.19 5&24.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Tempering out 81/80 is somewhat obvious, resulting in 2.3.5.11.13.17.19 5&24.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Primes 31 and 37 are also obvious to add, equating 37/32 to 22/19 and 37/31 to 19/16, resulting in 2.3.5.11.13.17.19.31.37 5&24. 67edo is roughly optimal due to its very mild meantone fourth being split in half. The 2.31.37 restriction is highly accurate in 43edo. A few important triads are found within 24:31:32:37:48.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Primes 31 and 37 are also obvious to add, equating 37/32 to 22/19 and 37/31 to 19/16, resulting in 2.3.5.11.13.17.19.31.37 5&24. 67edo is roughly optimal due to its very mild meantone fourth being split in half. The 2.31.37 restriction is highly accurate in 43edo. A few important triads are found within 24:31:32:37:48<ins style="font-weight: bold; text-decoration: none;">. The ultramajor seventh chord is particularly representative of the sound of prime 31, being just 16:24:31 with an added 31/24</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Primes 7, 23, and 29 are all more difficult to map due to their complexity, although their difficulty is in ascending order. They are more easily reached by splitting the semifourth generator in half in a manner similar to Negri.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Primes 7, 23, and 29 are all more difficult to map due to their complexity, although their difficulty is in ascending order. They are more easily reached by splitting the semifourth generator in half in a manner similar to Negri.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{| class="wikitable"</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{| class="wikitable"</div></td></tr>
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Ground
https://xenreference.com/wiki/index.php?title=Intergan&diff=7894&oldid=prev
Ground at 05:43, 27 July 2026
2026-07-27T05:43:46Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 05:43, 27 July 2026</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l5">Line 5:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* The most basic version is 2.3.11.13/5.17.19 5&24. 4/3 is split into two semifourths most simply represented by 15/13, and 22/17 is equated to 13/10 and 22/19 is equated to 15/13. It features the remarkably simple 10:13:15 ultramajor triad and its retroversion found in Island temperaments, along with the 16:19:22 +1+1 sub-diminished triad and 16:19:24:27 +3+5+3 minor add6 tetrad. 11:12:17:19 is present, although this adding 13, 14, or 15 to the subgroup will significantly improve its usefulness.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* The most basic version is 2.3.11.13/5.17.19 5&24. 4/3 is split into two semifourths most simply represented by 15/13, and 22/17 is equated to 13/10 and 22/19 is equated to 15/13. It features the remarkably simple 10:13:15 ultramajor triad and its retroversion found in Island temperaments, along with the 16:19:22 +1+1 sub-diminished triad and 16:19:24:27 +3+5+3 minor add6 tetrad. 11:12:17:19 is present, although this adding 13, 14, or 15 to the subgroup will significantly improve its usefulness.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Tempering out 81/80 is somewhat obvious, resulting in 2.3.5.11.13.17.19 5&24.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Tempering out 81/80 is somewhat obvious, resulting in 2.3.5.11.13.17.19 5&24.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Primes 31 and 37 are also obvious to add, equating 37/32 to 22/19 and 37/31 to 19/16, resulting in 2.3.5.11.13.17.19.31.37 5&24. 67edo is roughly optimal due to its very mild meantone fourth being split in half. The 2.31.37 restriction is highly accurate in 43edo.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Primes 31 and 37 are also obvious to add, equating 37/32 to 22/19 and 37/31 to 19/16, resulting in 2.3.5.11.13.17.19.31.37 5&24. 67edo is roughly optimal due to its very mild meantone fourth being split in half. The 2.31.37 restriction is highly accurate in 43edo<ins style="font-weight: bold; text-decoration: none;">. A few important triads are found within 24:31:32:37:48</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Primes 7, 23, and 29 are all more difficult to map due to their complexity, although their difficulty is in ascending order. They are more easily reached by splitting the semifourth generator in half in a manner similar to Negri.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Primes 7, 23, and 29 are all more difficult to map due to their complexity, although their difficulty is in ascending order. They are more easily reached by splitting the semifourth generator in half in a manner similar to Negri.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{| class="wikitable"</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{| class="wikitable"</div></td></tr>
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Ground
https://xenreference.com/wiki/index.php?title=Intergan&diff=7777&oldid=prev
Ground at 01:42, 14 July 2026
2026-07-14T01:42:54Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 01:42, 14 July 2026</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l461">Line 461:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Related temperaments ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Related temperaments ==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">An alternate simpler diminished temperament </del>in the basic Intergan subgroup (2.3.11.17.19) <del style="font-weight: bold; text-decoration: none;">is 20</del>&24, <del style="font-weight: bold; text-decoration: none;">which </del>has 16/11 at one quartertone above the half-octave and 3/2 at two. This is arguably the best temperament if just the 9:12:16:19:22 chord is desired due to the efficiency of 4L8s.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The simplest multi-period temperaments </ins>in the basic Intergan subgroup (2.3.11.17.19) <ins style="font-weight: bold; text-decoration: none;">are 2&24 (or 2[+19]&24), 3&24, 4&24, 6&24 (or 6[-17]</ins>&24<ins style="font-weight: bold; text-decoration: none;">)</ins>, <ins style="font-weight: bold; text-decoration: none;">8&24, and 12&24 (or 12[-11]&24).</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">3&24 </ins>has 16/11 at one quartertone above the half-octave and 3/2 at two. This is arguably the best temperament if just the 9:12:16:19:22 chord is desired due to the efficiency of 4L8s.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Navbox regtemp}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Navbox regtemp}}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Cat|temperaments}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Cat|temperaments}}</div></td></tr>
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Ground
https://xenreference.com/wiki/index.php?title=Intergan&diff=7776&oldid=prev
Ground at 01:09, 14 July 2026
2026-07-14T01:09:46Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 01:09, 14 July 2026</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l458">Line 458:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Diminished: 24, 52, 76[+5]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Diminished: 24, 52, 76[+5]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The different versions of Intergan may be defined by the sheer number of intervals it maps to ~19/16: 19/16, 25/21, 31/26, 32/27, 37/31, 44/37. The semiquartal temperament equates all of them besides 25/21 due to its sharp 5, instead equating it to 6/5 in the 7-limit. This includes an accurate otonal approximation of 0-1-2-3\4, 26:31:37:44.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The different versions of Intergan may be defined by the sheer number of intervals it maps to ~19/16: 19/16, 25/21, 31/26, 32/27, 37/31, 44/37. The semiquartal temperament equates all of them besides 25/21 due to its sharp 5, instead equating it to 6/5 in the 7-limit. This includes an accurate otonal approximation of 0-1-2-3\4, 26:31:37:44.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">== Related temperaments ==</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">An alternate simpler diminished temperament in the basic Intergan subgroup (2.3.11.17.19) is 20&24, which has 16/11 at one quartertone above the half-octave and 3/2 at two. This is arguably the best temperament if just the 9:12:16:19:22 chord is desired due to the efficiency of 4L8s.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Navbox regtemp}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Navbox regtemp}}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Cat|temperaments}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Cat|temperaments}}</div></td></tr>
</table>
Ground
https://xenreference.com/wiki/index.php?title=Intergan&diff=7768&oldid=prev
Ground at 05:22, 12 July 2026
2026-07-12T05:22:45Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 05:22, 12 July 2026</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l451">Line 451:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Being so close to 24edo means that 1/2, 1/3, 1/4, 1/6, and 1/8-octave temperaments are all available. 12edo's remarkable accuracy in 2.3.17.19 provides many ways to temper the subgroup and its extensions, but this requires more effort to produce a temperament that isn't virtually 12edo; Intergan's interseptimals are one option. The rank-3 temperament may be attached to one of numerous often multi-period temperaments in this subgroup to reduce it to rank-2.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Being so close to 24edo means that 1/2, 1/3, 1/4, 1/6, and 1/8-octave temperaments are all available. 12edo's remarkable accuracy in 2.3.17.19 provides many ways to temper the subgroup and its extensions, but this requires more effort to produce a temperament that isn't virtually 12edo; Intergan's interseptimals are one option. The rank-3 temperament may be attached to one of numerous often multi-period temperaments in this subgroup to reduce it to rank-2.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Third-octave: 121172^-11 = 2057/2048 <del style="font-weight: bold; text-decoration: none;">and (27/17)^3/4 = 19683/19652. The former is </del>called the Blume comma, and it is obscure despite being both accurate and low-complexity. The third-octave version of Intergan is especially useful when adding the elusive prime 29 because 29/23 is 401¢.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Third-octave: <ins style="font-weight: bold; text-decoration: none;">Add </ins>121172^-11 = 2057/2048<ins style="font-weight: bold; text-decoration: none;">, </ins>called the Blume comma, and it is obscure despite being both accurate and low-complexity. The third-octave version of Intergan is especially useful when adding the elusive prime 29 because 29/23 is 401¢<ins style="font-weight: bold; text-decoration: none;">. It is equivalent to adding the 2/(5/4)^3 = 128/125 Augmented comma. (27/17)^3/4 = 19683/19652 is a typical comma for third-octave temperaments but it has significantly more complex result</ins>.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Quarter-octave: <del style="font-weight: bold; text-decoration: none;">add </del>(<del style="font-weight: bold; text-decoration: none;">19</del>/<del style="font-weight: bold; text-decoration: none;">16</del>)^4/2=<del style="font-weight: bold; text-decoration: none;">130321</del>/131072. <del style="font-weight: bold; text-decoration: none;">This is one of very few </del>useful commas dividing the octave into four equal parts.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Quarter-octave: <ins style="font-weight: bold; text-decoration: none;">Add the </ins>(<ins style="font-weight: bold; text-decoration: none;">6</ins>/<ins style="font-weight: bold; text-decoration: none;">5</ins>)^4/2 = <ins style="font-weight: bold; text-decoration: none;">648/625 Diminished comma or the smaller 2/(19</ins>/<ins style="font-weight: bold; text-decoration: none;">16)^4 = </ins>131072<ins style="font-weight: bold; text-decoration: none;">/130321</ins>. <ins style="font-weight: bold; text-decoration: none;">These are the two most </ins>useful commas dividing the octave into four equal parts <ins style="font-weight: bold; text-decoration: none;">besides the (25/21)^4/2 = 390625/388962 Dimcomp comma.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">2.3.5.11.13</ins>.<ins style="font-weight: bold; text-decoration: none;">17.19.31.37 edos:</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* Meantone: 24, 19, 43, 5, 67, 110[+5, +19], 91[+5], 115[+5]</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* Augmented: 24, 9, 15, 33[+31], 57[+5, +31]</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* Diminished: 24, 52, 76[+5]</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The different versions of Intergan may be defined by the sheer number of intervals it maps to ~19/16: 19/16, 25/21, 31/26, 32/27, 37/31, 44/37. The semiquartal temperament equates all of them besides 25/21 due to its sharp 5, instead equating it to 6/5 in the 7-limit. This includes an accurate otonal approximation of 0-1-2-3\4, 26:31:37:44.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The different versions of Intergan may be defined by the sheer number of intervals it maps to ~19/16: 19/16, 25/21, 31/26, 32/27, 37/31, 44/37. The semiquartal temperament equates all of them besides 25/21 due to its sharp 5, instead equating it to 6/5 in the 7-limit. This includes an accurate otonal approximation of 0-1-2-3\4, 26:31:37:44.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Navbox regtemp}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Navbox regtemp}}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Cat|temperaments}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Cat|temperaments}}</div></td></tr>
</table>
Ground
https://xenreference.com/wiki/index.php?title=Intergan&diff=7767&oldid=prev
Ground at 04:53, 12 July 2026
2026-07-12T04:53:20Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 04:53, 12 July 2026</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l453">Line 453:</td>
<td colspan="2" class="diff-lineno">Line 453:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Third-octave: 121172^-11 = 2057/2048 and (27/17)^3/4 = 19683/19652. The former is called the Blume comma, and it is obscure despite being both accurate and low-complexity. The third-octave version of Intergan is especially useful when adding the elusive prime 29 because 29/23 is 401¢.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Third-octave: 121172^-11 = 2057/2048 and (27/17)^3/4 = 19683/19652. The former is called the Blume comma, and it is obscure despite being both accurate and low-complexity. The third-octave version of Intergan is especially useful when adding the elusive prime 29 because 29/23 is 401¢.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Quarter-octave: add (19/16)^4/2=130321/131072. This is one of very few useful commas dividing the octave into four equal parts.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Quarter-octave: add (19/16)^4/2=130321/131072. This is one of very few useful commas dividing the octave into four equal parts.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The different versions of Intergan may be defined by the sheer number of intervals it maps to ~19/16: 19/16, 25/21, 31/26, 32/27, 37/31, 44/37. The semiquartal temperament equates all of them besides 25/21 due to its sharp 5, instead equating it to 6/5 in the 7-limit. This includes <del style="font-weight: bold; text-decoration: none;">the </del>otonal approximation of <del style="font-weight: bold; text-decoration: none;">4edo</del>, 26:31:37:44.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The different versions of Intergan may be defined by the sheer number of intervals it maps to ~19/16: 19/16, 25/21, 31/26, 32/27, 37/31, 44/37. The semiquartal temperament equates all of them besides 25/21 due to its sharp 5, instead equating it to 6/5 in the 7-limit. This includes <ins style="font-weight: bold; text-decoration: none;">an accurate </ins>otonal approximation of <ins style="font-weight: bold; text-decoration: none;">0-1-2-3\4</ins>, 26:31:37:44.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Navbox regtemp}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Navbox regtemp}}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Cat|temperaments}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Cat|temperaments}}</div></td></tr>
</table>
Ground
https://xenreference.com/wiki/index.php?title=Intergan&diff=7766&oldid=prev
Ground at 04:51, 12 July 2026
2026-07-12T04:51:14Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 04:51, 12 July 2026</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l453">Line 453:</td>
<td colspan="2" class="diff-lineno">Line 453:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Third-octave: 121172^-11 = 2057/2048 and (27/17)^3/4 = 19683/19652. The former is called the Blume comma, and it is obscure despite being both accurate and low-complexity. The third-octave version of Intergan is especially useful when adding the elusive prime 29 because 29/23 is 401¢.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Third-octave: 121172^-11 = 2057/2048 and (27/17)^3/4 = 19683/19652. The former is called the Blume comma, and it is obscure despite being both accurate and low-complexity. The third-octave version of Intergan is especially useful when adding the elusive prime 29 because 29/23 is 401¢.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Quarter-octave: add (19/16)^4/2=130321/131072. This is one of very few useful commas dividing the octave into four equal parts.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Quarter-octave: add (19/16)^4/2=130321/131072. This is one of very few useful commas dividing the octave into four equal parts.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The different versions of Intergan may be defined by the sheer number of intervals it maps to <del style="font-weight: bold; text-decoration: none;">the </del>~19/16 <del style="font-weight: bold; text-decoration: none;">interval</del>: 19/16, 25/21, 31/26, 32/27, 37/31, 44/37, <del style="font-weight: bold; text-decoration: none;">and </del>the otonal <del style="font-weight: bold; text-decoration: none;">semifourth stack </del>26:31:37:44.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The different versions of Intergan may be defined by the sheer number of intervals it maps to ~19/16: 19/16, 25/21, 31/26, 32/27, 37/31, 44/37<ins style="font-weight: bold; text-decoration: none;">. The semiquartal temperament equates all of them besides 25/21 due to its sharp 5</ins>, <ins style="font-weight: bold; text-decoration: none;">instead equating it to 6/5 in the 7-limit. This includes </ins>the otonal <ins style="font-weight: bold; text-decoration: none;">approximation of 4edo, </ins>26:31:37:44.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
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Ground
https://xenreference.com/wiki/index.php?title=Intergan&diff=7765&oldid=prev
Ground at 04:46, 12 July 2026
2026-07-12T04:46:50Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 04:46, 12 July 2026</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l8">Line 8:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Primes 7, 23, and 29 are all more difficult to map due to their complexity, although their difficulty is in ascending order. They are more easily reached by splitting the semifourth generator in half in a manner similar to Negri.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Primes 7, 23, and 29 are all more difficult to map due to their complexity, although their difficulty is in ascending order. They are more easily reached by splitting the semifourth generator in half in a manner similar to Negri.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{| class="wikitable"</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{| class="wikitable"</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|+Semiquartal Intergan, 14\67 generator, 37-limit patent val</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|+Semiquartal Intergan, 14\67 generator, 37-limit patent val<ins style="font-weight: bold; text-decoration: none;">, 37-odd-limit</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>!Gens</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>!Gens</div></td></tr>
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Ground
https://xenreference.com/wiki/index.php?title=Intergan&diff=7764&oldid=prev
Ground at 04:43, 12 July 2026
2026-07-12T04:43:41Z
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<a href="https://xenreference.com/wiki/index.php?title=Intergan&diff=7764&oldid=7761">Show changes</a>
Ground
https://xenreference.com/wiki/index.php?title=Intergan&diff=7761&oldid=prev
Ground at 02:53, 12 July 2026
2026-07-12T02:53:05Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 02:53, 12 July 2026</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Intergan''' is a set of temperaments related to 24edo semiquartal. The term is short for "interseptimal Ganassi," after 12edo's 2.3.17.19 Ganassi temperament. It seeks to cover all of the notable concordances generated by a meantone-range semifourth.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Intergan''' is a set of temperaments related to 24edo semiquartal. The term is short for "interseptimal Ganassi," after 12edo's 2.3.17.19 Ganassi temperament. It seeks to cover all of the notable concordances generated by a meantone-range semifourth.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* The most basic version is 2.3.11.13/5.17.19 5&24. 4/3 is split into two semifourths most simply represented by 15/13, and 22/17 is equated to 13/10 and 22/19 is equated to 15/13. It <del style="font-weight: bold; text-decoration: none;">contains </del>the 16:19:22 +1+1 sub-diminished triad.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* The most basic version is 2.3.11.13/5.17.19 5&24. 4/3 is split into two semifourths most simply represented by 15/13, and 22/17 is equated to 13/10 and 22/19 is equated to 15/13. It <ins style="font-weight: bold; text-decoration: none;">features the remarkably simple 10:13:15 ultramajor triad and its retroversion found in Island temperaments, along with </ins>the 16:19:22 +1+1 sub-diminished triad <ins style="font-weight: bold; text-decoration: none;">and 16:19:24:27 +3+5+3 minor add6 tetrad. 11:12:17:19 is present, although this adding 13, 14, or 15 to the subgroup will significantly improve its usefulness</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Tempering out 81/80 is somewhat obvious, resulting in 2.3.5.11.13.17.19 5&24.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Tempering out 81/80 is somewhat obvious, resulting in 2.3.5.11.13.17.19 5&24.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Primes 31 and 37 are also obvious to add, equating 37/32 to 22/19 and 37/31 to 19/16, resulting in 2.3.5.11.13.17.19.31.37 5&24. 67edo is roughly optimal due to its very mild meantone fourth being split in half. The 2.31.37 restriction is highly accurate in 43edo.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Primes 31 and 37 are also obvious to add, equating 37/32 to 22/19 and 37/31 to 19/16, resulting in 2.3.5.11.13.17.19.31.37 5&24. 67edo is roughly optimal due to its very mild meantone fourth being split in half. The 2.31.37 restriction is highly accurate in 43edo.</div></td></tr>
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Ground