https://en.xen.wiki/index.php?action=history&feed=atom&title=Talk%3A7%2F4Talk:7/4 - Revision history2026-07-03T06:27:54ZRevision history for this page on the wikiMediaWiki 1.43.6https://en.xen.wiki/index.php?title=Talk:7/4&diff=51960&oldid=prevAura at 02:46, 26 October 20202020-10-26T02:46:59Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 02:46, 26 October 2020</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::::: I have the impression that we still have little experience in generalizing the multiplication of intervals, so the combinability of fifths is certainly undisputed, but on the other hand it is strongly oriented towards functional harmony since the Baroque. I don't know any other interval that could perform such an axis function, although I can imagine that one could try it with the third. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:45, 25 October 2020 (UTC)</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>::::: I have the impression that we still have little experience in generalizing the multiplication of intervals, so the combinability of fifths is certainly undisputed, but on the other hand it is strongly oriented towards functional harmony since the Baroque. I don't know any other interval that could perform such an axis function, although I can imagine that one could try it with the third. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:45, 25 October 2020 (UTC)</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>:::::: Remember what I said about the 11-limit being mathematically derivable as an excellent representation for quartertones in terms of ratio simplicity? One of the implications of this excellent representation- particualarly in light of the way it plays out- is that the paramajor fourth (that is, 11/8) can- and indeed it does- perform an axis function where quartertones are concerned. I've since checked the 11-limit's representation of quartertones against that of the intervals called "quarter tones" [https://en.wikipedia.org/wiki/List_of_pitch_intervals on Wikipedia's list of pitch intervals] and found the 11-limit's 33/32 to be better than any of them in terms of ratio simplicity. (multiple comments combined and edited by --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:02, 25 October 2020 (UTC))</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>:::::: Remember what I said about the 11-limit being mathematically derivable as an excellent representation for quartertones in terms of ratio simplicity? One of the implications of this excellent representation- particualarly in light of the way it plays out- is that the paramajor fourth (that is, 11/8) can- and indeed it does- perform an axis function where quartertones are concerned. I've since checked the 11-limit's representation of quartertones against that of the <ins style="font-weight: bold; text-decoration: none;">other rational </ins>intervals called "quarter tones" [https://en.wikipedia.org/wiki/List_of_pitch_intervals on Wikipedia's list of pitch intervals] and found the 11-limit's 33/32 to be better than any of them in terms of ratio simplicity. (multiple comments combined and edited by --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:02, 25 October 2020 (UTC))</div></td></tr>
</table>Aurahttps://en.xen.wiki/index.php?title=Talk:7/4&diff=51958&oldid=prevAura at 23:05, 25 October 20202020-10-25T23:05:22Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::::: I have the impression that we still have little experience in generalizing the multiplication of intervals, so the combinability of fifths is certainly undisputed, but on the other hand it is strongly oriented towards functional harmony since the Baroque. I don't know any other interval that could perform such an axis function, although I can imagine that one could try it with the third. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:45, 25 October 2020 (UTC)</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>::::: I have the impression that we still have little experience in generalizing the multiplication of intervals, so the combinability of fifths is certainly undisputed, but on the other hand it is strongly oriented towards functional harmony since the Baroque. I don't know any other interval that could perform such an axis function, although I can imagine that one could try it with the third. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:45, 25 October 2020 (UTC)</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>:::::: Remember what I said about the 11-limit being mathematically derivable as an excellent representation for quartertones in terms of ratio simplicity? One of the implications of this excellent representation is that the paramajor fourth (that is, 11/8) can- and indeed it does- perform an axis function where quartertones are concerned. I've since checked the 11-limit's representation of quartertones against that of the intervals called "quarter tones" [https://en.wikipedia.org/wiki/List_of_pitch_intervals on Wikipedia's list of pitch intervals] and found the 11-limit's 33/32 to be better than any of them in terms of ratio simplicity. (multiple comments combined and edited by --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:02, 25 October 2020 (UTC))</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>:::::: Remember what I said about the 11-limit being mathematically derivable as an excellent representation for quartertones in terms of ratio simplicity? One of the implications of this excellent representation<ins style="font-weight: bold; text-decoration: none;">- particualarly in light of the way it plays out- </ins>is that the paramajor fourth (that is, 11/8) can- and indeed it does- perform an axis function where quartertones are concerned. I've since checked the 11-limit's representation of quartertones against that of the intervals called "quarter tones" [https://en.wikipedia.org/wiki/List_of_pitch_intervals on Wikipedia's list of pitch intervals] and found the 11-limit's 33/32 to be better than any of them in terms of ratio simplicity. (multiple comments combined and edited by --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:02, 25 October 2020 (UTC))</div></td></tr>
</table>Aurahttps://en.xen.wiki/index.php?title=Talk:7/4&diff=51957&oldid=prevAura at 23:02, 25 October 20202020-10-25T23:02:05Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:02, 25 October 2020</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::::: I have the impression that we still have little experience in generalizing the multiplication of intervals, so the combinability of fifths is certainly undisputed, but on the other hand it is strongly oriented towards functional harmony since the Baroque. I don't know any other interval that could perform such an axis function, although I can imagine that one could try it with the third. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:45, 25 October 2020 (UTC)</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>::::: I have the impression that we still have little experience in generalizing the multiplication of intervals, so the combinability of fifths is certainly undisputed, but on the other hand it is strongly oriented towards functional harmony since the Baroque. I don't know any other interval that could perform such an axis function, although I can imagine that one could try it with the third. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:45, 25 October 2020 (UTC)</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>:::::: Remember what I said about the 11-limit being mathematically derivable as an excellent representation for quartertones in terms of ratio simplicity? <del style="font-weight: bold; text-decoration: none;">This means </del>that the paramajor fourth (that is, 11/8) <del style="font-weight: bold; text-decoration: none;">is also pretty good on this front, </del>and indeed it does perform an axis function where quartertones are concerned. <del style="font-weight: bold; text-decoration: none;">--[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:52, 25 October 2020 (UTC)</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>:::::: Remember what I said about the 11-limit being mathematically derivable as an excellent representation for quartertones in terms of ratio simplicity? <ins style="font-weight: bold; text-decoration: none;">One of the implications of this excellent representation is </ins>that the paramajor fourth (that is, 11/8) <ins style="font-weight: bold; text-decoration: none;">can- </ins>and indeed it does<ins style="font-weight: bold; text-decoration: none;">- </ins>perform an axis function where quartertones are concerned. <ins style="font-weight: bold; text-decoration: none;"> </ins>I've since checked the 11-limit's representation of quartertones against that of the intervals called "quarter tones" [https://en.wikipedia.org/wiki/List_of_pitch_intervals on Wikipedia's list of pitch intervals] and found the 11-limit's 33/32 to be better than any of them in terms of ratio simplicity. <ins style="font-weight: bold; text-decoration: none;">(multiple comments combined and edited by </ins>--[[User:Aura|Aura]] ([[User talk:Aura|talk]]) <ins style="font-weight: bold; text-decoration: none;">23</ins>:<ins style="font-weight: bold; text-decoration: none;">02</ins>, 25 October 2020 (UTC<ins style="font-weight: bold; text-decoration: none;">)</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> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">:::::: </del>I've since checked the 11-limit's representation of quartertones against that of the intervals called "quarter tones" [https://en.wikipedia.org/wiki/List_of_pitch_intervals on Wikipedia's list of pitch intervals] and found the 11-limit's 33/32 to be better than any of them in terms of ratio simplicity. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) <del style="font-weight: bold; text-decoration: none;">22</del>:<del style="font-weight: bold; text-decoration: none;">55</del>, 25 October 2020 (UTC)</div></td><td colspan="2" class="diff-side-added"></td></tr>
</table>Aurahttps://en.xen.wiki/index.php?title=Talk:7/4&diff=51956&oldid=prevAura at 22:56, 25 October 20202020-10-25T22:56:55Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:::::: Remember what I said about the 11-limit being mathematically derivable as an excellent representation for quartertones in terms of ratio simplicity? This means that the paramajor fourth (that is, 11/8) is also pretty good on this front, and indeed it does perform an axis function where quartertones are concerned. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:52, 25 October 2020 (UTC)</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>:::::: Remember what I said about the 11-limit being mathematically derivable as an excellent representation for quartertones in terms of ratio simplicity? This means that the paramajor fourth (that is, 11/8) is also pretty good on this front, and indeed it does perform an axis function where quartertones are concerned. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:52, 25 October 2020 (UTC)</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>:::::: I've since checked the 11-limit's representation of <del style="font-weight: bold; text-decoration: none;">quarter tones </del>against that <del style="font-weight: bold; text-decoration: none;">for </del>of the intervals called quarter tones [https://en.wikipedia.org/wiki/List_of_pitch_intervals on Wikipedia's list of pitch intervals] and found the 11-limit's 33/32 to be better than any of them in terms of ratio simplicity. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:55, 25 October 2020 (UTC)</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>:::::: I've since checked the 11-limit's representation of <ins style="font-weight: bold; text-decoration: none;">quartertones </ins>against that of the intervals called <ins style="font-weight: bold; text-decoration: none;">"</ins>quarter tones<ins style="font-weight: bold; text-decoration: none;">" </ins>[https://en.wikipedia.org/wiki/List_of_pitch_intervals on Wikipedia's list of pitch intervals] and found the 11-limit's 33/32 to be better than any of them in terms of ratio simplicity. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:55, 25 October 2020 (UTC)</div></td></tr>
</table>Aurahttps://en.xen.wiki/index.php?title=Talk:7/4&diff=51955&oldid=prevAura at 22:55, 25 October 20202020-10-25T22:55:09Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:::::: Remember what I said about the 11-limit being mathematically derivable as an excellent representation for quartertones in terms of ratio simplicity? This means that the paramajor fourth (that is, 11/8) is also pretty good on this front, and indeed it does perform an axis function where quartertones are concerned. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:52, 25 October 2020 (UTC)</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>:::::: Remember what I said about the 11-limit being mathematically derivable as an excellent representation for quartertones in terms of ratio simplicity? This means that the paramajor fourth (that is, 11/8) is also pretty good on this front, and indeed it does perform an axis function where quartertones are concerned. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:52, 25 October 2020 (UTC)</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;">:::::: I've since checked the 11-limit's representation of quarter tones against that for of the intervals called quarter tones [https://en.wikipedia.org/wiki/List_of_pitch_intervals on Wikipedia's list of pitch intervals] and found the 11-limit's 33/32 to be better than any of them in terms of ratio simplicity. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:55, 25 October 2020 (UTC)</ins></div></td></tr>
</table>Aurahttps://en.xen.wiki/index.php?title=Talk:7/4&diff=51954&oldid=prevAura at 22:52, 25 October 20202020-10-25T22:52:05Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::::: I have the impression that we still have little experience in generalizing the multiplication of intervals, so the combinability of fifths is certainly undisputed, but on the other hand it is strongly oriented towards functional harmony since the Baroque. I don't know any other interval that could perform such an axis function, although I can imagine that one could try it with the third. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:45, 25 October 2020 (UTC)</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>::::: I have the impression that we still have little experience in generalizing the multiplication of intervals, so the combinability of fifths is certainly undisputed, but on the other hand it is strongly oriented towards functional harmony since the Baroque. I don't know any other interval that could perform such an axis function, although I can imagine that one could try it with the third. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:45, 25 October 2020 (UTC)</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;">:::::: Remember what I said about the 11-limit being mathematically derivable as an excellent representation for quartertones in terms of ratio simplicity? This means that the paramajor fourth (that is, 11/8) is also pretty good on this front, and indeed it does perform an axis function where quartertones are concerned. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:52, 25 October 2020 (UTC)</ins></div></td></tr>
</table>Aurahttps://en.xen.wiki/index.php?title=Talk:7/4&diff=51953&oldid=prevAura at 22:48, 25 October 20202020-10-25T22:48:45Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:48, 25 October 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l13">Line 13:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::: I read ''half a step'' as 50% of 1\edo? Concerning the prime harmonics (their octave complements share the exact same table), is it actually that indisputable? I know the concept of [[consistency]] but I find it questionable already in cases like [[7/5]]: this interval can probably be used independently of the fact that it can be derived from [[7/4]] and [[5/4]]; another example is the great approximation of [[11/7]] in [[23edo]]. Whatever, would you say that tables would useful to you if there was this column with the amount of repetitions within the limit you described? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:53, 25 October 2020 (UTC)</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>::: I read ''half a step'' as 50% of 1\edo? Concerning the prime harmonics (their octave complements share the exact same table), is it actually that indisputable? I know the concept of [[consistency]] but I find it questionable already in cases like [[7/5]]: this interval can probably be used independently of the fact that it can be derived from [[7/4]] and [[5/4]]; another example is the great approximation of [[11/7]] in [[23edo]]. Whatever, would you say that tables would useful to you if there was this column with the amount of repetitions within the limit you described? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:53, 25 October 2020 (UTC)</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>:::: You are correct in your reading of half a step as 1\edo. While it is true that 7/5 can be used independently of the fact that it can be derived from 7/4 and 5/4, consistency is my main concern with these intervals. In my own work, it seems that wherever the p-limits from which intervals like 7/5 are derived are poorly represented and or subject to contortion in any given EDO, the consistency of the derived intervals is called the into question and or multiple possible representations in a given EDO occur. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:14, 25 October 2020 (UTC)</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>:::: You are correct in your reading of half a step as <ins style="font-weight: bold; text-decoration: none;">50% of </ins>1\edo. While it is true that 7/5 can be used independently of the fact that it can be derived from 7/4 and 5/4, consistency is my main concern with these intervals. In my own work, it seems that wherever the p-limits from which intervals like 7/5 are derived are poorly represented and or subject to contortion in any given EDO, the consistency of the derived intervals is called the into question and or multiple possible representations in a given EDO occur. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:14, 25 October 2020 (UTC)</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>:::: My end goal with including a table containing the number of times the tempered p-limit interval in question can be stacked without the absolute error between the tempered stack and its just counterpart exceeding 3.5 cents (or half a step- whichever is smaller), has more to do with mapping out the usable portions of the harmonic lattice for any given EDO. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:19, 25 October 2020 (UTC)</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>:::: My end goal with including a table containing the number of times the tempered p-limit interval in question can be stacked without the absolute error between the tempered stack and its just counterpart exceeding 3.5 cents (or half a step- whichever is smaller), has more to do with mapping out the usable portions of the harmonic lattice for any given EDO. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:19, 25 October 2020 (UTC)</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>::::: I have the impression that we still have little experience in generalizing the multiplication of intervals, so the combinability of fifths is certainly undisputed, but on the other hand it is strongly oriented towards functional harmony since the Baroque. I don't know any other interval that could perform such an axis function, although I can imagine that one could try it with the third. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:45, 25 October 2020 (UTC)</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>::::: I have the impression that we still have little experience in generalizing the multiplication of intervals, so the combinability of fifths is certainly undisputed, but on the other hand it is strongly oriented towards functional harmony since the Baroque. I don't know any other interval that could perform such an axis function, although I can imagine that one could try it with the third. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:45, 25 October 2020 (UTC)</div></td></tr>
</table>Aurahttps://en.xen.wiki/index.php?title=Talk:7/4&diff=51952&oldid=prevXenwolf: /* 7/4 in 94edo */ re2020-10-25T22:45:56Z<p><span class="autocomment">7/4 in 94edo: </span> re</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:45, 25 October 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l16">Line 16:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><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>:::: My end goal with including a table containing the number of times the tempered p-limit interval in question can be stacked without the absolute error between the tempered stack and its just counterpart exceeding 3.5 cents (or half a step- whichever is smaller), has more to do with mapping out the usable portions of the harmonic lattice for any given EDO. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:19, 25 October 2020 (UTC)</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>:::: My end goal with including a table containing the number of times the tempered p-limit interval in question can be stacked without the absolute error between the tempered stack and its just counterpart exceeding 3.5 cents (or half a step- whichever is smaller), has more to do with mapping out the usable portions of the harmonic lattice for any given EDO. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:19, 25 October 2020 (UTC)</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;">::::: I have the impression that we still have little experience in generalizing the multiplication of intervals, so the combinability of fifths is certainly undisputed, but on the other hand it is strongly oriented towards functional harmony since the Baroque. I don't know any other interval that could perform such an axis function, although I can imagine that one could try it with the third. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:45, 25 October 2020 (UTC)</ins></div></td></tr>
</table>Xenwolfhttps://en.xen.wiki/index.php?title=Talk:7/4&diff=51951&oldid=prevAura at 22:45, 25 October 20202020-10-25T22:45:42Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:45, 25 October 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l13">Line 13:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::: I read ''half a step'' as 50% of 1\edo? Concerning the prime harmonics (their octave complements share the exact same table), is it actually that indisputable? I know the concept of [[consistency]] but I find it questionable already in cases like [[7/5]]: this interval can probably be used independently of the fact that it can be derived from [[7/4]] and [[5/4]]; another example is the great approximation of [[11/7]] in [[23edo]]. Whatever, would you say that tables would useful to you if there was this column with the amount of repetitions within the limit you described? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:53, 25 October 2020 (UTC)</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>::: I read ''half a step'' as 50% of 1\edo? Concerning the prime harmonics (their octave complements share the exact same table), is it actually that indisputable? I know the concept of [[consistency]] but I find it questionable already in cases like [[7/5]]: this interval can probably be used independently of the fact that it can be derived from [[7/4]] and [[5/4]]; another example is the great approximation of [[11/7]] in [[23edo]]. Whatever, would you say that tables would useful to you if there was this column with the amount of repetitions within the limit you described? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:53, 25 October 2020 (UTC)</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>:::: You are correct in your reading of half a step as 1\edo. While it is true that 7/5 can be used independently of the fact that it can be derived from 7/4 and 5/4, consistency is my main concern with these intervals. In my own work, it seems that wherever the p-limits from which intervals like 7/5 are derived are poorly represented and or subject to contortion in any given EDO, the consistency of the derived intervals is called the into question and or <del style="font-weight: bold; text-decoration: none;">open up </del>multiple possible representations in a given EDO. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:14, 25 October 2020 (UTC)</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>:::: You are correct in your reading of half a step as 1\edo. While it is true that 7/5 can be used independently of the fact that it can be derived from 7/4 and 5/4, consistency is my main concern with these intervals. In my own work, it seems that wherever the p-limits from which intervals like 7/5 are derived are poorly represented and or subject to contortion in any given EDO, the consistency of the derived intervals is called the into question and or multiple possible representations in a given EDO <ins style="font-weight: bold; text-decoration: none;">occur</ins>. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:14, 25 October 2020 (UTC)</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>:::: My end goal with including a table containing the number of times the tempered p-limit interval in question can be stacked without the absolute error between the tempered stack and its just counterpart exceeding 3.5 cents (or half a step- whichever is smaller), has more to do with mapping out the usable portions of the harmonic lattice for any given EDO. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:19, 25 October 2020 (UTC)</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>:::: My end goal with including a table containing the number of times the tempered p-limit interval in question can be stacked without the absolute error between the tempered stack and its just counterpart exceeding 3.5 cents (or half a step- whichever is smaller), has more to do with mapping out the usable portions of the harmonic lattice for any given EDO. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:19, 25 October 2020 (UTC)</div></td></tr>
</table>Aurahttps://en.xen.wiki/index.php?title=Talk:7/4&diff=51950&oldid=prevAura at 22:43, 25 October 20202020-10-25T22:43:49Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:43, 25 October 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l13">Line 13:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::: I read ''half a step'' as 50% of 1\edo? Concerning the prime harmonics (their octave complements share the exact same table), is it actually that indisputable? I know the concept of [[consistency]] but I find it questionable already in cases like [[7/5]]: this interval can probably be used independently of the fact that it can be derived from [[7/4]] and [[5/4]]; another example is the great approximation of [[11/7]] in [[23edo]]. Whatever, would you say that tables would useful to you if there was this column with the amount of repetitions within the limit you described? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:53, 25 October 2020 (UTC)</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>::: I read ''half a step'' as 50% of 1\edo? Concerning the prime harmonics (their octave complements share the exact same table), is it actually that indisputable? I know the concept of [[consistency]] but I find it questionable already in cases like [[7/5]]: this interval can probably be used independently of the fact that it can be derived from [[7/4]] and [[5/4]]; another example is the great approximation of [[11/7]] in [[23edo]]. Whatever, would you say that tables would useful to you if there was this column with the amount of repetitions within the limit you described? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:53, 25 October 2020 (UTC)</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>:::: You are correct in your reading of half a step as 1\edo. While it is true that 7/5 can be used independently of the fact that it can be derived from 7/4 and 5/4, consistency is my main concern with these intervals, <del style="font-weight: bold; text-decoration: none;">as </del>wherever the p-limits from which intervals like 7/5 are derived are poorly represented and or subject to contortion in any given EDO, <del style="font-weight: bold; text-decoration: none;">it seems to either call </del>the consistency of the derived intervals into question and or open up multiple possible representations in a given EDO. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:14, 25 October 2020 (UTC)</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>:::: You are correct in your reading of half a step as 1\edo. While it is true that 7/5 can be used independently of the fact that it can be derived from 7/4 and 5/4, consistency is my main concern with these intervals<ins style="font-weight: bold; text-decoration: none;">. In my own work</ins>, <ins style="font-weight: bold; text-decoration: none;">it seems that </ins>wherever the p-limits from which intervals like 7/5 are derived are poorly represented and or subject to contortion in any given EDO, the consistency of the derived intervals <ins style="font-weight: bold; text-decoration: none;">is called the </ins>into question and or open up multiple possible representations in a given EDO. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:14, 25 October 2020 (UTC)</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>:::: My end goal with including a table containing the number of times the tempered p-limit interval in question can be stacked without the absolute error between the tempered stack and its just counterpart exceeding 3.5 cents (or half a step- whichever is smaller), has more to do with mapping out the usable portions of the harmonic lattice for any given EDO. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:19, 25 October 2020 (UTC)</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>:::: My end goal with including a table containing the number of times the tempered p-limit interval in question can be stacked without the absolute error between the tempered stack and its just counterpart exceeding 3.5 cents (or half a step- whichever is smaller), has more to do with mapping out the usable portions of the harmonic lattice for any given EDO. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:19, 25 October 2020 (UTC)</div></td></tr>
</table>Aura