https://en.xen.wiki/index.php?action=history&feed=atom&title=User%3AGodtone%2Fzeta 2026-07-01T12:46:46Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=User:Godtone/zeta&diff=193872&oldid=prev 2025-04-24T17:08:25Z

<p><span class="autocomment">Top 10: </span> move list to top</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 17:08, 24 April 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l187">Line 187:</td> <td colspan="2" class="diff-lineno">Line 187:</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>&lt;nowiki&gt;*&lt;/nowiki&gt; For this reason, we start the list at 10et (corresponding to 10edo) because all previous equal temperaments&#039; inclusion is unsurprising. (The first to be excluded is 18et, corresponding to [[18edo]] being close to a zeta valley.)</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>&lt;nowiki&gt;*&lt;/nowiki&gt; For this reason, we start the list at 10et (corresponding to 10edo) because all previous equal temperaments&#039; inclusion is unsurprising. (The first to be excluded is 18et, corresponding to [[18edo]] being close to a zeta valley.)</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 resulting sequence is: {{EDOs| 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 21, 22, 24, 26, 27, 29, 31, 34, 36, 37, 38, 39, 41, 43, 46, 48, 50, 53, 56, 58, 60, 62, 63, 65, 68, 72, 77, 80, 84, 87, 94, 99, 103, 106, 111, 113, 118, 121, 125, 130, 140, 149, 152, 159, 161, 171, 183, 190, 193, 198, 212, 217, 224, 229, 239, 243, 255, 270, 282, 289, 301, 311 }}.</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;">=== Top 10 placement data ===</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>[[10], 7, 9, 5, 8, 4, 6, 3, 2, 6]</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>[[10], 7, 9, 5, 8, 4, 6, 3, 2, 6]</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-lineno" id="mw-diff-left-l330">Line 330:</td> <td colspan="2" class="diff-lineno">Line 333:</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>[270, [311], 224, 301, 243, 217, 171, 183, 282, 289]</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>[270, [311], 224, 301, 243, 217, 171, 183, 282, 289]</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><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></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;">The resulting sequence is: {{EDOs| 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 21, 22, 24, 26, 27, 29, 31, 34, 36, 37, 38, 39, 41, 43, 46, 48, 50, 53, 56, 58, 60, 62, 63, 65, 68, 72, 77, 80, 84, 87, 94, 99, 103, 106, 111, 113, 118, 121, 125, 130, 140, 149, 152, 159, 161, 171, 183, 190, 193, 198, 212, 217, 224, 229, 239, 243, 255, 270, 282, 289, 301, 311 }}.</del></div></td><td colspan="2" class="diff-side-added"></td></tr> </table>

Godtone https://en.xen.wiki/index.php?title=User:Godtone/zeta&diff=193869&oldid=prev 2025-04-24T17:02:04Z

<p><span class="autocomment">Top 10: </span> change to top 10 as i deemed that cutoff as better (including more edos that people like and think are good) and change formatting</p> <a href="https://en.xen.wiki/index.php?title=User:Godtone/zeta&amp;diff=193869&amp;oldid=193868">Show changes</a>

Godtone https://en.xen.wiki/index.php?title=User:Godtone/zeta&diff=193868&oldid=prev 2025-04-24T16:50:56Z

<p>add top 20 up to 1280edo and add a top 10 up to 311edo as i deemed that the best cutoff</p> <a href="https://en.xen.wiki/index.php?title=User:Godtone/zeta&amp;diff=193868&amp;oldid=192724">Show changes</a>

Godtone https://en.xen.wiki/index.php?title=User:Godtone/zeta&diff=192724&oldid=prev 2025-04-17T18:04:50Z

<p>Godtone moved page <a href="/w/User:Godtone/Zeta" class="mw-redirect" title="User:Godtone/Zeta">User:Godtone/Zeta</a> to <a href="/w/User:Godtone/zeta" title="User:Godtone/zeta">User:Godtone/zeta</a>: capitalisation</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <tr class="diff-title" lang="en"> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:04, 17 April 2025</td> </tr><tr><td colspan="2" class="diff-notice" lang="en"><div class="mw-diff-empty">(No difference)</div> </td></tr></table>

Godtone https://en.xen.wiki/index.php?title=User:Godtone/zeta&diff=192718&oldid=prev 2025-04-17T17:45:11Z

<p>add zeta edos</p> <p><b>New page</b></p><div>Below is a list of [[equal temperaments]] (that is, [[edo]]s with octave-tempering) that the [[zeta]] function considers to be tuned well relative to their size, up to [[311edo|311et]].<br /> <br /> We can be confident in their notability because they appear in a wide range of odd-limits (19 thru 123) according to [[User:Godtone/optimal edo sequences|the &lt;code&gt;optimal_edo_sequence&lt;/code&gt;s for those odd-limits]]. (You can calculate them yourself by using my [[User:Godtone#My_Python_3_code|copyleft Python 3 code]] (which needs no dependencies).)<br /> <br /> Specifically, an equal temperament is included if it does better than the 9th-best-scoring equal temperament so far*, and the below details both what is added to the sequence and the top 9 at any given point. These can mostly be thought of as corresponding to [[edo]]s with the exception of 39 equal temperament, because 39edo is close to a zeta valley so that it isn&#039;t meaningfully considered in-tune by zeta without the 3.8{{cent}} flat [[2/1|octave]] that zeta recommends.<br /> <br /> &lt;nowiki&gt;*&lt;/nowiki&gt; For this reason, we start the list at 10et (corresponding to 10edo) because all previous equal temperaments&#039; inclusion is unsurprising. (The first to be excluded is 18et, corresponding to [[18edo]] being close to a zeta valley.)<br /> <br /> 10 [10, 7, 9, 5, 8, 4, 6, 3, 2]<br /> <br /> 11 [10, 7, 9, 5, 8, 4, 11, 6, 3]<br /> <br /> 12 [12, 10, 7, 9, 5, 8, 4, 11, 6]<br /> <br /> 13 [12, 10, 7, 9, 5, 8, 13, 4, 11]<br /> <br /> 14 [12, 14, 10, 7, 9, 5, 8, 13, 4]<br /> <br /> 15 [12, 15, 14, 10, 7, 9, 5, 8, 13]<br /> <br /> 16 [12, 15, 14, 10, 16, 7, 9, 5, 8]<br /> <br /> 17 [12, 17, 15, 14, 10, 16, 7, 9, 5]<br /> <br /> 19 [19, 12, 17, 15, 14, 10, 16, 7, 9]<br /> <br /> 21 [19, 12, 17, 15, 14, 10, 16, 7, 21]<br /> <br /> 22 [22, 19, 12, 17, 15, 14, 10, 16, 7]<br /> <br /> 24 [22, 19, 24, 12, 17, 15, 14, 10, 16]<br /> <br /> 26 [22, 19, 24, 26, 12, 17, 15, 14, 10]<br /> <br /> 27 [27, 22, 19, 24, 26, 12, 17, 15, 14]<br /> <br /> 29 [27, 22, 19, 24, 29, 26, 12, 17, 15]<br /> <br /> 31 [31, 27, 22, 19, 24, 29, 26, 12, 17]<br /> <br /> 34 [31, 34, 27, 22, 19, 24, 29, 26, 12]<br /> <br /> 36 [31, 34, 27, 22, 36, 19, 24, 29, 26]<br /> <br /> 38 [31, 34, 27, 22, 36, 19, 38, 24, 29]<br /> <br /> 39 [31, 34, 27, 22, 36, 19, 38, 24, 39]<br /> <br /> 41 [41, 31, 34, 27, 22, 36, 19, 38, 24]<br /> <br /> 43 [41, 31, 34, 43, 27, 22, 36, 19, 38]<br /> <br /> 46 [41, 46, 31, 34, 43, 27, 22, 36, 19]<br /> <br /> 50 [41, 46, 31, 34, 50, 43, 27, 22, 36]<br /> <br /> 53 [53, 41, 46, 31, 34, 50, 43, 27, 22]<br /> <br /> 58 [53, 58, 41, 46, 31, 34, 50, 43, 27]<br /> <br /> 60 [53, 58, 41, 46, 60, 31, 34, 50, 43]<br /> <br /> 62 [53, 58, 41, 46, 60, 31, 34, 50, 62]<br /> <br /> 63 [53, 58, 41, 46, 60, 31, 63, 34, 50]<br /> <br /> 65 [53, 58, 65, 41, 46, 60, 31, 63, 34]<br /> <br /> 68 [53, 58, 65, 68, 41, 46, 60, 31, 63]<br /> <br /> 72 [72, 53, 58, 65, 68, 41, 46, 60, 31]<br /> <br /> 77 [72, 53, 77, 58, 65, 68, 41, 46, 60]<br /> <br /> 80 [72, 53, 77, 80, 58, 65, 68, 41, 46]<br /> <br /> 84 [72, 53, 77, 84, 80, 58, 65, 68, 41]<br /> <br /> 87 [72, 87, 53, 77, 84, 80, 58, 65, 68]<br /> <br /> 94 [72, 87, 94, 53, 77, 84, 80, 58, 65]<br /> <br /> 99 [99, 72, 87, 94, 53, 77, 84, 80, 58]<br /> <br /> 103 [99, 72, 87, 94, 103, 53, 77, 84, 80]<br /> <br /> 106 [99, 72, 87, 94, 103, 53, 77, 106, 84]<br /> <br /> 111 [99, 72, 111, 87, 94, 103, 53, 77, 106]<br /> <br /> 113 [99, 72, 111, 87, 94, 103, 113, 53, 77]<br /> <br /> 118 [118, 99, 72, 111, 87, 94, 103, 113, 53]<br /> <br /> 121 [118, 99, 72, 111, 87, 94, 121, 103, 113]<br /> <br /> 125 [118, 99, 72, 111, 87, 94, 121, 125, 103]<br /> <br /> 130 [130, 118, 99, 72, 111, 87, 94, 121, 125]<br /> <br /> 140 [130, 140, 118, 99, 72, 111, 87, 94, 121]<br /> <br /> 149 [130, 140, 118, 99, 72, 149, 111, 87, 94]<br /> <br /> 152 [152, 130, 140, 118, 99, 72, 149, 111, 87]<br /> <br /> 159 [152, 130, 140, 118, 159, 99, 72, 149, 111]<br /> <br /> 171 [171, 152, 130, 140, 118, 159, 99, 72, 149]<br /> <br /> 183 [171, 183, 152, 130, 140, 118, 159, 99, 72]<br /> <br /> 190 [171, 183, 152, 190, 130, 140, 118, 159, 99]<br /> <br /> 193 [171, 183, 152, 190, 130, 193, 140, 118, 159]<br /> <br /> 198 [171, 183, 152, 190, 130, 198, 193, 140, 118]<br /> <br /> 217 [217, 171, 183, 152, 190, 130, 198, 193, 140]<br /> <br /> 224 [224, 217, 171, 183, 152, 190, 130, 198, 193]<br /> <br /> 239 [224, 217, 171, 183, 152, 190, 130, 198, 239]<br /> <br /> 243 [224, 243, 217, 171, 183, 152, 190, 130, 198]<br /> <br /> 255 [224, 243, 217, 171, 183, 152, 190, 130, 255]<br /> <br /> 270 [270, 224, 243, 217, 171, 183, 152, 190, 130]<br /> <br /> 282 [270, 224, 243, 217, 171, 282, 183, 152, 190]<br /> <br /> 289 [270, 224, 243, 217, 171, 282, 183, 289, 152]<br /> <br /> 301 [270, 224, 301, 243, 217, 171, 282, 183, 289]<br /> <br /> 311 [270, 311, 224, 301, 243, 217, 171, 282, 183]<br /> <br /> The resulting sequence is: {{EDOs| 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 21, 22, 24, 26, 27, 29, 31, 34, 36, 38, 39, 41, 43, 46, 50, 53, 58, 60, 62, 63, 65, 68, 72, 77, 80, 84, 87, 94, 99, 103, 106, 111, 113, 118, 121, 125, 130, 140, 149, 152, 159, 171, 183, 190, 193, 198, 217, 224, 239, 243, 255, 270, 282, 289, 301, 311 }}.</div>

Godtone