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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Interwiki |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | en = 128/125 |
| : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2014-02-05 17:46:51 UTC</tt>.<br>
| | | de = 128/125 |
| : The original revision id was <tt>487593392</tt>.<br>
| | }} |
| : The revision comment was: <tt></tt><br>
| | {{Infobox Interval |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | | Name = diesis, augmented comma, enharmonic diesis, enharmonic comma |
| <h4>Original Wikitext content:</h4>
| | | Color name = g<sup>3</sup>2, trigu 2nd,<br>Trigu comma |
| <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"><span style="display: block; text-align: right;">Other languages: [[xenharmonie/128_125|Deutsch]]</span><span style="display: block; text-align: left;">The 41.059 cent interval of **128/125** is called the **diesis** or **augmented [[comma]]**; it represents the gap between three [[5_4|5/4]] just major thirds and the [[octave]], or in other words 2/(5/4)^3. It is fairly accurately represented by a single step in [[28edo|28]], [[31edo|31]] or [[34edo|34]] EDO, and by two steps of [[53edo|53]], [[59edo|59]] or [[65edo|65]]. In any tuning with just major, thirds, such as [[Quarter-comma meantone|quarter comma meantone]], it will be exact. Furthermore, in quarter-comma.meantone it appears as difference between sharps and flats, e.g. between D# and Eb. It is also called **enharmonic comma** for this reason. Tempering it out leads to [[Augmented family|augmented temperament]].</span></pre></div>
| | | Comma = yes |
| <h4>Original HTML content:</h4>
| | }} |
| <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>128_125</title></head><body><span style="display: block; text-align: right;">Other languages: <a class="wiki_link" href="http://xenharmonie.wikispaces.com/128_125">Deutsch</a></span><span style="display: block; text-align: left;">The 41.059 cent interval of <strong>128/125</strong> is called the <strong>diesis</strong> or <strong>augmented <a class="wiki_link" href="/comma">comma</a></strong>; it represents the gap between three <a class="wiki_link" href="/5_4">5/4</a> just major thirds and the <a class="wiki_link" href="/octave">octave</a>, or in other words 2/(5/4)^3. It is fairly accurately represented by a single step in <a class="wiki_link" href="/28edo">28</a>, <a class="wiki_link" href="/31edo">31</a> or <a class="wiki_link" href="/34edo">34</a> EDO, and by two steps of <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/59edo">59</a> or <a class="wiki_link" href="/65edo">65</a>. In any tuning with just major, thirds, such as <a class="wiki_link" href="/Quarter-comma%20meantone">quarter comma meantone</a>, it will be exact. Furthermore, in quarter-comma.meantone it appears as difference between sharps and flats, e.g. between D# and Eb. It is also called <strong>enharmonic comma</strong> for this reason. Tempering it out leads to <a class="wiki_link" href="/Augmented%20family">augmented temperament</a>.</span></body></html></pre></div>
| | |
| | The 41.059-[[cent]] interval of '''128/125''' is called the '''diesis''' or '''augmented comma'''; it represents the gap between a stack of three [[5/4]] just major thirds and the [[octave]], or in other words 2/(5/4)<sup>3</sup>. |
| | |
| | == Approximations == |
| | This interval is fairly accurately represented by a single step in [[28edo|28-]], [[31edo|31-]] or [[34edo]], and by two steps of [[53edo|53-]], [[59edo|59-]] or [[65edo]]. In any tuning with pure octaves and just major thirds, such as [[quarter-comma meantone]], it will be exact. Furthermore, in meantone it appears as the difference between sharps and flats, e.g. between D# and Eb. It is also called '''enharmonic diesis''' or '''enharmonic comma''' for this reason. |
| | |
| | == Temperaments == |
| | === As a comma === |
| | [[Tempering out]] this comma leads to [[augmented]] temperament. See [[augmented family]] for the family where it is tempered out. |
| | |
| | === As an interval === |
| | If the diesis is treated as a musical interval in its own right as opposed to tempering it out, it is approximately a quarter-tone and so can be used to introduce [[7-limit]] and [[11-limit]] harmony into 5-limit scales. |
| | |
| | == Trivia == |
| | This interval represents the amount by which the binary definition of kilobyte, 1024 bytes, exceeds the nominal definition of "kilo" prefix, 1000. |
| | |
| | == See also == |
| | * [[Diesis]] (disambiguation page) |
| | |
| | [[Category:Augmented]] |
| | [[Category:Sonifications]] |
| | [[Category:Commas named after their interval size]] |
The 41.059-cent interval of 128/125 is called the diesis or augmented comma; it represents the gap between a stack of three 5/4 just major thirds and the octave, or in other words 2/(5/4)3.
Approximations
This interval is fairly accurately represented by a single step in 28-, 31- or 34edo, and by two steps of 53-, 59- or 65edo. In any tuning with pure octaves and just major thirds, such as quarter-comma meantone, it will be exact. Furthermore, in meantone it appears as the difference between sharps and flats, e.g. between D# and Eb. It is also called enharmonic diesis or enharmonic comma for this reason.
Temperaments
As a comma
Tempering out this comma leads to augmented temperament. See augmented family for the family where it is tempered out.
As an interval
If the diesis is treated as a musical interval in its own right as opposed to tempering it out, it is approximately a quarter-tone and so can be used to introduce 7-limit and 11-limit harmony into 5-limit scales.
Trivia
This interval represents the amount by which the binary definition of kilobyte, 1024 bytes, exceeds the nominal definition of "kilo" prefix, 1000.
See also