Comparison of mode notation systems: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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||< Meantone [12] if generator > 700¢ || C G D A E B F# C# G# D# A# E# ||= C G D A E B F# C# G# D# A# E# ||

An even larger problem is that Meantone[12] generated by 701¢ has a different genchain than Meantone[12] generated by 699¢, so slight differences in tempering result in different mode names. In other words the notation is overly tuning-dependent. One might address this problem by constraining meantone's fifth to be less than 700¢. Likewise one could constrain ~~superpyth~~'s fifth to be more than 700¢. But this approach fails with Dominant meantone, which tempers out both 81/80 and 64/63, and in which the fifth can reasonably be either more or less than 700¢. This makes every single UDP mode of Dominant[12] ambiguous. For example "Dominant 8|3" could mean either "4th Dominant[12]" or "9th Dominant[12]". Something similar happens with Meantone[19]. If the fifth is greater than 694¢ = 11\19, the generator is 3/2, but if less than 694¢, it's 4/3. This makes every UDP mode of Meantone[19] ambiguous. Another example is Dicot[7] when the neutral 3rd generator is ~~near~~ 2\7 = 343¢. In general, whenever the generator of a N-note MOS ~~crosses the boundary~~ of an N~~-edo EDOstep~~, ~~this ambiguity arises~~.

An even larger problem is that Meantone[12] generated by 701¢ has a different genchain than Meantone[12] generated by 699¢, so slight differences in tempering result in different mode names. In other words the notation is overly tuning-dependent. One might address this problem by reasonably constraining meantone's fifth to be less than 700¢. Likewise one could constrain Superpyth[12]'s fifth to be more than 700¢. But this approach fails with Dominant meantone, which tempers out both 81/80 and 64/63, and in which the fifth can reasonably be either more or less than 700¢. This makes every single UDP mode of Dominant[12] ambiguous. For example "Dominant 8|3" could mean either "4th Dominant[12]" or "9th Dominant[12]". Something similar happens with Meantone[19]. If the fifth is greater than 694¢ = 11\19, the generator is 3/2, but if less than 694¢, it's 4/3. This makes every UDP mode of Meantone[19] ambiguous. Another example is Dicot[7] when the neutral 3rd generator is greater or less than 2\7 = 343¢. In general, this ambiguity arises whenever the generator of an N-note MOS ranges from slightly flat of X\N to slightly sharp of it, for any positive integer X < N.

A fourth problem with UDP is more of a taste issue: UDP is mathematician-oriented whereas GMN is musician-oriented. For example, the most important piece of information, the number of notes in the scale, is hidden by UDP notation. It must be calculated by adding together the up, down, and period numbers (and the period number is often omitted). Also, as noted above, when comparing different MOS's of a temperament, with GMN but not with UDP, the Nth mode of the smaller MOS is always a subset of the Nth mode of the larger MOS. Furthermore, UDP uses the more mathematical [[https://en.wikipedia.org/wiki/Zero-based_numbering|zero-based counting]] and GMN uses the more intuitive one-based counting.

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An even larger problem is that Meantone[12] generated by 701¢ has a different genchain than Meantone[12] generated by 699¢, so slight differences in tempering result in different mode names. In other words the notation is overly tuning-dependent. One might address this problem by constraining meantone's fifth to be less than 700¢. Likewise one could constrain ~~superpyth~~'s fifth to be more than 700¢. But this approach fails with Dominant meantone, which tempers out both 81/80 and 64/63, and in which the fifth can reasonably be either more or less than 700¢. This makes every single UDP mode of Dominant[12] ambiguous. For example &quot;Dominant 8|3&quot; could mean either &quot;4th Dominant[12]&quot; or &quot;9th Dominant[12]&quot;. Something similar happens with Meantone[19]. If the fifth is greater than 694¢ = 11\19, the generator is 3/2, but if less than 694¢, it's 4/3. This makes every UDP mode of Meantone[19] ambiguous. Another example is Dicot[7] when the neutral 3rd generator is ~~near~~ 2\7 = 343¢. In general, whenever the generator of a N-note MOS ~~crosses the boundary~~ of an N~~-edo EDOstep~~, ~~this ambiguity arises~~.

An even larger problem is that Meantone[12] generated by 701¢ has a different genchain than Meantone[12] generated by 699¢, so slight differences in tempering result in different mode names. In other words the notation is overly tuning-dependent. One might address this problem by reasonably constraining meantone's fifth to be less than 700¢. Likewise one could constrain Superpyth[12]'s fifth to be more than 700¢. But this approach fails with Dominant meantone, which tempers out both 81/80 and 64/63, and in which the fifth can reasonably be either more or less than 700¢. This makes every single UDP mode of Dominant[12] ambiguous. For example &quot;Dominant 8|3&quot; could mean either &quot;4th Dominant[12]&quot; or &quot;9th Dominant[12]&quot;. Something similar happens with Meantone[19]. If the fifth is greater than 694¢ = 11\19, the generator is 3/2, but if less than 694¢, it's 4/3. This makes every UDP mode of Meantone[19] ambiguous. Another example is Dicot[7] when the neutral 3rd generator is greater or less than 2\7 = 343¢. In general, this ambiguity arises whenever the generator of an N-note MOS ranges from slightly flat of X\N to slightly sharp of it, for any positive integer X &lt; N.

A fourth problem with UDP is more of a taste issue: UDP is mathematician-oriented whereas GMN is musician-oriented. For example, the most important piece of information, the number of notes in the scale, is hidden by UDP notation. It must be calculated by adding together the up, down, and period numbers (and the period number is often omitted). Also, as noted above, when comparing different MOS's of a temperament, with GMN but not with UDP, the Nth mode of the smaller MOS is always a subset of the Nth mode of the larger MOS. Furthermore, UDP uses the more mathematical <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Zero-based_numbering" rel="nofollow">zero-based counting</a> and GMN uses the more intuitive one-based counting.

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-04-22 03:12:43 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-04-22 03:19:14 UTC</tt>.<br>
-: The original revision id was <tt>580877955</tt>.<br>
+: The original revision id was <tt>580878159</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 152: / Line 152: @@
 ||&lt; Meantone [12] if generator &gt; 700¢ || C G D A E B F# C# G# D# A# E# ||= C G D A E B F# C# G# D# A# E# ||
-An even larger problem is that Meantone[12] generated by 701¢ has a different genchain than Meantone[12] generated by 699¢, so slight differences in tempering result in different mode names. In other words the notation is overly tuning-dependent. One might address this problem by constraining meantone's fifth to be less than 700¢. Likewise one could constrain superpyth's fifth to be more than 700¢. But this approach fails with Dominant meantone, which tempers out both 81/80 and 64/63, and in which the fifth can reasonably be either more or less than 700¢. This makes every single UDP mode of Dominant[12] ambiguous. For example "Dominant 8|3" could mean either "4th Dominant[12]" or "9th Dominant[12]". Something similar happens with Meantone[19]. If the fifth is greater than 694¢ = 11\19, the generator is 3/2, but if less than 694¢, it's 4/3. This makes every UDP mode of Meantone[19] ambiguous. Another example is Dicot[7] when the neutral 3rd generator is near 2\7 = 343¢. In general, whenever the generator of a N-note MOS crosses the boundary of an N-edo EDOstep, this ambiguity arises.
+An even larger problem is that Meantone[12] generated by 701¢ has a different genchain than Meantone[12] generated by 699¢, so slight differences in tempering result in different mode names. In other words the notation is overly tuning-dependent. One might address this problem by reasonably constraining meantone's fifth to be less than 700¢. Likewise one could constrain Superpyth[12]'s fifth to be more than 700¢. But this approach fails with Dominant meantone, which tempers out both 81/80 and 64/63, and in which the fifth can reasonably be either more or less than 700¢. This makes every single UDP mode of Dominant[12] ambiguous. For example "Dominant 8|3" could mean either "4th Dominant[12]" or "9th Dominant[12]". Something similar happens with Meantone[19]. If the fifth is greater than 694¢ = 11\19, the generator is 3/2, but if less than 694¢, it's 4/3. This makes every UDP mode of Meantone[19] ambiguous. Another example is Dicot[7] when the neutral 3rd generator is greater or less than 2\7 = 343¢. In general, this ambiguity arises whenever the generator of an N-note MOS ranges from slightly flat of X\N to slightly sharp of it, for any positive integer X &lt; N.
 A fourth problem with UDP is more of a taste issue: UDP is mathematician-oriented whereas GMN is musician-oriented. For example, the most important piece of information, the number of notes in the scale, is hidden by UDP notation. It must be calculated by adding together the up, down, and period numbers (and the period number is often omitted). Also, as noted above, when comparing different MOS's of a temperament, with GMN but not with UDP, the Nth mode of the smaller MOS is always a subset of the Nth mode of the larger MOS. Furthermore, UDP uses the more mathematical [[https://en.wikipedia.org/wiki/Zero-based_numbering|zero-based counting]] and GMN uses the more intuitive one-based counting.
@@ Line 1,167: / Line 1,167: @@
 &lt;br /&gt;
-An even larger problem is that Meantone[12] generated by 701¢ has a different genchain than Meantone[12] generated by 699¢, so slight differences in tempering result in different mode names. In other words the notation is overly tuning-dependent. One might address this problem by constraining meantone's fifth to be less than 700¢. Likewise one could constrain superpyth's fifth to be more than 700¢. But this approach fails with Dominant meantone, which tempers out both 81/80 and 64/63, and in which the fifth can reasonably be either more or less than 700¢. This makes every single UDP mode of Dominant[12] ambiguous. For example &amp;quot;Dominant 8|3&amp;quot; could mean either &amp;quot;4th Dominant[12]&amp;quot; or &amp;quot;9th Dominant[12]&amp;quot;. Something similar happens with Meantone[19]. If the fifth is greater than 694¢ = 11\19, the generator is 3/2, but if less than 694¢, it's 4/3. This makes every UDP mode of Meantone[19] ambiguous. Another example is Dicot[7] when the neutral 3rd generator is near 2\7 = 343¢. In general, whenever the generator of a N-note MOS crosses the boundary of an N-edo EDOstep, this ambiguity arises.&lt;br /&gt;
+An even larger problem is that Meantone[12] generated by 701¢ has a different genchain than Meantone[12] generated by 699¢, so slight differences in tempering result in different mode names. In other words the notation is overly tuning-dependent. One might address this problem by reasonably constraining meantone's fifth to be less than 700¢. Likewise one could constrain Superpyth[12]'s fifth to be more than 700¢. But this approach fails with Dominant meantone, which tempers out both 81/80 and 64/63, and in which the fifth can reasonably be either more or less than 700¢. This makes every single UDP mode of Dominant[12] ambiguous. For example &amp;quot;Dominant 8|3&amp;quot; could mean either &amp;quot;4th Dominant[12]&amp;quot; or &amp;quot;9th Dominant[12]&amp;quot;. Something similar happens with Meantone[19]. If the fifth is greater than 694¢ = 11\19, the generator is 3/2, but if less than 694¢, it's 4/3. This makes every UDP mode of Meantone[19] ambiguous. Another example is Dicot[7] when the neutral 3rd generator is greater or less than 2\7 = 343¢. In general, this ambiguity arises whenever the generator of an N-note MOS ranges from slightly flat of X\N to slightly sharp of it, for any positive integer X &amp;lt; N.&lt;br /&gt;
 &lt;br /&gt;
 A fourth problem with UDP is more of a taste issue: UDP is mathematician-oriented whereas GMN is musician-oriented. For example, the most important piece of information, the number of notes in the scale, is hidden by UDP notation. It must be calculated by adding together the up, down, and period numbers (and the period number is often omitted). Also, as noted above, when comparing different MOS's of a temperament, with GMN but not with UDP, the Nth mode of the smaller MOS is always a subset of the Nth mode of the larger MOS. Furthermore, UDP uses the more mathematical &lt;a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Zero-based_numbering" rel="nofollow"&gt;zero-based counting&lt;/a&gt; and GMN uses the more intuitive one-based counting.&lt;br /&gt;