20ed5: 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:Kosmorsky|Kosmorsky]] and made on <tt>2011-09-02 20:46:12 UTC</tt>.

: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-09-02 20:48:11 UTC</tt>.

: The original revision id was <tt>~~250427982~~</tt>.

: The original revision id was <tt>250428170</tt>.

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

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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An [[harmonic entropy]] minimum, that has better approximations of a variety of just intervals than Bohlen Pierce (of course, not the same intervals) among which are 13/12, 7/6, 14/11, 11/8, 3/2, 13/8, 7/4, 21/11, 33/32, ~9/4, 39/32, 21/16, 10/7, 20/13, 10/3 ... etc. In terms of strict 5/1 equivalence and high-limit harmony, it also approximates the harmonics and their pentave reductions: ‎8, 12 (or 61), 23, 27, 32, 44, 48, 52, 56, 66, 71, 77, etc. within 20 cents. Note that there are only two or three pentaves within human hearing range, imagine if that were the case with octaves (yes that is a helpful analogy).

One way of looking at it comes by constructing it via four tempered 3/2 ~~each of which is divided~~ ~~into five tones~~ ([[meantone]] without octaves), which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on the "pentave", 5/1, wherein the scale repeats itself. By analogy to common practice, this is familiar extended meantone but //turned entirely inside-out//. Interestingly, while Hieronymus does not repeat at the octave or even approximate it well, factors of 2 are nevertheless important to its perception and structure; it might even be helpful to think of the 3/2 intervals as a cellular structure of sorts.

One way of looking at it comes by constructing it via four tempered 3/2 ([[meantone]] without octaves) each of which is divided into five tones, which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on the "pentave", 5/1, wherein the scale repeats itself. By analogy to common practice, this is familiar extended meantone but //turned entirely inside-out//. Interestingly, while Hieronymus does not repeat at the octave or even approximate it well, factors of 2 are nevertheless important to its perception and structure; it might even be helpful to think of the 3/2 intervals as a cellular structure of sorts.

Adding octaves makes it [[Meantone family#Jerome|jerome temperament]], with generator a meantone fifth divided in five, and Hieronymus is the generator chain of that. Jerome/Hieronymus only really comes into its own as a higher limit temperament, as a 13, or even higher limit system.

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An <a class="wiki_link" href="/harmonic%20entropy">harmonic entropy</a> minimum, that has better approximations of a variety of just intervals than Bohlen Pierce (of course, not the same intervals) among which are 13/12, 7/6, 14/11, 11/8, 3/2, 13/8, 7/4, 21/11, 33/32, ~9/4, 39/32, 21/16, 10/7, 20/13, 10/3 ... etc. In terms of strict 5/1 equivalence and high-limit harmony, it also approximates the harmonics and their pentave reductions: ‎8, 12 (or 61), 23, 27, 32, 44, 48, 52, 56, 66, 71, 77, etc. within 20 cents. Note that there are only two or three pentaves within human hearing range, imagine if that were the case with octaves (yes that is a helpful analogy).

One way of looking at it comes by constructing it via four tempered 3/2 ~~each of which is divided~~ ~~into five tones~~ (<a class="wiki_link" href="/meantone">meantone</a> without octaves), which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on the &quot;pentave&quot;, 5/1, wherein the scale repeats itself. By analogy to common practice, this is familiar extended meantone but turned entirely inside-out. Interestingly, while Hieronymus does not repeat at the octave or even approximate it well, factors of 2 are nevertheless important to its perception and structure; it might even be helpful to think of the 3/2 intervals as a cellular structure of sorts.

One way of looking at it comes by constructing it via four tempered 3/2 (<a class="wiki_link" href="/meantone">meantone</a> without octaves) each of which is divided into five tones, which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on the &quot;pentave&quot;, 5/1, wherein the scale repeats itself. By analogy to common practice, this is familiar extended meantone but turned entirely inside-out. Interestingly, while Hieronymus does not repeat at the octave or even approximate it well, factors of 2 are nevertheless important to its perception and structure; it might even be helpful to think of the 3/2 intervals as a cellular structure of sorts.

Adding octaves makes it <a class="wiki_link" href="/Meantone%20family#Jerome">jerome temperament</a>, with generator a meantone fifth divided in five, and Hieronymus is the generator chain of that. Jerome/Hieronymus only really comes into its own as a higher limit temperament, as a 13, or even higher limit system.

[As an endorsement, this is the strangest most mind-blowing scale Kosmorsky has yet heard, not as dissonance, but as a supremely peculiar arrangement of consonance.]</body></html></pre></div>

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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:<br>
-: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-09-02 20:46:12 UTC</tt>.<br>
+: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-09-02 20:48:11 UTC</tt>.<br>
-: The original revision id was <tt>250427982</tt>.<br>
+: The original revision id was <tt>250428170</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>
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 An [[harmonic entropy]] minimum, that has better approximations of a variety of just intervals than Bohlen Pierce (of course, not the same intervals) among which are &lt;span class="commentBody"&gt;13/12, 7/6, 14/11, 11/8, 3/2, 13/8, 7/4, 21/11, 33/32, ~9/4, 39/32, 21/16, 10/7, 20/13, 10/3 ... etc. In terms of strict 5/1 equivalence and high-limit harmony, it also approximates the harmonics and their pentave reductions: ‎8, 12 (or 61), 23, 27, 32, 44, 48, 52, 56, 66, 71, 77, etc. within 20 cents. Note that there are only two or three pentaves within human hearing range, imagine if that were the case with octaves (yes that is a helpful analogy).&lt;/span&gt;
-&lt;span class="commentBody"&gt;One way of looking at it comes by constructing it via four tempered 3/2 each of which is divided&lt;/span&gt; into five tones ([[meantone]] without octaves), which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on the "pentave", 5/1, wherein the scale repeats itself. By analogy to common practice, this is familiar extended meantone but //turned entirely inside-out//. Interestingly, while Hieronymus does not repeat at the octave or even approximate it well, factors of 2 are nevertheless important to its perception and structure; it might even be helpful to think of the 3/2 intervals as a cellular structure of sorts.
+&lt;span class="commentBody"&gt;One way of looking at it comes by constructing it via four tempered 3/2&lt;/span&gt; ([[meantone]] without octaves) &lt;span class="commentBody"&gt;each of which is divided&lt;/span&gt; into five tones, which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on the "pentave", 5/1, wherein the scale repeats itself. By analogy to common practice, this is familiar extended meantone but //turned entirely inside-out//. Interestingly, while Hieronymus does not repeat at the octave or even approximate it well, factors of 2 are nevertheless important to its perception and structure; it might even be helpful to think of the 3/2 intervals as a cellular structure of sorts.
 Adding octaves makes it [[Meantone family#Jerome|jerome temperament]], with generator a meantone fifth divided in five, and Hieronymus is the generator chain of that. Jerome/Hieronymus only really comes into its own as a higher limit temperament, as a 13, or even higher limit system.
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 An &lt;a class="wiki_link" href="/harmonic%20entropy"&gt;harmonic entropy&lt;/a&gt; minimum, that has better approximations of a variety of just intervals than Bohlen Pierce (of course, not the same intervals) among which are &lt;span class="commentBody"&gt;13/12, 7/6, 14/11, 11/8, 3/2, 13/8, 7/4, 21/11, 33/32, ~9/4, 39/32, 21/16, 10/7, 20/13, 10/3 ... etc. In terms of strict 5/1 equivalence and high-limit harmony, it also approximates the harmonics and their pentave reductions: ‎8, 12 (or 61), 23, 27, 32, 44, 48, 52, 56, 66, 71, 77, etc. within 20 cents. Note that there are only two or three pentaves within human hearing range, imagine if that were the case with octaves (yes that is a helpful analogy).&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;span class="commentBody"&gt;One way of looking at it comes by constructing it via four tempered 3/2 each of which is divided&lt;/span&gt; into five tones (&lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; without octaves), which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on the &amp;quot;pentave&amp;quot;, 5/1, wherein the scale repeats itself. By analogy to common practice, this is familiar extended meantone but &lt;em&gt;turned entirely inside-out&lt;/em&gt;. Interestingly, while Hieronymus does not repeat at the octave or even approximate it well, factors of 2 are nevertheless important to its perception and structure; it might even be helpful to think of the 3/2 intervals as a cellular structure of sorts.&lt;br /&gt;
+&lt;span class="commentBody"&gt;One way of looking at it comes by constructing it via four tempered 3/2&lt;/span&gt; (&lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; without octaves) &lt;span class="commentBody"&gt;each of which is divided&lt;/span&gt; into five tones, which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on the &amp;quot;pentave&amp;quot;, 5/1, wherein the scale repeats itself. By analogy to common practice, this is familiar extended meantone but &lt;em&gt;turned entirely inside-out&lt;/em&gt;. Interestingly, while Hieronymus does not repeat at the octave or even approximate it well, factors of 2 are nevertheless important to its perception and structure; it might even be helpful to think of the 3/2 intervals as a cellular structure of sorts.&lt;br /&gt;
 &lt;br /&gt;
 Adding octaves makes it &lt;a class="wiki_link" href="/Meantone%20family#Jerome"&gt;jerome temperament&lt;/a&gt;, with generator a meantone fifth divided in five, and Hieronymus is the generator chain of that. Jerome/Hieronymus only really comes into its own as a higher limit temperament, as a 13, or even higher limit system.&lt;br /&gt;
 &lt;br /&gt;
 [As an endorsement, this is the strangest most mind-blowing scale Kosmorsky has yet heard, not as dissonance, but as a supremely peculiar arrangement of consonance.]&lt;/body&gt;&lt;/html&gt;</pre></div>