100edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-06-17 02:23:01 UTC</tt>.

: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-06-17 02:29:07 UTC</tt>.

: The original revision id was <tt>~~585712775~~</tt>.

: The original revision id was <tt>585712845</tt>.

: The revision comment was: <tt></tt>

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The 100bddd val (which maps 3/2 onto 59\100, 5/4 onto its patent value of 32\100, and 7/4 onto 82\100) is of special interest as it provides a good alternative to [[22edo]] for [[pajara]] temperament and for tuning Paul Erlich's decatonic scales, as well as diatonic scales (via superpyth temperament). This alternative tuning prioritizes the 3- and 5-limits over the 7-limit (although the latter is still within striking distance); its pure intervals are also all closer to their 12edo counterparts, and for both reasons it is much less xenharmonic overall. Melodically its properties are superior as well; decatonic scales are more expressive due to the larger difference between step sizes, and the superpyth diatonic scale has a minor second of 60¢ which just barely falls within the 60-80 cent range [[http://www.anaphoria.com/Secor17puzzle.pdf|favored by George Secor]] for neomedieval compositions.

The 22-note MODMOS 5 4 5 4 5 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 could be used to construct a 22-tone piano; this tuning has two chains of fifths (one with 10 notes in it and one with 12), and thus has two "wolf" fifths. Much like meantone, this tuning has "wolf" intervals but in this case they are only twelve cents away from their pure counterparts, and as such they don't sound nearly as bad. They are xenharmonic but not unpleasant and could easily be used in compositions, which makes this tuning akin to well temperaments as well as to meantone. Because most if not all of them are still usable (albeit xenharmonic), it might be better to use the term //dog// rather than wolf for these intervals. Dog intervals frequently provide //closer// matches to intervals involving the 7th and 11th harmonics. Even //if// the dog intervals are completely avoided, this MODMOS still allows for decatonic music in 10 different keys, and diatonic (superpyth) music ~~also~~ in 10 different keys, and thus the freedom of modulation and key choice is still comparable to 12edo.

The 22-note MODMOS 5 4 5 4 5 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 could be used to construct a 22-tone piano; this tuning has two chains of fifths (one with 10 notes in it and one with 12), and thus has two "wolf" fifths. Much like meantone, this tuning has "wolf" intervals but in this case they are only twelve cents away from their pure counterparts, and as such they don't sound nearly as bad. They are xenharmonic but not unpleasant and could easily be used in compositions, which makes this tuning akin to well temperaments as well as to meantone. Because most if not all of them are still usable (albeit xenharmonic), it might be better to use the term //dog// rather than wolf for these intervals. Dog intervals frequently provide //closer// matches to intervals involving the 7th and 11th harmonics. Even //if// the dog intervals are completely avoided, this MODMOS still allows for decatonic music in 12 different keys, and diatonic (superpyth) music in 10 different keys, and thus the freedom of modulation and key choice is still comparable to 12edo.

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The 100bddd val (which maps 3/2 onto 59\100, 5/4 onto its patent value of 32\100, and 7/4 onto 82\100) is of special interest as it provides a good alternative to <a class="wiki_link" href="/22edo">22edo</a> for <a class="wiki_link" href="/pajara">pajara</a> temperament and for tuning Paul Erlich's decatonic scales, as well as diatonic scales (via superpyth temperament). This alternative tuning prioritizes the 3- and 5-limits over the 7-limit (although the latter is still within striking distance); its pure intervals are also all closer to their 12edo counterparts, and for both reasons it is much less xenharmonic overall. Melodically its properties are superior as well; decatonic scales are more expressive due to the larger difference between step sizes, and the superpyth diatonic scale has a minor second of 60¢ which just barely falls within the 60-80 cent range <a class="wiki_link_ext" href="http://www.anaphoria.com/Secor17puzzle.pdf" rel="nofollow">favored by George Secor</a> for neomedieval compositions.

The 22-note MODMOS 5 4 5 4 5 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 could be used to construct a 22-tone piano; this tuning has two chains of fifths (one with 10 notes in it and one with 12), and thus has two &quot;wolf&quot; fifths. Much like meantone, this tuning has &quot;wolf&quot; intervals but in this case they are only twelve cents away from their pure counterparts, and as such they don't sound nearly as bad. They are xenharmonic but not unpleasant and could easily be used in compositions, which makes this tuning akin to well temperaments as well as to meantone. Because most if not all of them are still usable (albeit xenharmonic), it might be better to use the term dog rather than wolf for these intervals. Dog intervals frequently provide closer matches to intervals involving the 7th and 11th harmonics. Even if the dog intervals are completely avoided, this MODMOS still allows for decatonic music in 10 different keys, and diatonic (superpyth) music ~~also~~ in 10 different keys, and thus the freedom of modulation and key choice is still comparable to 12edo.

The 22-note MODMOS 5 4 5 4 5 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 could be used to construct a 22-tone piano; this tuning has two chains of fifths (one with 10 notes in it and one with 12), and thus has two &quot;wolf&quot; fifths. Much like meantone, this tuning has &quot;wolf&quot; intervals but in this case they are only twelve cents away from their pure counterparts, and as such they don't sound nearly as bad. They are xenharmonic but not unpleasant and could easily be used in compositions, which makes this tuning akin to well temperaments as well as to meantone. Because most if not all of them are still usable (albeit xenharmonic), it might be better to use the term dog rather than wolf for these intervals. Dog intervals frequently provide closer matches to intervals involving the 7th and 11th harmonics. Even if the dog intervals are completely avoided, this MODMOS still allows for decatonic music in 12 different keys, and diatonic (superpyth) music in 10 different keys, and thus the freedom of modulation and key choice is still comparable to 12edo.

@@ 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:MasonGreen1|MasonGreen1]] and made on <tt>2016-06-17 02:23:01 UTC</tt>.<br>
+: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-06-17 02:29:07 UTC</tt>.<br>
-: The original revision id was <tt>585712775</tt>.<br>
+: The original revision id was <tt>585712845</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 23: / Line 23: @@
 The 100bddd val (which maps 3/2 onto 59\100, 5/4 onto its patent value of 32\100, and 7/4 onto 82\100) is of special interest as it provides a good alternative to [[22edo]] for [[pajara]] temperament and for tuning Paul Erlich's decatonic scales, as well as diatonic scales (via superpyth temperament). This alternative tuning prioritizes the 3- and 5-limits over the 7-limit (although the latter is still within striking distance); its pure intervals are also all closer to their 12edo counterparts, and for both reasons it is much less xenharmonic overall. Melodically its properties are superior as well; decatonic scales are more expressive due to the larger difference between step sizes, and the superpyth diatonic scale has a minor second of 60¢ which just barely falls within the 60-80 cent range [[http://www.anaphoria.com/Secor17puzzle.pdf|favored by George Secor]] for neomedieval compositions.
-The 22-note MODMOS 5 4 5 4 5 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 could be used to construct a 22-tone piano; this tuning has two chains of fifths (one with 10 notes in it and one with 12), and thus has two "wolf" fifths. Much like meantone, this tuning has "wolf" intervals but in this case they are only twelve cents away from their pure counterparts, and as such they don't sound nearly as bad. They are xenharmonic but not unpleasant and could easily be used in compositions, which makes this tuning akin to well temperaments as well as to meantone. Because most if not all of them are still usable (albeit xenharmonic), it might be better to use the term //dog// rather than wolf for these intervals. Dog intervals frequently provide //closer// matches to intervals involving the 7th and 11th harmonics. Even //if// the dog intervals are completely avoided, this MODMOS still allows for decatonic music in 10 different keys, and diatonic (superpyth) music also in 10 different keys, and thus the freedom of modulation and key choice is still comparable to 12edo.
+The 22-note MODMOS 5 4 5 4 5 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 could be used to construct a 22-tone piano; this tuning has two chains of fifths (one with 10 notes in it and one with 12), and thus has two "wolf" fifths. Much like meantone, this tuning has "wolf" intervals but in this case they are only twelve cents away from their pure counterparts, and as such they don't sound nearly as bad. They are xenharmonic but not unpleasant and could easily be used in compositions, which makes this tuning akin to well temperaments as well as to meantone. Because most if not all of them are still usable (albeit xenharmonic), it might be better to use the term //dog// rather than wolf for these intervals. Dog intervals frequently provide //closer// matches to intervals involving the 7th and 11th harmonics. Even //if// the dog intervals are completely avoided, this MODMOS still allows for decatonic music in 12 different keys, and diatonic (superpyth) music in 10 different keys, and thus the freedom of modulation and key choice is still comparable to 12edo.
@@ Line 74: / Line 74: @@
 The 100bddd val (which maps 3/2 onto 59\100, 5/4 onto its patent value of 32\100, and 7/4 onto 82\100) is of special interest as it provides a good alternative to &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; for &lt;a class="wiki_link" href="/pajara"&gt;pajara&lt;/a&gt; temperament and for tuning Paul Erlich's decatonic scales, as well as diatonic scales (via superpyth temperament). This alternative tuning prioritizes the 3- and 5-limits over the 7-limit (although the latter is still within striking distance); its pure intervals are also all closer to their 12edo counterparts, and for both reasons it is much less xenharmonic overall. Melodically its properties are superior as well; decatonic scales are more expressive due to the larger difference between step sizes, and the superpyth diatonic scale has a minor second of 60¢ which just barely falls within the 60-80 cent range &lt;a class="wiki_link_ext" href="http://www.anaphoria.com/Secor17puzzle.pdf" rel="nofollow"&gt;favored by George Secor&lt;/a&gt; for neomedieval compositions.&lt;br /&gt;
 &lt;br /&gt;
-The 22-note MODMOS 5 4 5 4 5 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 could be used to construct a 22-tone piano; this tuning has two chains of fifths (one with 10 notes in it and one with 12), and thus has two &amp;quot;wolf&amp;quot; fifths. Much like meantone, this tuning has &amp;quot;wolf&amp;quot; intervals but in this case they are only twelve cents away from their pure counterparts, and as such they don't sound nearly as bad. They are xenharmonic but not unpleasant and could easily be used in compositions, which makes this tuning akin to well temperaments as well as to meantone. Because most if not all of them are still usable (albeit xenharmonic), it might be better to use the term &lt;em&gt;dog&lt;/em&gt; rather than wolf for these intervals. Dog intervals frequently provide &lt;em&gt;closer&lt;/em&gt; matches to intervals involving the 7th and 11th harmonics. Even &lt;em&gt;if&lt;/em&gt; the dog intervals are completely avoided, this MODMOS still allows for decatonic music in 10 different keys, and diatonic (superpyth) music also in 10 different keys, and thus the freedom of modulation and key choice is still comparable to 12edo.&lt;br /&gt;
+The 22-note MODMOS 5 4 5 4 5 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 could be used to construct a 22-tone piano; this tuning has two chains of fifths (one with 10 notes in it and one with 12), and thus has two &amp;quot;wolf&amp;quot; fifths. Much like meantone, this tuning has &amp;quot;wolf&amp;quot; intervals but in this case they are only twelve cents away from their pure counterparts, and as such they don't sound nearly as bad. They are xenharmonic but not unpleasant and could easily be used in compositions, which makes this tuning akin to well temperaments as well as to meantone. Because most if not all of them are still usable (albeit xenharmonic), it might be better to use the term &lt;em&gt;dog&lt;/em&gt; rather than wolf for these intervals. Dog intervals frequently provide &lt;em&gt;closer&lt;/em&gt; matches to intervals involving the 7th and 11th harmonics. Even &lt;em&gt;if&lt;/em&gt; the dog intervals are completely avoided, this MODMOS still allows for decatonic music in 12 different keys, and diatonic (superpyth) music in 10 different keys, and thus the freedom of modulation and key choice is still comparable to 12edo.&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;