https://en.xen.wiki/index.php?action=history&feed=atom&title=Expanding_tonal_space%2Fthird_dimension 2026-06-26T18:24:08Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=Expanding_tonal_space/third_dimension&diff=193566&oldid=prev 2025-04-22T14:07:08Z

<p><span class="autocomment">Coda: </span> link to &quot;Adaptive just intonation (adaptive JI)&quot; added</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 14:07, 22 April 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l141">Line 141:</td> <td colspan="2" class="diff-lineno">Line 141:</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>The 3D interval system of the model forms a static framework that provides &#039;&#039;”all the notes&#039;&#039; [pitches] &#039;&#039;or intervals theoretically available to a composer”.&#039;&#039;&lt;ref&gt;Quotation from the [[Tuning system]] page&lt;/ref&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The 3D interval system of the model forms a static framework that provides &#039;&#039;”all the notes&#039;&#039; [pitches] &#039;&#039;or intervals theoretically available to a composer”.&#039;&#039;&lt;ref&gt;Quotation from the [[Tuning system]] page&lt;/ref&gt;</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>No floating tonic ["floating tonal center"] appears for adaptive just intonation, possible target tonics are well defined and already part of the model.</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>No floating tonic [<ins style="font-weight: bold; text-decoration: none;">[Adaptive just intonation|''(</ins>"floating tonal center"<ins style="font-weight: bold; text-decoration: none;">)'']</ins>] appears for adaptive just intonation, possible target tonics are well defined and already part of the model.</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>When the total number of available pitches is added up, the model of tonal space can become quite large. The exact number of possible intervals depends on the highest implemented mode &lt;math&gt;n&lt;/math&gt; of the overtone scale and the applied [[Just intonation#Constrained just|constraints]] necessary for the practical application in an instrument.</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>When the total number of available pitches is added up, the model of tonal space can become quite large. The exact number of possible intervals depends on the highest implemented mode &lt;math&gt;n&lt;/math&gt; of the overtone scale and the applied [[Just intonation#Constrained just|constraints]] necessary for the practical application in an instrument.</div></td></tr> </table>

Holger Stoltenberg https://en.xen.wiki/index.php?title=Expanding_tonal_space/third_dimension&diff=190037&oldid=prev 2025-04-06T12:44:26Z

<p>added categories</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 12:44, 6 April 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l164">Line 164:</td> <td colspan="2" class="diff-lineno">Line 164:</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>== References ==</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>== References ==</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>&lt;references/&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;references/&gt;</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Pitch space]]</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Just intonation]]</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Scale]]</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Harmonic series]]</ins></div></td></tr> </table>

Holger Stoltenberg https://en.xen.wiki/index.php?title=Expanding_tonal_space/third_dimension&diff=190036&oldid=prev 2025-04-06T12:40:20Z

<p>content transferred from User:Holger Stoltenberg/... to main namespace</p> <a href="https://en.xen.wiki/index.php?title=Expanding_tonal_space/third_dimension&amp;diff=190036&amp;oldid=190035">Show changes</a>

Holger Stoltenberg https://en.xen.wiki/index.php?title=Expanding_tonal_space/third_dimension&diff=190035&oldid=prev 2025-04-06T12:34:19Z

<p>Page creation in main namespace for .../third dimension</p> <p><b>New page</b></p><div>{{breadcrumb}}<br /> This is &#039;&#039;&#039;Part IV&#039;&#039;&#039; of a small series of articles discussing the &#039;&#039;model of tonal space&#039;&#039;.&lt;br&gt;<br /> On this subpage, we will discuss the extension of the model ([[Expanding tonal space|see Part I]]) to three dimensions. <br /> <br /> __TOC__</div>

Holger Stoltenberg