Wikispaces>Andrew_Heathwaite |
|
| (23 intermediate revisions by 16 users not shown) |
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | [[de:100/99]] |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{Infobox Interval |
| : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-09-14 19:27:40 UTC</tt>.<br>
| | | Name = ptolemisma, Ptolemy's comma |
| : The original revision id was <tt>254141930</tt>.<br>
| | | Color name = 1uyy1, luyoyo 1sn,<br>Luyoyo comma |
| : The revision comment was: <tt></tt><br>
| | | Comma = yes |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | }} |
| <h4>Original Wikitext content:</h4>
| | In [[just intonation]], '''100/99''', the '''ptolemisma''' or '''Ptolemy's comma''', is a [[small comma|small]] [[superparticular ratio|superparticular]] [[comma]] of around 17.4¢ which makes the difference between [[11/10]], the greater undecimal neutral second of about 165¢, and [[10/9]], the 5-limit minor whole tone of about 182.4¢. It is also the difference between [[25/24]] and [[33/32]]. In terms of commatic relations it notably factors into [[225/224]] and [[896/891]]. |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">In [[Just Intonation]],100/99 is a [[superparticular]] interval around 17.4¢ which makes the difference between [[11_10|11/10]], the greater undecimal neutral second of about 165¢, and [[10_9|10/9]], the 5-limit minor whole tone of about 182.4¢. Temperaments in which 100/99 is tempered out include [[22edo]], [[41edo]] and others; in such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of [[81_80|81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9_8|9/8]].
| |
|
| |
|
| See: [[Gallery of Just Intervals|Galley of Just Intervals]]</pre></div>
| | == Temperaments == |
| <h4>Original HTML content:</h4>
| | [[Tempering out]] this interval in the 11-limit results in the rank-4 ptolemismic temperament (→ [[Rank-4 temperament #Ptolemismic (100/99)]]). [[Equal temperament]]s in which 100/99 is tempered out include [[22edo]], [[41edo]] and others. In such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of [[81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9/8]]. However, meantone and ptolemismic are not necessarily mutually exclusive–the [[flattone]] temperament (known as "hypnotone" in the 2.3.5.11 subgroup) merges both and has [[11/10]], [[10/9]] and [[9/8]] all tempered to a 10/9-like interval. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[11/8]] and two [[6/5]]'s fall short of an octave, so that tempering out 100/99 allows for the [[ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5. |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>100_99</title></head><body>In <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>,100/99 is a <a class="wiki_link" href="/superparticular">superparticular</a> interval around 17.4¢ which makes the difference between <a class="wiki_link" href="/11_10">11/10</a>, the greater undecimal neutral second of about 165¢, and <a class="wiki_link" href="/10_9">10/9</a>, the 5-limit minor whole tone of about 182.4¢. Temperaments in which 100/99 is tempered out include <a class="wiki_link" href="/22edo">22edo</a>, <a class="wiki_link" href="/41edo">41edo</a> and others; in such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of <a class="wiki_link" href="/81_80">81/80</a>, which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with <a class="wiki_link" href="/9_8">9/8</a>.<br />
| | |
| <br />
| | See [[Ptolemismic clan]] for the clan of rank-3 temperaments where it is tempered out. |
| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Galley of Just Intervals</a></body></html></pre></div> | | |
| | == Approximation == |
| | If the interval is not tempered out and instead treated as an identity, it is extremely closely represented by one step of [[69edo]]. The associated unnoticeable comma, [[ptolemi-nicema]], represents the difference between 69 100/99's and the octave, is only 0.56 cents wide. Nice. |
| | |
| | == See also == |
| | * [[List of superparticular intervals]] |
| | * [[Gallery of just intervals]] |
| | * [[:File: Demo 100 99 tempered.pdf]] |
| | |
| | [[Category:Ptolemismic]] |
| | [[Category:Commas named after polymaths]] |