https://en.xen.wiki/index.php?action=history&feed=atom&title=Essential_tempering_comma 2026-06-16T21:48:10Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=Essential_tempering_comma&diff=217043&oldid=prev 2025-11-15T12:40:18Z

<p><span class="autocomment">List of small essential tempering commas by odd limit</span></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 12:40, 15 November 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l45">Line 45:</td> <td colspan="2" class="diff-lineno">Line 45:</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>; 25-odd-limit (incomplete)</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>; 25-odd-limit (incomplete)</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>: 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2093/2090, 2185/2184, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2875/2873, 2926/2925, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3179/3174, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3705/3703, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4352/4347, 4394/4389, 4693/4692, 4761/4760, 4807/4800, 4914/4913, 5083/5082, 5175/5168, 5415/5408, 5491/5488, 5776/5775, 5819/5814, 5824/5819, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 7942/7935, 8625/8624, 9261/9248, 10626/10625, 12168/12167.  </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>: 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1311/1309, 1331/1330<ins style="font-weight: bold; text-decoration: none;">, 1377/1375</ins>, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2093/2090<ins style="font-weight: bold; text-decoration: none;">, 2128/2125</ins>, 2185/2184, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2875/2873, 2926/2925, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3179/3174, 3213/3211, 3250/3249<ins style="font-weight: bold; text-decoration: none;">, 3328/3325</ins>, 3381/3380, 3520/3519, 3553/3549, 3705/3703, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4352/4347, 4394/4389, 4693/4692, 4761/4760, 4807/4800, 4914/4913, 5083/5082, 5175/5168, 5415/5408, 5491/5488, 5776/5775, 5819/5814, 5824/5819, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 7942/7935, 8625/8624, 9261/9248, 10626/10625, 12168/12167.  </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>; 27-odd-limit (incomplete)</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>; 27-odd-limit (incomplete)</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>: 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2187/2185, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2875/2873, 2926/2925, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3705/3703, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4352/4347, 4375/4374, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5175/5168, 5415/5408, 5491/5488, 5776/5775, 5819/5814, 5824/5819, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 7942/7935, 8075/8073, 8625/8624, 10626/10625, 12168/12167.  </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>: 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2187/2185, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2875/2873, 2926/2925, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3213/3211, 3250/3249<ins style="font-weight: bold; text-decoration: none;">, 3328/3325</ins>, 3381/3380, 3520/3519, 3553/3549, 3705/3703, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4352/4347, 4375/4374, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5175/5168, 5415/5408, 5491/5488, 5776/5775, 5819/5814, 5824/5819, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 7942/7935, 8075/8073, 8625/8624, 10626/10625, 12168/12167.  </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>; 29-odd-limit (incomplete)</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>; 29-odd-limit (incomplete)</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>: 875/874, 897/896, 936/935, 969/968, 1001/1000, 1015/1014, 1045/1044, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1445/1444, 1450/1449, 1496/1495, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1863/1862, 2001/2000, 2002/2001, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2187/2185, 2205/2204, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2530/2527, 2601/2600, 2640/2639, 2646/2645, 2720/2717, 2737/2736, 2755/2754, 2784/2783, 2875/2873, 2926/2925, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3553/3549, 3705/3703, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4352/4347, 4375/4374, 4394/4389, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 5083/5082, 5104/5103, 5491/5488, 5684/5681, 5776/5775, 5819/5814, 5824/5819, 5888/5887, 5985/5984, 6144/6137, 6175/6174, 6670/6669, 6864/6859, 6877/6875, 7425/7424, 7942/7935, 8075/8073, 8625/8624, 8671/8670, 9251/9248, 10557/10556, 10626/10625, 10935/10933, 11340/11339, 12168/12167, 12673/12672, 13225/13224, 13312/13311.  </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>: 875/874, 897/896, 936/935, 969/968, 1001/1000, 1015/1014, 1045/1044, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1445/1444, 1450/1449, 1496/1495, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1863/1862, 2001/2000, 2002/2001, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2187/2185, 2205/2204, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2530/2527, 2601/2600, 2640/2639, 2646/2645, 2720/2717, 2737/2736, 2755/2754, 2784/2783, 2875/2873, 2926/2925, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3213/3211, 3249/3248, 3250/3249<ins style="font-weight: bold; text-decoration: none;">, 3328/3325</ins>, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3553/3549, 3705/3703, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4352/4347, 4375/4374, 4394/4389, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 5083/5082, 5104/5103, 5491/5488, 5684/5681, 5776/5775, 5819/5814, 5824/5819, 5888/5887, 5985/5984, 6144/6137, 6175/6174, 6670/6669, 6864/6859, 6877/6875, 7425/7424, 7942/7935, 8075/8073, 8625/8624, 8671/8670, 9251/9248, 10557/10556, 10626/10625, 10935/10933, 11340/11339, 12168/12167, 12673/12672, 13225/13224, 13312/13311.  </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>; 31-odd-limit (incomplete)</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>; 31-odd-limit (incomplete)</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>: 969/968, 1001/1000, 1015/1014, 1024/1023, 1045/1044, 1054/1053, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1210/1209, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1365/1364, 1426/1425, 1445/1444, 1450/1449, 1496/1495, 1519/1518, 1520/1519, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1768/1767, 1860/1859, 1863/1862, 1955/1953, 2001/2000, 2002/2001, 2016/2015, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2187/2185, 2205/2204, 2233/2232, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2601/2600, 2640/2639, 2646/2645, 2737/2736, 2755/2754, 2784/2783, 2875/2873, 2926/2925, 2945/2944, 2976/2975, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3565/3564, 3627/3625, 3705/3703, 3751/3750, 3876/3875, 3888/3887, 3969/3968, 3971/3968, 3971/3969, 4096/4095, 4186/4185, 4200/4199, 4225/4224, 4375/4374, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4807/4805, 4901/4900, 4914/4913, 4960/4959, 4992/4991, 5083/5082, 5104/5103, 5244/5239, 5425/5423, 5491/5488, 5643/5642, 5684/5681, 5776/5775, 5797/5796, 5819/5814, 5824/5819, 5888/5887, 5985/5984, 6076/6075, 6138/6137, 6175/6174, 6293/6292, 6325/6324, 6480/6479, 6670/6669, 6728/6727, 6864/6859, 6877/6875, 7425/7424, 7657/7656, 7905/7904, 7936/7935, 7942/7935, 8075/8073, 8092/8091, 8464/8463, 8526/8525, 8625/8624, 8671/8670, 8960/8959, 9251/9248, 9425/9424, 10557/10556, 10626/10625, 10881/10880, 10935/10933, 11340/11339, 12122/12121, 12168/12167, 12673/12672, 13225/13224, 13312/13311, 15625/15624, 17577/17576, 19344/19343, 21142/21141, 24025/24024, 29792/29791.  </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>: 969/968, 1001/1000, 1015/1014, 1024/1023, 1045/1044, 1054/1053, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1210/1209, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1365/1364, 1426/1425, 1445/1444, 1450/1449, 1496/1495, 1519/1518, 1520/1519, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1768/1767, 1860/1859, 1863/1862, 1955/1953, 2001/2000, 2002/2001, 2016/2015, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2187/2185, 2205/2204, 2233/2232, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2601/2600, 2640/2639, 2646/2645, 2737/2736, 2755/2754, 2784/2783, 2875/2873, 2926/2925, 2945/2944, 2976/2975, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3213/3211, 3249/3248, 3250/3249<ins style="font-weight: bold; text-decoration: none;">, 3328/3325</ins>, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3565/3564, 3627/3625, 3705/3703, 3751/3750, 3876/3875, 3888/3887, 3969/3968, 3971/3968, 3971/3969, 4096/4095<ins style="font-weight: bold; text-decoration: none;">, 4125/4123</ins>, 4186/4185, 4200/4199, 4225/4224, 4375/4374, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4807/4805, 4901/4900, 4914/4913, 4960/4959, 4992/4991, 5083/5082, 5104/5103, 5244/5239, 5425/5423, 5491/5488, 5643/5642, 5684/5681, 5776/5775, 5797/5796, 5819/5814, 5824/5819, 5888/5887, 5985/5984, 6076/6075, 6138/6137, 6175/6174, 6293/6292, 6325/6324, 6480/6479, 6670/6669, 6728/6727, 6864/6859, 6877/6875, 7425/7424, 7657/7656, 7905/7904, 7936/7935, 7942/7935, 8075/8073, 8092/8091, 8464/8463, 8526/8525, 8625/8624, 8671/8670, 8960/8959, 9251/9248, 9425/9424, 10557/10556, 10626/10625, 10881/10880, 10935/10933, 11340/11339, 12122/12121, 12168/12167, 12673/12672, 13225/13224, 13312/13311, 15625/15624, 17577/17576, 19344/19343, 21142/21141, 24025/24024, 29792/29791.  </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>It is not necessary to use the full &#039;&#039;q&#039;&#039;-odd-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 243/242, 385/384, 441/440, 540/539, 3388/3375.</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>It is not necessary to use the full &#039;&#039;q&#039;&#039;-odd-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 243/242, 385/384, 441/440, 540/539, 3388/3375.</div></td></tr> </table>

Xenllium https://en.xen.wiki/index.php?title=Essential_tempering_comma&diff=217029&oldid=prev 2025-11-15T10:37:51Z

<p><span class="autocomment">List of small essential tempering commas by odd limit</span></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 10:37, 15 November 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l42">Line 42:</td> <td colspan="2" class="diff-lineno">Line 42:</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>; 23-odd-limit (incomplete)</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>; 23-odd-limit (incomplete)</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>: 540/539, 561/560, 576/575, 595/594, 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1127/1125, 1156/1155, 1197/1196, 1216/1215, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1771/1768, 1862/1859, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2093/2090, 2185/2184, 2200/2197, 2299/2295, 2300/2299, 2431/2430, 2432/2431, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2912/2907, 2926/2925, 3060/3059, 3136/3135, 3179/3174, 3213/3211, 3381/3380, 3520/3519, 3553/3549, 3705/3703, 3762/3757, 3888/3887, 3971/3969, 3978/3971, 4096/4095, 4200/4199, 4352/4347, 4394/4389, 4693/4692, 4761/4760, 4807/4800, 4914/4913, 5083/5082, 5175/5168, 5415/5408, 5491/5488, 5985/5984, 6080/6069, 6144/6137, 6864/6859, 7942/7935, 9261/9248, 12168/12167.  </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>: 540/539, 561/560, 576/575, 595/594, 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1127/1125, 1156/1155, 1197/1196, 1216/1215, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1771/1768, 1862/1859, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2093/2090, 2185/2184, 2200/2197, 2299/2295, 2300/2299, 2431/2430, 2432/2431, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2912/2907, 2926/2925, 3060/3059, 3136/3135, 3179/3174, 3213/3211, 3381/3380, 3520/3519, 3553/3549, 3705/3703, 3762/3757, 3888/3887, 3971/3969, 3978/3971, 4096/4095, 4200/4199, 4352/4347, 4394/4389, 4693/4692, 4761/4760, 4807/4800, 4914/4913, 5083/5082, 5175/5168, 5415/5408, 5491/5488<ins style="font-weight: bold; text-decoration: none;">, 5819/5814, 5824/5819</ins>, 5985/5984, 6080/6069, 6144/6137, 6864/6859, 7942/7935, 9261/9248, 12168/12167.  </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>; 25-odd-limit (incomplete)</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>; 25-odd-limit (incomplete)</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>: 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2093/2090, 2185/2184, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2875/2873, 2926/2925, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3179/3174, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3705/3703, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4352/4347, 4394/4389, 4693/4692, 4761/4760, 4807/4800, 4914/4913, 5083/5082, 5175/5168, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 7942/7935, 8625/8624, 9261/9248, 10626/10625, 12168/12167.  </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>: 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2093/2090, 2185/2184, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2875/2873, 2926/2925, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3179/3174, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3705/3703, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4352/4347, 4394/4389, 4693/4692, 4761/4760, 4807/4800, 4914/4913, 5083/5082, 5175/5168, 5415/5408, 5491/5488, 5776/5775<ins style="font-weight: bold; text-decoration: none;">, 5819/5814, 5824/5819</ins>, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 7942/7935, 8625/8624, 9261/9248, 10626/10625, 12168/12167.  </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>; 27-odd-limit (incomplete)</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>; 27-odd-limit (incomplete)</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>: 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2187/2185, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2875/2873, 2926/2925, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3705/3703, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4352/4347, 4375/4374, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5175/5168, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 7942/7935, 8075/8073, 8625/8624, 10626/10625, 12168/12167.  </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>: 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2187/2185, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2875/2873, 2926/2925, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3705/3703, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4352/4347, 4375/4374, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5175/5168, 5415/5408, 5491/5488, 5776/5775<ins style="font-weight: bold; text-decoration: none;">, 5819/5814, 5824/5819</ins>, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 7942/7935, 8075/8073, 8625/8624, 10626/10625, 12168/12167.  </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>; 29-odd-limit (incomplete)</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>; 29-odd-limit (incomplete)</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>: 875/874, 897/896, 936/935, 969/968, 1001/1000, 1015/1014, 1045/1044, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1445/1444, 1450/1449, 1496/1495, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1863/1862, 2001/2000, 2002/2001, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2187/2185, 2205/2204, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2530/2527, 2601/2600, 2640/2639, 2646/2645, 2720/2717, 2737/2736, 2755/2754, 2784/2783, 2875/2873, 2926/2925, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3553/3549, 3705/3703, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4352/4347, 4375/4374, 4394/4389, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 5083/5082, 5104/5103, 5491/5488, 5776/5775, 5888/5887, 5985/5984, 6144/6137, 6175/6174, 6670/6669, 6864/6859, 6877/6875, 7425/7424, 7942/7935, 8075/8073, 8625/8624, 8671/8670, 9251/9248, 10557/10556, 10626/10625, 10935/10933, 11340/11339, 12168/12167, 12673/12672, 13225/13224, 13312/13311.  </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>: 875/874, 897/896, 936/935, 969/968, 1001/1000, 1015/1014, 1045/1044, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1445/1444, 1450/1449, 1496/1495, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1863/1862, 2001/2000, 2002/2001, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2187/2185, 2205/2204, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2530/2527, 2601/2600, 2640/2639, 2646/2645, 2720/2717, 2737/2736, 2755/2754, 2784/2783, 2875/2873, 2926/2925, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3553/3549, 3705/3703, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4352/4347, 4375/4374, 4394/4389, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 5083/5082, 5104/5103, 5491/5488<ins style="font-weight: bold; text-decoration: none;">, 5684/5681</ins>, 5776/5775<ins style="font-weight: bold; text-decoration: none;">, 5819/5814, 5824/5819</ins>, 5888/5887, 5985/5984, 6144/6137, 6175/6174, 6670/6669, 6864/6859, 6877/6875, 7425/7424, 7942/7935, 8075/8073, 8625/8624, 8671/8670, 9251/9248, 10557/10556, 10626/10625, 10935/10933, 11340/11339, 12168/12167, 12673/12672, 13225/13224, 13312/13311.  </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>; 31-odd-limit (incomplete)</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>; 31-odd-limit (incomplete)</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>: 969/968, 1001/1000, 1015/1014, 1024/1023, 1045/1044, 1054/1053, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1210/1209, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1365/1364, 1426/1425, 1445/1444, 1450/1449, 1496/1495, 1519/1518, 1520/1519, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1768/1767, 1860/1859, 1863/1862, 1955/1953, 2001/2000, 2002/2001, 2016/2015, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2187/2185, 2205/2204, 2233/2232, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2601/2600, 2640/2639, 2646/2645, 2737/2736, 2755/2754, 2784/2783, 2875/2873, 2926/2925, 2945/2944, 2976/2975, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3565/3564, 3627/3625, 3705/3703, 3751/3750, 3876/3875, 3888/3887, 3969/3968, 3971/3968, 3971/3969, 4096/4095, 4186/4185, 4200/4199, 4225/4224, 4375/4374, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4807/4805, 4901/4900, 4914/4913, 4960/4959, 4992/4991, 5083/5082, 5104/5103, 5425/5423, 5491/5488, 5643/5642, 5776/5775, 5797/5796, 5888/5887, 5985/5984, 6076/6075, 6138/6137, 6175/6174, 6293/6292, 6325/6324, 6480/6479, 6670/6669, 6728/6727, 6864/6859, 6877/6875, 7425/7424, 7657/7656, 7905/7904, 7936/7935, 7942/7935, 8075/8073, 8092/8091, 8464/8463, 8526/8525, 8625/8624, 8671/8670, 8960/8959, 9251/9248, 9425/9424, 10557/10556, 10626/10625, 10881/10880, 10935/10933, 11340/11339, 12122/12121, 12168/12167, 12673/12672, 13225/13224, 13312/13311, 15625/15624, 17577/17576, 19344/19343, 21142/21141, 24025/24024, 29792/29791.  </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>: 969/968, 1001/1000, 1015/1014, 1024/1023, 1045/1044, 1054/1053, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1210/1209, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1365/1364, 1426/1425, 1445/1444, 1450/1449, 1496/1495, 1519/1518, 1520/1519, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1768/1767, 1860/1859, 1863/1862, 1955/1953, 2001/2000, 2002/2001, 2016/2015, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2187/2185, 2205/2204, 2233/2232, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2601/2600, 2640/2639, 2646/2645, 2737/2736, 2755/2754, 2784/2783, 2875/2873, 2926/2925, 2945/2944, 2976/2975, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3565/3564, 3627/3625, 3705/3703, 3751/3750, 3876/3875, 3888/3887, 3969/3968, 3971/3968, 3971/3969, 4096/4095, 4186/4185, 4200/4199, 4225/4224, 4375/4374, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4807/4805, 4901/4900, 4914/4913, 4960/4959, 4992/4991, 5083/5082, 5104/5103<ins style="font-weight: bold; text-decoration: none;">, 5244/5239</ins>, 5425/5423, 5491/5488, 5643/5642<ins style="font-weight: bold; text-decoration: none;">, 5684/5681</ins>, 5776/5775, 5797/5796<ins style="font-weight: bold; text-decoration: none;">, 5819/5814, 5824/5819</ins>, 5888/5887, 5985/5984, 6076/6075, 6138/6137, 6175/6174, 6293/6292, 6325/6324, 6480/6479, 6670/6669, 6728/6727, 6864/6859, 6877/6875, 7425/7424, 7657/7656, 7905/7904, 7936/7935, 7942/7935, 8075/8073, 8092/8091, 8464/8463, 8526/8525, 8625/8624, 8671/8670, 8960/8959, 9251/9248, 9425/9424, 10557/10556, 10626/10625, 10881/10880, 10935/10933, 11340/11339, 12122/12121, 12168/12167, 12673/12672, 13225/13224, 13312/13311, 15625/15624, 17577/17576, 19344/19343, 21142/21141, 24025/24024, 29792/29791.  </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>It is not necessary to use the full &#039;&#039;q&#039;&#039;-odd-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 243/242, 385/384, 441/440, 540/539, 3388/3375.</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>It is not necessary to use the full &#039;&#039;q&#039;&#039;-odd-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 243/242, 385/384, 441/440, 540/539, 3388/3375.</div></td></tr> </table>

Xenllium https://en.xen.wiki/index.php?title=Essential_tempering_comma&diff=207810&oldid=prev 2025-08-20T17:52:41Z

<p>Restore credit to Gene</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 17:52, 20 August 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l2">Line 2:</td> <td colspan="2" class="diff-lineno">Line 2:</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>== Finding small essential tempering commas ==</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>== Finding small essential tempering commas ==</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>Consider a set of "consonances" composed of octave-reduced JI ratios, including the unison and octave, such that any interval and its octave complement are both "consonances". A JI interval ''c'' is an essential tempering comma for this set of consonances if:</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;">[[Gene Ward Smith]] derived the following method to find essential tempering commas. </ins>Consider a set of "consonances" composed of octave-reduced JI ratios, including the unison and octave, such that any interval and its octave complement are both "consonances". A JI interval ''c'' is an essential tempering comma for this set of consonances if:</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># &#039;&#039;c&#039;&#039; is not the unison, but it is smaller than any interval between two consonances.</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># &#039;&#039;c&#039;&#039; is not the unison, but it is smaller than any interval between two consonances.</div></td></tr> </table>

FloraC https://en.xen.wiki/index.php?title=Essential_tempering_comma&diff=207550&oldid=prev 2025-08-19T22:47:51Z

<p>how did this not use the terms &quot;octave complement&quot;, &quot;unison&quot;, &quot;octave&quot;, or &quot;octave-reduced&quot;</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 22:47, 19 August 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</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>An &#039;&#039;&#039;essential tempering comma&#039;&#039;&#039; is a [[comma]] that induces [[Dyadic chord #Essentially tempered dyadic chords|essentially tempered chords]].  </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>An &#039;&#039;&#039;essential tempering comma&#039;&#039;&#039; is a [[comma]] that induces [[Dyadic chord #Essentially tempered dyadic chords|essentially tempered chords]].  </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;">Gene's derivation </del>==</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;">Finding small essential tempering commas </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><del style="font-weight: bold; text-decoration: none;">Suppose ''S'' is </del>a set of JI ratios <del style="font-weight: bold; text-decoration: none;">''r'' </del>including <del style="font-weight: bold; text-decoration: none;">1 </del>and <del style="font-weight: bold; text-decoration: none;">2 with 1 ≤ ''r'' ≤ 2 </del>such that <del style="font-weight: bold; text-decoration: none;">if ''r'' is in ''S'', so is 2/''r''. ''S'' is intended to represent a set of pitch classes defining </del>"<del style="font-weight: bold; text-decoration: none;">consonance</del>". A JI interval ''c'' is an essential tempering comma for <del style="font-weight: bold; text-decoration: none;">''S'' </del>if:</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;">Consider </ins>a set of <ins style="font-weight: bold; text-decoration: none;">"consonances" composed of octave-reduced </ins>JI ratios<ins style="font-weight: bold; text-decoration: none;">, </ins>including <ins style="font-weight: bold; text-decoration: none;">the unison </ins>and <ins style="font-weight: bold; text-decoration: none;">octave, </ins>such that <ins style="font-weight: bold; text-decoration: none;">any interval and its octave complement are both </ins>"<ins style="font-weight: bold; text-decoration: none;">consonances</ins>". A JI interval ''c'' is an essential tempering comma for <ins style="font-weight: bold; text-decoration: none;">this set of consonances </ins>if:</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># ''c'' is <del style="font-weight: bold; text-decoration: none;">greater than 1 </del>but <del style="font-weight: bold; text-decoration: none;">less </del>than <del style="font-weight: bold; text-decoration: none;">the smallest </del>interval between <del style="font-weight: bold; text-decoration: none;">any </del>two <del style="font-weight: bold; text-decoration: none;">members of ''S''</del>.  </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># ''c'' is <ins style="font-weight: bold; text-decoration: none;">not the unison, </ins>but <ins style="font-weight: bold; text-decoration: none;">it is smaller </ins>than <ins style="font-weight: bold; text-decoration: none;">any </ins>interval between two <ins style="font-weight: bold; text-decoration: none;">consonances</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># There are three <del style="font-weight: bold; text-decoration: none;">ratios </del>''r''&lt;sub&gt;1&lt;/sub&gt;, ''r''&lt;sub&gt;2&lt;/sub&gt;, and ''r''&lt;sub&gt;3&lt;/sub&gt; <del style="font-weight: bold; text-decoration: none;">in ''S'' </del>such that ''c'' = ''r''&lt;sub&gt;1&lt;/sub&gt;''r''&lt;sub&gt;2&lt;/sub&gt;/''r''&lt;sub&gt;3&lt;/sub&gt;.  </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># There are three <ins style="font-weight: bold; text-decoration: none;">consonances </ins>''r''&lt;sub&gt;1&lt;/sub&gt;, ''r''&lt;sub&gt;2&lt;/sub&gt;, and ''r''&lt;sub&gt;3&lt;/sub&gt; such that ''c'' = ''r''&lt;sub&gt;1&lt;/sub&gt;''r''&lt;sub&gt;2&lt;/sub&gt;/''r''&lt;sub&gt;3&lt;/sub&gt;.  </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>This derivation is a sufficient and not necessary condition for identifying essentially tempered triads due to how aggressively it rejects commas that are too large. This does come with the benefit of discarding absurdly large commas. For example, 125/108 is a comma whose essentially tempered chord is a stack of three 6/5&#039;s closing at the octave. Assume pure octaves, it requires each 6/5 to be tuned sharper than the just value of 5/4, and is rejected, in fact leaving 128/125 as the only 5-odd-limit essential tempering comma. However, some commas are reasonably sized but still rejected, such as 121/120 in the 11-odd-limit (→ [[biyatismic chords]]).  </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>This derivation is a sufficient and not necessary condition for identifying essentially tempered triads due to how aggressively it rejects commas that are too large. This does come with the benefit of discarding absurdly large commas. For example, 125/108 is a comma whose essentially tempered chord is a stack of three 6/5&#039;s closing at the octave. Assume pure octaves, it requires each 6/5 to be tuned sharper than the just value of 5/4, and is rejected, in fact leaving 128/125 as the only 5-odd-limit essential tempering comma. However, some commas are reasonably sized but still rejected, such as 121/120 in the 11-odd-limit (→ [[biyatismic chords]]).  </div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l11">Line 11:</td> <td colspan="2" class="diff-lineno">Line 11:</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>Note also that it only identifies &#039;&#039;triads&#039;&#039;. There are commas that induce essentially tempered chords whose basic forms are &#039;&#039;tetrads&#039;&#039;. For example, 81/80 induces an essentially tempered tetrad (→ [[didymic chords]]), despite that any three of the components are essentially just.</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>Note also that it only identifies &#039;&#039;triads&#039;&#039;. There are commas that induce essentially tempered chords whose basic forms are &#039;&#039;tetrads&#039;&#039;. For example, 81/80 induces an essentially tempered tetrad (→ [[didymic chords]]), despite that any three of the components are essentially just.</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>== List of essential tempering commas by odd limit ==</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>== List of <ins style="font-weight: bold; text-decoration: none;">small </ins>essential tempering commas by odd limit ==</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>For various odd limit diamonds, we get the following essential tempering commas using the derivation above:</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>For various odd limit diamonds, we get the following essential tempering commas using the derivation above:</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> </table>

VectorGraphics https://en.xen.wiki/index.php?title=Essential_tempering_comma&diff=198625&oldid=prev 2025-06-04T07:57:45Z

<p><span class="autocomment">List of essential tempering commas by odd limit</span></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 07:57, 4 June 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l42">Line 42:</td> <td colspan="2" class="diff-lineno">Line 42:</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>; 23-odd-limit (incomplete)</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>; 23-odd-limit (incomplete)</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>: 540/539, 561/560, 576/575, 595/594, 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1127/1125, 1156/1155, 1197/1196, 1216/1215, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1771/1768, 1862/1859, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2093/2090, 2185/2184, 2200/2197, 2299/2295, 2300/2299, 2431/2430, 2432/2431, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2912/2907, 2926/2925, 3060/3059, 3136/3135, 3179/3174, 3213/3211, 3381/3380, 3520/3519, 3553/3549, 3705/3703, 3762/3757, 3888/3887, 3971/3969, 3978/3971, 4096/4095, 4200/4199, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5985/5984, 6080/6069, 6144/6137, 6864/6859, 7942/7935, 9261/9248, 12168/12167.  </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>: 540/539, 561/560, 576/575, 595/594, 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1127/1125, 1156/1155, 1197/1196, 1216/1215, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1771/1768, 1862/1859, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2093/2090, 2185/2184, 2200/2197, 2299/2295, 2300/2299, 2431/2430, 2432/2431, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2912/2907, 2926/2925, 3060/3059, 3136/3135, 3179/3174, 3213/3211, 3381/3380, 3520/3519, 3553/3549, 3705/3703, 3762/3757, 3888/3887, 3971/3969, 3978/3971, 4096/4095, 4200/4199<ins style="font-weight: bold; text-decoration: none;">, 4352/4347</ins>, 4394/4389, 4693/4692, 4761/4760<ins style="font-weight: bold; text-decoration: none;">, 4807/4800</ins>, 4914/4913, 5083/5082<ins style="font-weight: bold; text-decoration: none;">, 5175/5168</ins>, 5415/5408, 5491/5488, 5985/5984, 6080/6069, 6144/6137, 6864/6859, 7942/7935, 9261/9248, 12168/12167.  </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>; 25-odd-limit (incomplete)</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>; 25-odd-limit (incomplete)</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>: 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2093/2090, 2185/2184, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2875/2873, 2926/2925, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3179/3174, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3705/3703, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 7942/7935, 8625/8624, 9261/9248, 10626/10625, 12168/12167.  </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>: 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2093/2090, 2185/2184, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2875/2873, 2926/2925, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3179/3174, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3705/3703, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224<ins style="font-weight: bold; text-decoration: none;">, 4352/4347</ins>, 4394/4389, 4693/4692, 4761/4760<ins style="font-weight: bold; text-decoration: none;">, 4807/4800</ins>, 4914/4913, 5083/5082<ins style="font-weight: bold; text-decoration: none;">, 5175/5168</ins>, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 7942/7935, 8625/8624, 9261/9248, 10626/10625, 12168/12167.  </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>; 27-odd-limit (incomplete)</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>; 27-odd-limit (incomplete)</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>: 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2187/2185, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2875/2873, 2926/2925, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3705/3703, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 7942/7935, 8075/8073, 8625/8624, 10626/10625, 12168/12167.  </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>: 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2187/2185, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2875/2873, 2926/2925, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3705/3703, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224<ins style="font-weight: bold; text-decoration: none;">, 4352/4347</ins>, 4375/4374, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082<ins style="font-weight: bold; text-decoration: none;">, 5175/5168</ins>, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 7942/7935, 8075/8073, 8625/8624, 10626/10625, 12168/12167.  </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>; 29-odd-limit (incomplete)</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>; 29-odd-limit (incomplete)</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>: 875/874, 897/896, 936/935, 969/968, 1001/1000, 1015/1014, 1045/1044, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1445/1444, 1450/1449, 1496/1495, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1863/1862, 2001/2000, 2002/2001, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2187/2185, 2205/2204, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2530/2527, 2601/2600, 2640/2639, 2646/2645, 2720/2717, 2737/2736, 2755/2754, 2784/2783, 2875/2873, 2926/2925, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3553/3549, 3705/3703, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 5083/5082, 5104/5103, 5491/5488, 5776/5775, 5888/5887, 5985/5984, 6144/6137, 6175/6174, 6670/6669, 6864/6859, 6877/6875, 7425/7424, 7942/7935, 8075/8073, 8625/8624, 8671/8670, 9251/9248, 10557/10556, 10626/10625, 10935/10933, 11340/11339, 12168/12167, 12673/12672, 13225/13224, 13312/13311.  </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>: 875/874, 897/896, 936/935, 969/968, 1001/1000, 1015/1014, 1045/1044, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1445/1444, 1450/1449, 1496/1495, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1863/1862, 2001/2000, 2002/2001, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2187/2185, 2205/2204, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2530/2527, 2601/2600, 2640/2639, 2646/2645, 2720/2717, 2737/2736, 2755/2754, 2784/2783, 2875/2873, 2926/2925, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3553/3549, 3705/3703, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224<ins style="font-weight: bold; text-decoration: none;">, 4352/4347</ins>, 4375/4374, 4394/4389, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 5083/5082, 5104/5103, 5491/5488, 5776/5775, 5888/5887, 5985/5984, 6144/6137, 6175/6174, 6670/6669, 6864/6859, 6877/6875, 7425/7424, 7942/7935, 8075/8073, 8625/8624, 8671/8670, 9251/9248, 10557/10556, 10626/10625, 10935/10933, 11340/11339, 12168/12167, 12673/12672, 13225/13224, 13312/13311.  </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>; 31-odd-limit (incomplete)</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>; 31-odd-limit (incomplete)</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>: 969/968, 1001/1000, 1015/1014, 1024/1023, 1045/1044, 1054/1053, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1210/1209, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1365/1364, 1426/1425, 1445/1444, 1450/1449, 1496/1495, 1519/1518, 1520/1519, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1768/1767, 1860/1859, 1863/1862, 1955/1953, 2001/2000, 2002/2001, 2016/2015, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2187/2185, 2205/2204, 2233/2232, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2601/2600, 2640/2639, 2646/2645, 2737/2736, 2755/2754, 2784/2783, 2875/2873, 2926/2925, 2945/2944, 2976/2975, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3565/3564, 3627/3625, 3705/3703, 3751/3750, 3876/3875, 3888/3887, 3969/3968, 3971/3968, 3971/3969, 4096/4095, 4186/4185, 4200/4199, 4225/4224, 4375/4374, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 4960/4959, 4992/4991, 5083/5082, 5104/5103, 5425/5423, 5491/5488, 5643/5642, 5776/5775, 5797/5796, 5888/5887, 5985/5984, 6076/6075, 6138/6137, 6175/6174, 6293/6292, 6325/6324, 6480/6479, 6670/6669, 6728/6727, 6864/6859, 6877/6875, 7425/7424, 7657/7656, 7905/7904, 7936/7935, 7942/7935, 8075/8073, 8092/8091, 8464/8463, 8526/8525, 8625/8624, 8671/8670, 8960/8959, 9251/9248, 9425/9424, 10557/10556, 10626/10625, 10881/10880, 10935/10933, 11340/11339, 12122/12121, 12168/12167, 12673/12672, 13225/13224, 13312/13311, 15625/15624, 17577/17576, 19344/19343, 21142/21141, 24025/24024, 29792/29791.  </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>: 969/968, 1001/1000, 1015/1014, 1024/1023, 1045/1044, 1054/1053, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1210/1209, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1365/1364, 1426/1425, 1445/1444, 1450/1449, 1496/1495, 1519/1518, 1520/1519, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1768/1767, 1860/1859, 1863/1862, 1955/1953, 2001/2000, 2002/2001, 2016/2015, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2187/2185, 2205/2204, 2233/2232, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2601/2600, 2640/2639, 2646/2645, 2737/2736, 2755/2754, 2784/2783, 2875/2873, 2926/2925, 2945/2944, 2976/2975, 3025/3024, 3060/3059, 3128/3125, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3565/3564, 3627/3625, 3705/3703, 3751/3750, 3876/3875, 3888/3887, 3969/3968, 3971/3968, 3971/3969, 4096/4095, 4186/4185, 4200/4199, 4225/4224, 4375/4374, 4641/4640, 4693/4692, 4761/4760, 4785/4784<ins style="font-weight: bold; text-decoration: none;">, 4807/4805</ins>, 4901/4900, 4914/4913, 4960/4959, 4992/4991, 5083/5082, 5104/5103, 5425/5423, 5491/5488, 5643/5642, 5776/5775, 5797/5796, 5888/5887, 5985/5984, 6076/6075, 6138/6137, 6175/6174, 6293/6292, 6325/6324, 6480/6479, 6670/6669, 6728/6727, 6864/6859, 6877/6875, 7425/7424, 7657/7656, 7905/7904, 7936/7935, 7942/7935, 8075/8073, 8092/8091, 8464/8463, 8526/8525, 8625/8624, 8671/8670, 8960/8959, 9251/9248, 9425/9424, 10557/10556, 10626/10625, 10881/10880, 10935/10933, 11340/11339, 12122/12121, 12168/12167, 12673/12672, 13225/13224, 13312/13311, 15625/15624, 17577/17576, 19344/19343, 21142/21141, 24025/24024, 29792/29791.  </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>It is not necessary to use the full &#039;&#039;q&#039;&#039;-odd-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 243/242, 385/384, 441/440, 540/539, 3388/3375.</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>It is not necessary to use the full &#039;&#039;q&#039;&#039;-odd-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 243/242, 385/384, 441/440, 540/539, 3388/3375.</div></td></tr> </table>

Xenllium https://en.xen.wiki/index.php?title=Essential_tempering_comma&diff=197910&oldid=prev 2025-05-28T11:17:32Z

<p><span class="autocomment">List of essential tempering commas by odd limit: </span>added several commas</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 11:17, 28 May 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l42">Line 42:</td> <td colspan="2" class="diff-lineno">Line 42:</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>; 23-odd-limit (incomplete)</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>; 23-odd-limit (incomplete)</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>: 540/539, 561/560, 576/575, 595/594, 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1127/1125, 1156/1155, 1197/1196, 1216/1215, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1771/1768, 1862/1859, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2093/2090, 2185/2184, 2200/2197, 2299/2295, 2300/2299, 2431/2430, 2432/2431, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2912/2907, 2926/2925, 3060/3059, 3136/3135, 3213/3211, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 3978/3971, 4096/4095, 4200/4199, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5985/5984, 6080/6069, 6144/6137, 6864/6859, 9261/9248, 12168/12167.  </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>: 540/539, 561/560, 576/575, 595/594, 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1127/1125, 1156/1155, 1197/1196, 1216/1215, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1771/1768, 1862/1859, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2093/2090, 2185/2184, 2200/2197, 2299/2295, 2300/2299, 2431/2430, 2432/2431, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2912/2907, 2926/2925, 3060/3059, 3136/3135<ins style="font-weight: bold; text-decoration: none;">, 3179/3174</ins>, 3213/3211, 3381/3380, 3520/3519, 3553/3549<ins style="font-weight: bold; text-decoration: none;">, 3705/3703</ins>, 3762/3757, 3888/3887, 3971/3969, 3978/3971, 4096/4095, 4200/4199, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5985/5984, 6080/6069, 6144/6137, 6864/6859<ins style="font-weight: bold; text-decoration: none;">, 7942/7935</ins>, 9261/9248, 12168/12167.  </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>; 25-odd-limit (incomplete)</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>; 25-odd-limit (incomplete)</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>: 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2093/2090, 2185/2184, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 8625/8624, 9261/9248, 10626/10625, 12168/12167.  </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>: 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2093/2090, 2185/2184, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736<ins style="font-weight: bold; text-decoration: none;">, 2875/2873</ins>, 2926/2925, 3025/3024, 3060/3059<ins style="font-weight: bold; text-decoration: none;">, 3128/3125</ins>, 3136/3135<ins style="font-weight: bold; text-decoration: none;">, 3179/3174</ins>, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549<ins style="font-weight: bold; text-decoration: none;">, 3705/3703</ins>, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875<ins style="font-weight: bold; text-decoration: none;">, 7942/7935</ins>, 8625/8624, 9261/9248, 10626/10625, 12168/12167.  </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>; 27-odd-limit (incomplete)</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>; 27-odd-limit (incomplete)</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>: 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2187/2185, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 8075/8073, 8625/8624, 10626/10625, 12168/12167.  </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>: 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2187/2185, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2530/2527, 2601/2600, 2646/2645, 2720/2717, 2737/2736<ins style="font-weight: bold; text-decoration: none;">, 2875/2873</ins>, 2926/2925, 3025/3024, 3060/3059<ins style="font-weight: bold; text-decoration: none;">, 3128/3125</ins>, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549<ins style="font-weight: bold; text-decoration: none;">, 3705/3703</ins>, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875<ins style="font-weight: bold; text-decoration: none;">, 7942/7935</ins>, 8075/8073, 8625/8624, 10626/10625, 12168/12167.  </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>; 29-odd-limit (incomplete)</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>; 29-odd-limit (incomplete)</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>: 875/874, 897/896, 936/935, 969/968, 1001/1000, 1015/1014, 1045/1044, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1445/1444, 1450/1449, 1496/1495, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1863/1862, 2001/2000, 2002/2001, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2187/2185, 2205/2204, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2530/2527, 2601/2600, 2640/2639, 2646/2645, 2720/2717, 2737/2736, 2755/2754, 2784/2783, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3553/3549, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 5083/5082, 5104/5103, 5491/5488, 5776/5775, 5888/5887, 5985/5984, 6144/6137, 6175/6174, 6670/6669, 6864/6859, 6877/6875, 7425/7424, 8075/8073, 8625/8624, 8671/8670, 9251/9248, 10557/10556, 10626/10625, 10935/10933, 11340/11339, 12168/12167, 12673/12672, 13225/13224, 13312/13311.  </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>: 875/874, 897/896, 936/935, 969/968, 1001/1000, 1015/1014, 1045/1044, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1445/1444, 1450/1449, 1496/1495, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1863/1862, 2001/2000, 2002/2001, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2187/2185, 2205/2204, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2530/2527, 2601/2600, 2640/2639, 2646/2645, 2720/2717, 2737/2736, 2755/2754, 2784/2783<ins style="font-weight: bold; text-decoration: none;">, 2875/2873</ins>, 2926/2925, 3025/3024, 3060/3059<ins style="font-weight: bold; text-decoration: none;">, 3128/3125</ins>, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3553/3549<ins style="font-weight: bold; text-decoration: none;">, 3705/3703</ins>, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 5083/5082, 5104/5103, 5491/5488, 5776/5775, 5888/5887, 5985/5984, 6144/6137, 6175/6174, 6670/6669, 6864/6859, 6877/6875, 7425/7424<ins style="font-weight: bold; text-decoration: none;">, 7942/7935</ins>, 8075/8073, 8625/8624, 8671/8670, 9251/9248, 10557/10556, 10626/10625, 10935/10933, 11340/11339, 12168/12167, 12673/12672, 13225/13224, 13312/13311.  </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>; 31-odd-limit (incomplete)</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>; 31-odd-limit (incomplete)</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>: 969/968, 1001/1000, 1015/1014, 1024/1023, 1045/1044, 1054/1053, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1210/1209, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1365/1364, 1426/1425, 1445/1444, 1450/1449, 1496/1495, 1519/1518, 1520/1519, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1768/1767, 1860/1859, 1863/1862, 1955/1953, 2001/2000, 2002/2001, 2016/2015, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2187/2185, 2205/2204, 2233/2232, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2601/2600, 2640/2639, 2646/2645, 2737/2736, 2755/2754, 2784/2783, 2926/2925, 2945/2944, 2976/2975, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3565/3564, 3627/3625, 3751/3750, 3876/3875, 3888/3887, 3969/3968, 3971/3968, 3971/3969, 4096/4095, 4186/4185, 4200/4199, 4225/4224, 4375/4374, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 4960/4959, 4992/4991, 5083/5082, 5104/5103, 5425/5423, 5491/5488, 5643/5642, 5776/5775, 5797/5796, 5888/5887, 5985/5984, 6076/6075, 6138/6137, 6175/6174, 6293/6292, 6325/6324, 6480/6479, 6670/6669, 6728/6727, 6864/6859, 6877/6875, 7425/7424, 7657/7656, 7905/7904, 7936/7935, 8075/8073, 8092/8091, 8464/8463, 8526/8525, 8625/8624, 8671/8670, 8960/8959, 9251/9248, 9425/9424, 10557/10556, 10626/10625, 10881/10880, 10935/10933, 11340/11339, 12122/12121, 12168/12167, 12673/12672, 13225/13224, 13312/13311, 15625/15624, 17577/17576, 19344/19343, 21142/21141, 24025/24024, 29792/29791.  </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>: 969/968, 1001/1000, 1015/1014, 1024/1023, 1045/1044, 1054/1053, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1210/1209, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1365/1364, 1426/1425, 1445/1444, 1450/1449, 1496/1495, 1519/1518, 1520/1519, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1768/1767, 1860/1859, 1863/1862, 1955/1953, 2001/2000, 2002/2001, 2016/2015, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2187/2185, 2205/2204, 2233/2232, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2601/2600, 2640/2639, 2646/2645, 2737/2736, 2755/2754, 2784/2783<ins style="font-weight: bold; text-decoration: none;">, 2875/2873</ins>, 2926/2925, 2945/2944, 2976/2975, 3025/3024, 3060/3059<ins style="font-weight: bold; text-decoration: none;">, 3128/3125</ins>, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3565/3564, 3627/3625<ins style="font-weight: bold; text-decoration: none;">, 3705/3703</ins>, 3751/3750, 3876/3875, 3888/3887, 3969/3968, 3971/3968, 3971/3969, 4096/4095, 4186/4185, 4200/4199, 4225/4224, 4375/4374, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 4960/4959, 4992/4991, 5083/5082, 5104/5103, 5425/5423, 5491/5488, 5643/5642, 5776/5775, 5797/5796, 5888/5887, 5985/5984, 6076/6075, 6138/6137, 6175/6174, 6293/6292, 6325/6324, 6480/6479, 6670/6669, 6728/6727, 6864/6859, 6877/6875, 7425/7424, 7657/7656, 7905/7904, 7936<ins style="font-weight: bold; text-decoration: none;">/7935, 7942</ins>/7935, 8075/8073, 8092/8091, 8464/8463, 8526/8525, 8625/8624, 8671/8670, 8960/8959, 9251/9248, 9425/9424, 10557/10556, 10626/10625, 10881/10880, 10935/10933, 11340/11339, 12122/12121, 12168/12167, 12673/12672, 13225/13224, 13312/13311, 15625/15624, 17577/17576, 19344/19343, 21142/21141, 24025/24024, 29792/29791.  </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>It is not necessary to use the full &#039;&#039;q&#039;&#039;-odd-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 243/242, 385/384, 441/440, 540/539, 3388/3375.</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>It is not necessary to use the full &#039;&#039;q&#039;&#039;-odd-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 243/242, 385/384, 441/440, 540/539, 3388/3375.</div></td></tr> </table>

Xenllium https://en.xen.wiki/index.php?title=Essential_tempering_comma&diff=188695&oldid=prev 2025-03-29T03:08:29Z

<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 03:08, 29 March 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l54">Line 54:</td> <td colspan="2" class="diff-lineno">Line 54:</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>; 31-odd-limit (incomplete)</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>; 31-odd-limit (incomplete)</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>: 969/968, 1001/1000, 1015/1014, 1024/1023, 1045/1044, 1054/1053, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1210/1209, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1365/1364, 1426/1425, 1445/1444, 1450/1449, 1496/1495, 1519/1518, 1520/1519, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1768/1767, 1860/1859, 1863/1862, 1955/1953, 2001/2000, 2002/2001, 2016/2015, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2187/2185, 2205/2204, 2233/2232, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2601/2600, 2640/2639, 2646/2645, 2737/2736, 2755/2754, 2784/2783, 2926/2925, 2945/2944, 2976/2975, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3565/3564, 3627/3625, 3751/3750, 3876/3875, 3888/3887, 3969/3968, 3971/3968, 3971/3969, 4096/4095, 4186/4185, 4200/4199, 4225/4224, 4375/4374, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 4960/4959, 4992/4991, 5083/5082, 5104/5103, 5425/5423, 5491/5488, 5643/5642, 5776/5775, 5797/5796, 5888/5887, 5985/5984, 6076/6075, 6138/6137, 6175/6174, 6293/6292, 6325/6324, 6480/6479, 6670/6669, 6728/6727, 6864/6859, 6877/6875, 7425/7424, 7657/7656, 7905/7904, 7936/7935, 8075/8073, 8092/8091, 8464/8463, 8625/8624, 8671/8670, 8960/8959, 9251/9248, 10557/10556, 10626/10625, 10935/10933, 11340/11339, 12168/12167, 12673/12672, 13225/13224, 13312/13311, 15625/15624, 17577/17576, 19344/19343, 24025/24024, 29792/29791.  </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>: 969/968, 1001/1000, 1015/1014, 1024/1023, 1045/1044, 1054/1053, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1210/1209, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1365/1364, 1426/1425, 1445/1444, 1450/1449, 1496/1495, 1519/1518, 1520/1519, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1768/1767, 1860/1859, 1863/1862, 1955/1953, 2001/2000, 2002/2001, 2016/2015, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2187/2185, 2205/2204, 2233/2232, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2601/2600, 2640/2639, 2646/2645, 2737/2736, 2755/2754, 2784/2783, 2926/2925, 2945/2944, 2976/2975, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3565/3564, 3627/3625, 3751/3750, 3876/3875, 3888/3887, 3969/3968, 3971/3968, 3971/3969, 4096/4095, 4186/4185, 4200/4199, 4225/4224, 4375/4374, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 4960/4959, 4992/4991, 5083/5082, 5104/5103, 5425/5423, 5491/5488, 5643/5642, 5776/5775, 5797/5796, 5888/5887, 5985/5984, 6076/6075, 6138/6137, 6175/6174, 6293/6292, 6325/6324, 6480/6479, 6670/6669, 6728/6727, 6864/6859, 6877/6875, 7425/7424, 7657/7656, 7905/7904, 7936/7935, 8075/8073, 8092/8091, 8464/8463<ins style="font-weight: bold; text-decoration: none;">, 8526/8525</ins>, 8625/8624, 8671/8670, 8960/8959, 9251/9248<ins style="font-weight: bold; text-decoration: none;">, 9425/9424</ins>, 10557/10556, 10626/10625<ins style="font-weight: bold; text-decoration: none;">, 10881/10880</ins>, 10935/10933, 11340/11339<ins style="font-weight: bold; text-decoration: none;">, 12122/12121</ins>, 12168/12167, 12673/12672, 13225/13224, 13312/13311, 15625/15624, 17577/17576, 19344/19343<ins style="font-weight: bold; text-decoration: none;">, 21142/21141</ins>, 24025/24024, 29792/29791.  </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>It is not necessary to use the full &#039;&#039;q&#039;&#039;-odd-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 243/242, 385/384, 441/440, 540/539, 3388/3375.</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>It is not necessary to use the full &#039;&#039;q&#039;&#039;-odd-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 243/242, 385/384, 441/440, 540/539, 3388/3375.</div></td></tr> </table>

Xenllium https://en.xen.wiki/index.php?title=Essential_tempering_comma&diff=188651&oldid=prev 2025-03-29T00:19:08Z

<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 00:19, 29 March 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l42">Line 42:</td> <td colspan="2" class="diff-lineno">Line 42:</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>; 23-odd-limit (incomplete)</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>; 23-odd-limit (incomplete)</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>: 540/539, 561/560, 576/575, 595/594, 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1127/1125, 1156/1155, 1197/1196, 1216/1215, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1771/1768, 1862/1859, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2093/2090, 2185/2184, 2200/2197, 2299/2295, 2300/2299, 2431/2430, 2432/2431, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2912/2907, 2926/2925, 3060/3059, 3136/3135, 3213/3211, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 3978/3971, 4096/4095, 4200/4199, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5985/5984, 6080/6069, 6144/6137, 6864/6859, 9261/9248, 12168/12167.  </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>: 540/539, 561/560, 576/575, 595/594, 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1127/1125, 1156/1155, 1197/1196, 1216/1215, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1771/1768, 1862/1859, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2093/2090, 2185/2184, 2200/2197, 2299/2295, 2300/2299, 2431/2430, 2432/2431<ins style="font-weight: bold; text-decoration: none;">, 2530/2527</ins>, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2912/2907, 2926/2925, 3060/3059, 3136/3135, 3213/3211, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 3978/3971, 4096/4095, 4200/4199, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5985/5984, 6080/6069, 6144/6137, 6864/6859, 9261/9248, 12168/12167.  </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>; 25-odd-limit (incomplete)</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>; 25-odd-limit (incomplete)</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>: 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2093/2090, 2185/2184, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 8625/8624, 9261/9248, 10626/10625, 12168/12167.  </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>: 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2093/2090, 2185/2184, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499<ins style="font-weight: bold; text-decoration: none;">, 2530/2527</ins>, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 8625/8624, 9261/9248, 10626/10625, 12168/12167.  </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>; 27-odd-limit (incomplete)</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>; 27-odd-limit (incomplete)</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>: 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 8075/8073, 8625/8624, 10626/10625, 12168/12167.  </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>: 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184<ins style="font-weight: bold; text-decoration: none;">, 2187/2185</ins>, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499<ins style="font-weight: bold; text-decoration: none;">, 2530/2527</ins>, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 8075/8073, 8625/8624, 10626/10625, 12168/12167.  </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>; 29-odd-limit (incomplete)</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>; 29-odd-limit (incomplete)</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>: 875/874, 897/896, 936/935, 969/968, 1001/1000, 1015/1014, 1045/1044, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1445/1444, 1450/1449, 1496/1495, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1863/1862, 2001/2000, 2002/2001, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2205/2204, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2601/2600, 2640/2639, 2646/2645, 2720/2717, 2737/2736, 2755/2754, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3553/3549, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 5083/5082, 5104/5103, 5491/5488, 5776/5775, 5888/5887, 5985/5984, 6144/6137, 6175/6174, 6670/6669, 6864/6859, 6877/6875, 7425/7424, 8075/8073, 8625/8624, 8671/8670, 9251/9248, 10557/10556, 10626/10625, 10935/10933, 11340/11339, 12168/12167, 12673/12672, 13225/13224, 13312/13311.  </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>: 875/874, 897/896, 936/935, 969/968, 1001/1000, 1015/1014, 1045/1044, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1445/1444, 1450/1449, 1496/1495, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1863/1862, 2001/2000, 2002/2001, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184<ins style="font-weight: bold; text-decoration: none;">, 2187/2185</ins>, 2205/2204, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499<ins style="font-weight: bold; text-decoration: none;">, 2530/2527</ins>, 2601/2600, 2640/2639, 2646/2645, 2720/2717, 2737/2736, 2755/2754<ins style="font-weight: bold; text-decoration: none;">, 2784/2783</ins>, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3553/3549, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 5083/5082, 5104/5103, 5491/5488, 5776/5775, 5888/5887, 5985/5984, 6144/6137, 6175/6174, 6670/6669, 6864/6859, 6877/6875, 7425/7424, 8075/8073, 8625/8624, 8671/8670, 9251/9248, 10557/10556, 10626/10625, 10935/10933, 11340/11339, 12168/12167, 12673/12672, 13225/13224, 13312/13311.  </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>; 31-odd-limit (incomplete)</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>; 31-odd-limit (incomplete)</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>: 969/968, 1001/1000, 1015/1014, 1024/1023, 1045/1044, 1054/1053, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1210/1209, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1365/1364, 1426/1425, 1445/1444, 1450/1449, 1496/1495, 1519/1518, 1520/1519, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1768/1767, 1860/1859, 1863/1862, 1955/1953, 2001/2000, 2002/2001, 2016/2015, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2205/2204, 2233/2232, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2601/2600, 2640/2639, 2646/2645, 2737/2736, 2755/2754, 2926/2925, 2945/2944, 2976/2975, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3565/3564, 3627/3625, 3751/3750, 3876/3875, 3888/3887, 3969/3968, 3971/3968, 3971/3969, 4096/4095, 4186/4185, 4200/4199, 4225/4224, 4375/4374, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 4960/4959, 4992/4991, 5083/5082, 5104/5103, 5425/5423, 5491/5488, 5643/5642, 5776/5775, 5797/5796, 5888/5887, 5985/5984, 6076/6075, 6138/6137, 6175/6174, 6293/6292, 6325/6324, 6480/6479, 6670/6669, 6728/6727, 6864/6859, 6877/6875, 7425/7424, 7657/7656, 7905/7904, 7936/7935, 8075/8073, 8092/8091, 8464/8463, 8625/8624, 8671/8670, 8960/8959, 9251/9248, 10557/10556, 10626/10625, 10935/10933, 11340/11339, 12168/12167, 12673/12672, 13225/13224, 13312/13311, 15625/15624, 17577/17576, 19344/19343, 24025/24024, 29792/29791.  </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>: 969/968, 1001/1000, 1015/1014, 1024/1023, 1045/1044, 1054/1053, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1210/1209, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1365/1364, 1426/1425, 1445/1444, 1450/1449, 1496/1495, 1519/1518, 1520/1519, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1768/1767, 1860/1859, 1863/1862, 1955/1953, 2001/2000, 2002/2001, 2016/2015, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184<ins style="font-weight: bold; text-decoration: none;">, 2187/2185</ins>, 2205/2204, 2233/2232, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2601/2600, 2640/2639, 2646/2645, 2737/2736, 2755/2754<ins style="font-weight: bold; text-decoration: none;">, 2784/2783</ins>, 2926/2925, 2945/2944, 2976/2975, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3565/3564, 3627/3625, 3751/3750, 3876/3875, 3888/3887, 3969/3968, 3971/3968, 3971/3969, 4096/4095, 4186/4185, 4200/4199, 4225/4224, 4375/4374, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 4960/4959, 4992/4991, 5083/5082, 5104/5103, 5425/5423, 5491/5488, 5643/5642, 5776/5775, 5797/5796, 5888/5887, 5985/5984, 6076/6075, 6138/6137, 6175/6174, 6293/6292, 6325/6324, 6480/6479, 6670/6669, 6728/6727, 6864/6859, 6877/6875, 7425/7424, 7657/7656, 7905/7904, 7936/7935, 8075/8073, 8092/8091, 8464/8463, 8625/8624, 8671/8670, 8960/8959, 9251/9248, 10557/10556, 10626/10625, 10935/10933, 11340/11339, 12168/12167, 12673/12672, 13225/13224, 13312/13311, 15625/15624, 17577/17576, 19344/19343, 24025/24024, 29792/29791.  </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>It is not necessary to use the full &#039;&#039;q&#039;&#039;-odd-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 243/242, 385/384, 441/440, 540/539, 3388/3375.</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>It is not necessary to use the full &#039;&#039;q&#039;&#039;-odd-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 243/242, 385/384, 441/440, 540/539, 3388/3375.</div></td></tr> </table>

Xenllium https://en.xen.wiki/index.php?title=Essential_tempering_comma&diff=188644&oldid=prev 2025-03-28T22:35:44Z

<p><span class="autocomment">List of essential tempering commas by odd limit</span></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 22:35, 28 March 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l42">Line 42:</td> <td colspan="2" class="diff-lineno">Line 42:</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>; 23-odd-limit (incomplete)</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>; 23-odd-limit (incomplete)</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>: 540/539, 561/560, 576/575, 595/594, 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1862/1859, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2200/2197, 2299/2295, 2300/2299, 2431/2430, 2432/2431, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2912/2907, 2926/2925, 3060/3059, 3136/3135, 3213/3211, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 3978/3971, 4096/4095, 4200/4199, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5985/5984, 6080/6069, 6144/6137, 6864/6859, 9261/9248, 12168/12167.  </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>: 540/539, 561/560, 576/575, 595/594, 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104<ins style="font-weight: bold; text-decoration: none;">, 1127/1125</ins>, 1156/1155, 1197/1196, 1216/1215, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728<ins style="font-weight: bold; text-decoration: none;">, 1771/1768</ins>, 1862/1859, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079<ins style="font-weight: bold; text-decoration: none;">, 2093/2090</ins>, 2185/2184, 2200/2197, 2299/2295, 2300/2299, 2431/2430, 2432/2431, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2912/2907, 2926/2925, 3060/3059, 3136/3135, 3213/3211, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 3978/3971, 4096/4095, 4200/4199, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5985/5984, 6080/6069, 6144/6137, 6864/6859, 9261/9248, 12168/12167.  </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>; 25-odd-limit (incomplete)</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>; 25-odd-limit (incomplete)</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>: 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 8625/8624, 9261/9248, 10626/10625, 12168/12167.  </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>: 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1311/1309, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079<ins style="font-weight: bold; text-decoration: none;">, 2093/2090</ins>, 2185/2184, 2200/2197, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 8625/8624, 9261/9248, 10626/10625, 12168/12167.  </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>; 27-odd-limit (incomplete)</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>; 27-odd-limit (incomplete)</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l51">Line 51:</td> <td colspan="2" class="diff-lineno">Line 51:</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>; 29-odd-limit (incomplete)</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>; 29-odd-limit (incomplete)</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>: 875/874, 897/896, 936/935, 969/968, 1001/1000, 1015/1014, 1045/1044, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1445/1444, 1450/1449, 1496/1495, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1863/1862, 2001/2000, 2002/2001, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2205/2204, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2601/2600, 2640/2639, 2646/2645, 2720/2717, 2737/2736, 2755/2754, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3553/3549, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 5083/5082, 5104/5103, 5491/5488, 5776/5775, 5888/5887, 5985/5984, 6144/6137, 6175/6174, 6670/6669, 6864/6859, 6877/6875, 7425/7424, 8075/8073, 8625/8624, 8671/8670, 10557/10556, 10626/10625, 10935/10933, 11340/11339, 12168/12167, 12673/12672, 13225/13224, 13312/13311.  </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>: 875/874, 897/896, 936/935, 969/968, 1001/1000, 1015/1014, 1045/1044, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1445/1444, 1450/1449, 1496/1495, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1863/1862, 2001/2000, 2002/2001, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2205/2204, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2601/2600, 2640/2639, 2646/2645, 2720/2717, 2737/2736, 2755/2754, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3553/3549, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 5083/5082, 5104/5103, 5491/5488, 5776/5775, 5888/5887, 5985/5984, 6144/6137, 6175/6174, 6670/6669, 6864/6859, 6877/6875, 7425/7424, 8075/8073, 8625/8624, 8671/8670<ins style="font-weight: bold; text-decoration: none;">, 9251/9248</ins>, 10557/10556, 10626/10625, 10935/10933, 11340/11339, 12168/12167, 12673/12672, 13225/13224, 13312/13311.  </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>; 31-odd-limit (incomplete)</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>; 31-odd-limit (incomplete)</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>: 969/968, 1001/1000, 1015/1014, 1024/1023, 1045/1044, 1054/1053, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1210/1209, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1365/1364, 1426/1425, 1445/1444, 1450/1449, 1496/1495, 1519/1518, 1520/1519, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1768/1767, 1860/1859, 1863/1862, 2001/2000, 2002/2001, 2016/2015, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2205/2204, 2233/2232, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2601/2600, 2640/2639, 2646/2645, 2737/2736, 2755/2754, 2926/2925, 2945/2944, 2976/2975, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3565/3564, 3627/3625, 3751/3750, 3876/3875, 3888/3887, 3969/3968, 3971/3968, 3971/3969, 4096/4095, 4186/4185, 4200/4199, 4225/4224, 4375/4374, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 4960/4959, 4992/4991, 5083/5082, 5104/5103, 5425/5423, 5491/5488, 5643/5642, 5776/5775, 5797/5796, 5888/5887, 5985/5984, 6076/6075, 6138/6137, 6175/6174, 6293/6292, 6325/6324, 6480/6479, 6670/6669, 6728/6727, 6864/6859, 6877/6875, 7425/7424, 7657/7656, 7905/7904, 7936/7935, 8075/8073, 8092/8091, 8464/8463, 8625/8624, 8671/8670, 8960/8959, 10557/10556, 10626/10625, 10935/10933, 11340/11339, 12168/12167, 12673/12672, 13225/13224, 13312/13311, 15625/15624, 17577/17576, 19344/19343, 24025/24024, 29792/29791.  </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>: 969/968, 1001/1000, 1015/1014, 1024/1023, 1045/1044, 1054/1053, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1210/1209, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1365/1364, 1426/1425, 1445/1444, 1450/1449, 1496/1495, 1519/1518, 1520/1519, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1768/1767, 1860/1859, 1863/1862<ins style="font-weight: bold; text-decoration: none;">, 1955/1953</ins>, 2001/2000, 2002/2001, 2016/2015, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2205/2204, 2233/2232, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2465/2464, 2500/2499, 2601/2600, 2640/2639, 2646/2645, 2737/2736, 2755/2754, 2926/2925, 2945/2944, 2976/2975, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3565/3564, 3627/3625, 3751/3750, 3876/3875, 3888/3887, 3969/3968, 3971/3968, 3971/3969, 4096/4095, 4186/4185, 4200/4199, 4225/4224, 4375/4374, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 4960/4959, 4992/4991, 5083/5082, 5104/5103, 5425/5423, 5491/5488, 5643/5642, 5776/5775, 5797/5796, 5888/5887, 5985/5984, 6076/6075, 6138/6137, 6175/6174, 6293/6292, 6325/6324, 6480/6479, 6670/6669, 6728/6727, 6864/6859, 6877/6875, 7425/7424, 7657/7656, 7905/7904, 7936/7935, 8075/8073, 8092/8091, 8464/8463, 8625/8624, 8671/8670, 8960/8959<ins style="font-weight: bold; text-decoration: none;">, 9251/9248</ins>, 10557/10556, 10626/10625, 10935/10933, 11340/11339, 12168/12167, 12673/12672, 13225/13224, 13312/13311, 15625/15624, 17577/17576, 19344/19343, 24025/24024, 29792/29791.  </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>It is not necessary to use the full &#039;&#039;q&#039;&#039;-odd-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 243/242, 385/384, 441/440, 540/539, 3388/3375.</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>It is not necessary to use the full &#039;&#039;q&#039;&#039;-odd-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 243/242, 385/384, 441/440, 540/539, 3388/3375.</div></td></tr> </table>

Xenllium https://en.xen.wiki/index.php?title=Essential_tempering_comma&diff=188626&oldid=prev 2025-03-28T14:06:02Z

<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 14:06, 28 March 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l54">Line 54:</td> <td colspan="2" class="diff-lineno">Line 54:</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>; 31-odd-limit (incomplete)</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>; 31-odd-limit (incomplete)</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>: 969/968, 1001/1000, 1015/1014, 1024/1023, 1045/1044, 1054/1053, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1210/1209, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1365/1364, 1426/1425, 1445/1444, 1450/1449, 1496/1495, 1519/1518, 1520/1519, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1768/1767, 1860/1859, 1863/1862, 2001/2000, 2002/2001, 2016/2015, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2205/2204, 2233/2232, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2640/2639, 2646/2645, 2737/2736, 2755/2754, 2926/2925, 2945/2944, 2976/2975, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3565/3564, 3751/3750, 3876/3875, 3888/3887, 3969/3968, 3971/3968, 3971/3969, 4096/4095, 4186/4185, 4200/4199, 4225/4224, 4375/4374, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 4960/4959, 4992/4991, 5083/5082, 5104/5103, 5491/5488, 5643/5642, 5776/5775, 5797/5796, 5888/5887, 5985/5984, 6076/6075, 6138/6137, 6175/6174, 6293/6292, 6325/6324, 6480/6479, 6670/6669, 6728/6727, 6864/6859, 6877/6875, 7425/7424, 7657/7656, 7905/7904, 7936/7935, 8075/8073, 8092/8091, 8464/8463, 8625/8624, 8671/8670, 10557/10556, 10626/10625, 10935/10933, 11340/11339, 12168/12167, 12673/12672, 13225/13224, 13312/13311, 15625/15624, 17577/17576, 19344/19343, 24025/24024, 29792/29791.  </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>: 969/968, 1001/1000, 1015/1014, 1024/1023, 1045/1044, 1054/1053, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1210/1209, 1216/1215, 1225/1224, 1275/1274, 1276/1275, 1288/1287, 1331/1330, 1365/1364, 1426/1425, 1445/1444, 1450/1449, 1496/1495, 1519/1518, 1520/1519, 1521/1520, 1540/1539, 1596/1595, 1625/1624, 1683/1682, 1701/1700, 1729/1728, 1768/1767, 1860/1859, 1863/1862, 2001/2000, 2002/2001, 2016/2015, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2176/2175, 2185/2184, 2205/2204, 2233/2232, 2262/2261, 2277/2275, 2300/2299, 2376/2375, 2431/2430, 2432/2431<ins style="font-weight: bold; text-decoration: none;">, 2465/2464</ins>, 2500/2499, 2601/2600, 2640/2639, 2646/2645, 2737/2736, 2755/2754, 2926/2925, 2945/2944, 2976/2975, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3249/3248, 3250/3249, 3381/3380, 3451/3450, 3510/3509, 3520/3519, 3565/3564<ins style="font-weight: bold; text-decoration: none;">, 3627/3625</ins>, 3751/3750, 3876/3875, 3888/3887, 3969/3968, 3971/3968, 3971/3969, 4096/4095, 4186/4185, 4200/4199, 4225/4224, 4375/4374, 4641/4640, 4693/4692, 4761/4760, 4785/4784, 4901/4900, 4914/4913, 4960/4959, 4992/4991, 5083/5082, 5104/5103<ins style="font-weight: bold; text-decoration: none;">, 5425/5423</ins>, 5491/5488, 5643/5642, 5776/5775, 5797/5796, 5888/5887, 5985/5984, 6076/6075, 6138/6137, 6175/6174, 6293/6292, 6325/6324, 6480/6479, 6670/6669, 6728/6727, 6864/6859, 6877/6875, 7425/7424, 7657/7656, 7905/7904, 7936/7935, 8075/8073, 8092/8091, 8464/8463, 8625/8624, 8671/8670<ins style="font-weight: bold; text-decoration: none;">, 8960/8959</ins>, 10557/10556, 10626/10625, 10935/10933, 11340/11339, 12168/12167, 12673/12672, 13225/13224, 13312/13311, 15625/15624, 17577/17576, 19344/19343, 24025/24024, 29792/29791.  </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>It is not necessary to use the full &#039;&#039;q&#039;&#039;-odd-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 243/242, 385/384, 441/440, 540/539, 3388/3375.</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>It is not necessary to use the full &#039;&#039;q&#039;&#039;-odd-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 243/242, 385/384, 441/440, 540/539, 3388/3375.</div></td></tr> </table>

Xenllium