Comparison of mode notation systems: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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These [[MOSScales|MOS scales]] are formed from a segment of the [[periods and generators|generator-chain]], or genchain. The first note in the genchain is the tonic of mode #1, the 2nd note is the tonic of mode #2, etc., somewhat analogous to harmonica positions. 4th Meantone[7] is spoken as "fourth meantone heptatonic". If in D, as above, it would be "D fourth meantone heptatonic".

The same seven modes, all with C as the tonic, to illustrate the difference between modes. Similar modes are grouped together. The modes~~' progression is~~ from sharper to flatter.

The same seven modes, all with C as the tonic, to illustrate the difference between modes. Similar modes are grouped together. The modes proceed from sharper (Lydian) to flatter (Locrian).

|| old scale name || new scale name || Ls pattern || example in C || ------------------- genchain --------------- ||

|| Lydian || 1st Meantone[7] || LLLs LLs || C D E F# G A B C ||> __**C**__ G D A E B F# ||

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The octave inverse of a generator is also a generator. To avoid ambiguity in mode numbers, the smaller of the two generators is chosen. An exception is made for 3/2, which is preferred over 4/3 for historical reasons. **Unlike modal UDP notation, the generator isn't always chroma-positive.** This is necessary to keep the same generator for different MOS's of the same [[Regular Temperaments|temperament]], which guarantees that the smaller MOS will always be a subset of the larger MOS.

For example, Meantone[5] is generated by 3/2, not 4/3. Because the generator is chroma-negative, the modes~~' progression is~~ from flatter to sharper. Because Meantone[5] and Meantone[7]have the same generator, C 2nd Meantone[5] = CDFGAC is a subset of C 2nd Meantone[7] = CDEFGABC.

For example, Meantone[5] is generated by 3/2, not 4/3. Because the generator is chroma-negative, the modes proceed from flatter to sharper. Because Meantone[5] and Meantone[7]have the same generator, C 2nd Meantone[5] = CDFGAC is a subset of C 2nd Meantone[7] = CDEFGABC.

Pentatonic meantone scales:

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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 ~~a reasonable range of <~~ 700¢. Likewise one could constrain superpyth's fifth to be ~~>~~ 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 ~~< 700¢~~ or ~~>~~ 700¢. ~~Every~~ single UDP mode of Dominant[12] is ambiguous. For example "Dominant 8|3" could mean either "4th Dominant[12]" or "9th Dominant[12]".

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.

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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These <a class="wiki_link" href="/MOSScales">MOS scales</a> are formed from a segment of the <a class="wiki_link" href="/periods%20and%20generators">generator-chain</a>, or genchain. The first note in the genchain is the tonic of mode #1, the 2nd note is the tonic of mode #2, etc., somewhat analogous to harmonica positions. 4th Meantone[7] is spoken as &quot;fourth meantone heptatonic&quot;. If in D, as above, it would be &quot;D fourth meantone heptatonic&quot;.

The same seven modes, all with C as the tonic, to illustrate the difference between modes. Similar modes are grouped together. The modes~~' progression is~~ from sharper to flatter.

The same seven modes, all with C as the tonic, to illustrate the difference between modes. Similar modes are grouped together. The modes proceed from sharper (Lydian) to flatter (Locrian).

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The octave inverse of a generator is also a generator. To avoid ambiguity in mode numbers, the smaller of the two generators is chosen. An exception is made for 3/2, which is preferred over 4/3 for historical reasons. Unlike modal UDP notation, the generator isn't always chroma-positive. This is necessary to keep the same generator for different MOS's of the same <a class="wiki_link" href="/Regular%20Temperaments">temperament</a>, which guarantees that the smaller MOS will always be a subset of the larger MOS.

For example, Meantone[5] is generated by 3/2, not 4/3. Because the generator is chroma-negative, the modes~~' progression is~~ from flatter to sharper. Because Meantone[5] and Meantone[7]have the same generator, C 2nd Meantone[5] = CDFGAC is a subset of C 2nd Meantone[7] = CDEFGABC.

For example, Meantone[5] is generated by 3/2, not 4/3. Because the generator is chroma-negative, the modes proceed from flatter to sharper. Because Meantone[5] and Meantone[7]have the same generator, C 2nd Meantone[5] = CDFGAC is a subset of C 2nd Meantone[7] = CDEFGABC.

Pentatonic meantone scales:

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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 ~~a reasonable range of &lt;~~ 700¢. Likewise one could constrain superpyth's fifth to be ~~&gt;~~ 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 ~~&lt; 700¢~~ or ~~&gt;~~ 700¢. ~~Every~~ single UDP mode of Dominant[12] is ambiguous. For example &quot;Dominant 8|3&quot; could mean either &quot;4th Dominant[12]&quot; or &quot;9th Dominant[12]&quot;.

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.

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 00:10:28 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-04-22 03:12:43 UTC</tt>.<br>
-: The original revision id was <tt>580871995</tt>.<br>
+: The original revision id was <tt>580877955</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 18: / Line 18: @@
 These [[MOSScales|MOS scales]] are formed from a segment of the [[periods and generators|generator-chain]], or genchain. The first note in the genchain is the tonic of mode #1, the 2nd note is the tonic of mode #2, etc., somewhat analogous to harmonica positions. 4th Meantone[7] is spoken as "fourth meantone heptatonic". If in D, as above, it would be "D fourth meantone heptatonic".
-The same seven modes, all with C as the tonic, to illustrate the difference between modes. Similar modes are grouped together. The modes' progression is from sharper to flatter.
+The same seven modes, all with C as the tonic, to illustrate the difference between modes. Similar modes are grouped together. The modes proceed from sharper (Lydian) to flatter (Locrian).
 || old scale name || new scale name || Ls pattern || example in C || ------------------- genchain --------------- ||
 || Lydian || 1st Meantone[7] || LLLs LLs || C D E F# G A B C ||&gt; __**C**__ G D A E B F# ||
@@ Line 30: / Line 30: @@
 The octave inverse of a generator is also a generator. To avoid ambiguity in mode numbers, the smaller of the two generators is chosen. An exception is made for 3/2, which is preferred over 4/3 for historical reasons. **Unlike modal UDP notation, the generator isn't always chroma-positive.** This is necessary to keep the same generator for different MOS's of the same [[Regular Temperaments|temperament]], which guarantees that the smaller MOS will always be a subset of the larger MOS.
-For example, Meantone[5] is generated by 3/2, not 4/3. Because the generator is chroma-negative, the modes' progression is from flatter to sharper. Because Meantone[5] and Meantone[7]have the same generator, C 2nd Meantone[5] = CDFGAC is a subset of C 2nd Meantone[7] = CDEFGABC.
+For example, Meantone[5] is generated by 3/2, not 4/3. Because the generator is chroma-negative, the modes proceed from flatter to sharper. Because Meantone[5] and Meantone[7]have the same generator, C 2nd Meantone[5] = CDFGAC is a subset of C 2nd Meantone[7] = CDEFGABC.
 Pentatonic meantone scales:
@@ 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 a reasonable range of &lt; 700¢. Likewise one could constrain superpyth's fifth to be &gt; 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 &lt; 700¢ or &gt; 700¢. Every single UDP mode of Dominant[12] is ambiguous. For example "Dominant 8|3" could mean either "4th Dominant[12]" or "9th Dominant[12]".
+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.
 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 266: / Line 266: @@
 These &lt;a class="wiki_link" href="/MOSScales"&gt;MOS scales&lt;/a&gt; are formed from a segment of the &lt;a class="wiki_link" href="/periods%20and%20generators"&gt;generator-chain&lt;/a&gt;, or genchain. The first note in the genchain is the tonic of mode #1, the 2nd note is the tonic of mode #2, etc., somewhat analogous to harmonica positions. 4th Meantone[7] is spoken as &amp;quot;fourth meantone heptatonic&amp;quot;. If in D, as above, it would be &amp;quot;D fourth meantone heptatonic&amp;quot;.&lt;br /&gt;
 &lt;br /&gt;
-The same seven modes, all with C as the tonic, to illustrate the difference between modes. Similar modes are grouped together. The modes' progression is from sharper to flatter.&lt;br /&gt;
+The same seven modes, all with C as the tonic, to illustrate the difference between modes. Similar modes are grouped together. The modes proceed from sharper (Lydian) to flatter (Locrian).&lt;br /&gt;
@@ Line 371: / Line 371: @@
 The octave inverse of a generator is also a generator. To avoid ambiguity in mode numbers, the smaller of the two generators is chosen. An exception is made for 3/2, which is preferred over 4/3 for historical reasons. &lt;strong&gt;Unlike modal UDP notation, the generator isn't always chroma-positive.&lt;/strong&gt; This is necessary to keep the same generator for different MOS's of the same &lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;temperament&lt;/a&gt;, which guarantees that the smaller MOS will always be a subset of the larger MOS.&lt;br /&gt;
 &lt;br /&gt;
-For example, Meantone[5] is generated by 3/2, not 4/3. Because the generator is chroma-negative, the modes' progression is from flatter to sharper. Because Meantone[5] and Meantone[7]have the same generator, C 2nd Meantone[5] = CDFGAC is a subset of C 2nd Meantone[7] = CDEFGABC.&lt;br /&gt;
+For example, Meantone[5] is generated by 3/2, not 4/3. Because the generator is chroma-negative, the modes proceed from flatter to sharper. Because Meantone[5] and Meantone[7]have the same generator, C 2nd Meantone[5] = CDFGAC is a subset of C 2nd Meantone[7] = CDEFGABC.&lt;br /&gt;
 &lt;br /&gt;
 Pentatonic meantone scales:&lt;br /&gt;
@@ 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 a reasonable range of &amp;lt; 700¢. Likewise one could constrain superpyth's fifth to be &amp;gt; 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 &amp;lt; 700¢ or &amp;gt; 700¢. Every single UDP mode of Dominant[12] is 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;.&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;
 &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;