Gradus suavitatis - Revision history

https://en.xen.wiki/index.php?action=history&feed=atom&title=Gradus_suavitatis Gradus suavitatis - Revision history 2026-06-15T02:35:24Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=Gradus_suavitatis&diff=200032&oldid=prev Sintel: translation 2025-06-19T16:55:04Z

<p>translation</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 16:55, 19 June 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" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The '''gradus suavitatis''', also known as '''Euler complexity''' is probably the first complexity measure historically.<ref>Leonhard Euler (1739) ''Tentamen novae theoriae musicae'' (Attempt at a New Theory of Music), St. Petersburg.</ref></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The '''gradus suavitatis''' <ins style="font-weight: bold; text-decoration: none;">(Latin for ''degree of sweetness'')</ins>, also known as '''Euler complexity''' is probably the first complexity measure historically.<ref>Leonhard Euler (1739) ''Tentamen novae theoriae musicae'' (Attempt at a New Theory of Music), St. Petersburg.</ref></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>It is somewhat similar to the [[Wilson norm]], in that it depends on the prime factorization.</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 somewhat similar to the [[Wilson norm]], in that it depends on the prime factorization.</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>

Sintel https://en.xen.wiki/index.php?title=Gradus_suavitatis&diff=200029&oldid=prev Sintel at 16:46, 19 June 2025 2025-06-19T16:46:19Z

<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 16:46, 19 June 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" 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;">Euler's </del>'''gradus suavitatis''',<ref>Leonhard Euler (1739) ''Tentamen novae theoriae musicae'' (Attempt at a New Theory of Music), St. Petersburg.</ref> <del style="font-weight: bold; text-decoration: none;">which is probably the first complexity measure historically.</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;">The </ins>'''gradus suavitatis''', <ins style="font-weight: bold; text-decoration: none;">also known as '''Euler complexity''' is probably the first complexity measure historically.</ins><ref>Leonhard Euler (1739) ''Tentamen novae theoriae musicae'' (Attempt at a New Theory of Music), St. Petersburg.</ref></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>It is somewhat similar to the [[Wilson norm]], in that it depends on the prime factorization.</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 somewhat similar to the [[Wilson norm]], in that it depends on the prime factorization.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l7">Line 7:</td> <td colspan="2" class="diff-lineno">Line 7:</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>{{stub}}</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>{{stub}}</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Interval complexity measures]]</ins></div></td></tr> </table>

Sintel https://en.xen.wiki/index.php?title=Gradus_suavitatis&diff=200027&oldid=prev Sintel: bold lemma 2025-06-19T16:44:23Z

<p>bold lemma</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 16:44, 19 June 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" 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>Euler's ''gradus suavitatis'',<ref>Leonhard Euler (1739) ''Tentamen novae theoriae musicae'' (Attempt at a New Theory of Music), St. Petersburg.</ref> which is probably the first complexity measure historically.</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>Euler's <ins style="font-weight: bold; text-decoration: none;">'</ins>''gradus suavitatis<ins style="font-weight: bold; text-decoration: none;">'</ins>'',<ref>Leonhard Euler (1739) ''Tentamen novae theoriae musicae'' (Attempt at a New Theory of Music), St. Petersburg.</ref> which is probably the first complexity measure historically.</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>It is somewhat similar to the [[Wilson norm]], in that it depends on the prime factorization.</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 somewhat similar to the [[Wilson norm]], in that it depends on the prime factorization.</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>

Sintel https://en.xen.wiki/index.php?title=Gradus_suavitatis&diff=200026&oldid=prev Sintel: Created page with "Euler's ''gradus suavitatis'',<ref>Leonhard Euler (1739) ''Tentamen novae theoriae musicae'' (Attempt at a New Theory of Music), St. Petersburg.</ref> which is probably the first complexity measure historically. It is somewhat similar to the Wilson norm, in that it depends on the prime factorization. == Definition == Given ''s'', the sum of prime factors, and ''n'' the number of prime factors, Euler's gradus function is {{nowrap|''s'' - ''n'' + 1}}. For example <mat..." 2025-06-19T16:43:54Z

<p>Created page with "Euler's ''gradus suavitatis'',<ref>Leonhard Euler (1739) ''Tentamen novae theoriae musicae'' (Attempt at a New Theory of Music), St. Petersburg.</ref> which is probably the first complexity measure historically. It is somewhat similar to the <a href="/w/Wilson_norm" title="Wilson norm">Wilson norm</a>, in that it depends on the prime factorization. == Definition == Given ''s'', the sum of prime factors, and ''n'' the number of prime factors, Euler's gradus function is {{nowrap|''s'' - ''n'' + 1}}. For example <mat..."</p> <p><b>New page</b></p><div>Euler's ''gradus suavitatis'',<ref>Leonhard Euler (1739) ''Tentamen novae theoriae musicae'' (Attempt at a New Theory of Music), St. Petersburg.</ref> which is probably the first complexity measure historically.<br /> It is somewhat similar to the [[Wilson norm]], in that it depends on the prime factorization.<br /> <br /> == Definition ==<br /> Given ''s'', the sum of prime factors, and ''n'' the number of prime factors, Euler's gradus function is {{nowrap|''s'' - ''n'' + 1}}.<br /> For example <math>\text{Gradus}\left(\tfrac{15}{8}\right) = 14 - 5 + 1 = 10</math>.<br /> <br /> {{stub}}</div>

Sintel