Wikispaces>Andrew_Heathwaite |
|
| (30 intermediate revisions by 17 users not shown) |
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox Interval |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | Name = tridecimal minor third, major minthmic minor third |
| : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-01 09:25:47 UTC</tt>.<br>
| | | Color name = 3o1u3, tholu 3rd |
| : The original revision id was <tt>260456498</tt>.<br>
| | | Sound = jid_13_11_pluck_adu_dr220.mp3 |
| : 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>
| |
| <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">In [[13-limit]] [[Just Intonation]], 13/11 is the tridecimal minor third (a Neo-Gothic minor third), measuring about 289.2¢. It is the difference between the 11th and 13th harmonics. The 11th harmonic ([[11_8|11/8]], about 551.3¢) and the 13th harmonic ([[13_8|13/8]], about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third. It can even function as such in a 13-limit [[Neo-Gothic]] minor triad of 22:26:33, with a [[3_2|3/2]] perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant [[16_11|16/11]] in place of 3/2. The latter triad sounds more like a very xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7.
| |
|
| |
|
| 13/11 is the classic [[mediant]] between the simpler and more familiar ratios [[6_5|6/5]] and [[7_6|7/6]], and can be given as (6+7)/(5+6). This puts in between the latter ratios, slightly closer to 7/6. It is [[78_77|78/77]] (about 22.3¢) wider than 7/6 and [[66_65|66/65]] (26.4¢) narrower than 6/5. It is also [[352_351]] (about 4.9¢) narrower than [[32_27|32/27]], the minor third in Pythagorean ([[3-limit]]) tuning. | | In [[13-limit]] [[just intonation]], '''13/11''' is a '''tridecimal minor third''', specifically the '''major minthmic minor third''', measuring about 289.2 [[cent]]s. It is the difference between the [[11/1|11th]] and [[13/1|13th]] [[harmonic]]s. The octave-reduced 11th harmonic ([[11/8]], about 551.3{{c}}) and 13th harmonic ([[13/8]], about 840.5{{c}}) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third – it is a [[352/351|major minthma (352/351)]] narrower than the [[32/27|Pythagorean minor third (32/27)]]. It is the simplest [[neogothic major and minor|neogothic minor third]], and can function as such in a 13-limit neogothic minor triad of [[22:26:33]], with a [[3/2]] perfect fifth between 33 and 22<ref group="note">This is a [[minor minthmic chords|minor minthmic chord]] where 13/11 and [[14/11]] sum to a perfect fifth. Shown here is the simplest JI representation. </ref>. Compare this to 22:26:32 ([[11:13:16]]), which has the much more dissonant [[16/11]] as the outside interval in place of 3/2. The latter triad sounds more like a xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as [[5:6:7]]. |
|
| |
|
| See: [[Gallery of Just Intervals|Gallery of Just Intonation Intervals]], [[gentle chords]], [[List of root-3rd-P5 triads in JI]]
| | 13/11 is the classic [[mediant]] between the simpler and more familiar ratios [[6/5]] and [[7/6]], as it can be given as (6 + 7)/(5 + 6). This puts it in between the latter ratios, slightly closer to 7/6. More complex minor thirds can be generated by taking the mediant between 13/11 and 7/6 (which yields (13 + 7)/(11 + 6) = [[20/17]], the septendecimal subminor third, about 281.4{{c}}) and between 13/11 and 6/5 (which yields (13 + 6)/(11 + 5) = [[19/16]], the overtone minor third of [[19-limit]] JI, about 297.5{{c}}). See the diagram below. |
|
| |
|
| [[http://dkeenan.com/Music/NobleMediant.txt|The Noble Mediant]] (earliest description of 13:11 as the "Neo-Gothic" minor third)</pre></div>
| | {| class="wikitable center-all" |
| <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>13_11</title></head><body>In <a class="wiki_link" href="/13-limit">13-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 13/11 is the tridecimal minor third (a Neo-Gothic minor third), measuring about 289.2¢. It is the difference between the 11th and 13th harmonics. The 11th harmonic (<a class="wiki_link" href="/11_8">11/8</a>, about 551.3¢) and the 13th harmonic (<a class="wiki_link" href="/13_8">13/8</a>, about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third. It can even function as such in a 13-limit <a class="wiki_link" href="/Neo-Gothic">Neo-Gothic</a> minor triad of 22:26:33, with a <a class="wiki_link" href="/3_2">3/2</a> perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant <a class="wiki_link" href="/16_11">16/11</a> in place of 3/2. The latter triad sounds more like a very xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7.<br />
| | ! Subminor and minor third |
| <br />
| | | 7/6 <br> 266.9{{c}} |
| 13/11 is the classic <a class="wiki_link" href="/mediant">mediant</a> between the simpler and more familiar ratios <a class="wiki_link" href="/6_5">6/5</a> and <a class="wiki_link" href="/7_6">7/6</a>, and can be given as (6+7)/(5+6). This puts in between the latter ratios, slightly closer to 7/6. It is <a class="wiki_link" href="/78_77">78/77</a> (about 22.3¢) wider than 7/6 and <a class="wiki_link" href="/66_65">66/65</a> (26.4¢) narrower than 6/5. It is also <a class="wiki_link" href="/352_351">352_351</a> (about 4.9¢) narrower than <a class="wiki_link" href="/32_27">32/27</a>, the minor third in Pythagorean (<a class="wiki_link" href="/3-limit">3-limit</a>) tuning.<br />
| | | colspan="7" | |
| <br />
| | | 6/5 <br> 315.6{{c}} |
| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intonation Intervals</a>, <a class="wiki_link" href="/gentle%20chords">gentle chords</a>, <a class="wiki_link" href="/List%20of%20root-3rd-P5%20triads%20in%20JI">List of root-3rd-P5 triads in JI</a><br /> | | |- |
| <br />
| | ! Interval in between |
| <a class="wiki_link_ext" href="http://dkeenan.com/Music/NobleMediant.txt" rel="nofollow">The Noble Mediant</a> (earliest description of 13:11 as the &quot;Neo-Gothic&quot; minor third)</body></html></pre></div>
| | | |
| | | colspan="3" | << |
| | | [[36/35|36:35]] <br> 48.7{{c}} |
| | | colspan="3" | >> |
| | | |
| | |- |
| | ! |
| | | colspan="9" | |
| | |- |
| | ! Add mediant (13/11) |
| | | 7/6 <br> 266.9{{c}} |
| | | colspan="3" | |
| | | 13/11 <br> 289.2{{c}} |
| | | colspan="3" | |
| | | 6/5 <br> 315.6{{c}} |
| | |- |
| | ! Intervals in between |
| | | |
| | | << |
| | | [[78/77|78:77]] <br> 22.3{{c}} |
| | | >> |
| | | |
| | | << |
| | | [[66/65|66:65]] <br> 26.4{{c}} |
| | | >> |
| | | |
| | |- |
| | ! |
| | | colspan="9" | |
| | |- |
| | ! Add mediants (20/17 and 19/16) |
| | | 7/6 <br> 266.9{{c}} |
| | | |
| | | [[20/17]] <br> 281.4{{c}} |
| | | |
| | | '''13/11''' <br> '''289.2{{c}}''' |
| | | |
| | | [[19/16]] <br> 297.5{{c}} |
| | | |
| | | 6/5 <br> 315.6{{c}} |
| | |- |
| | ! Intervals in between |
| | | |
| | | << [[120/119|120:119]] >> <br> 14.5{{c}} |
| | | |
| | | << [[221/220|221:220]] >> <br> 7.9{{c}} |
| | | |
| | | << [[209/208|209:208]] >> <br> 8.3{{c}} |
| | | |
| | | << [[96/95|96:95]] >> <br> 18.1{{c}} |
| | | |
| | |} |
| | |
| | == Approximation == |
| | This interval is well approximated by [[17edo|4\17]] (282.353 cents), and even better, by [[29edo|7\29]] (289.655 cents). |
| | |
| | {{Interval edo approximation|13/11}} |
| | |
| | == See also == |
| | * [[22/13]] – its [[octave complement]] |
| | * [[33/26]] – its [[fifth complement]] |
| | * [[44/39]] – its [[fourth complement]] |
| | * [[Ed13/11]] |
| | * [[Gallery of just intervals]] |
| | * [[Gentle chords]] |
| | * [[List of root-3rd-P5 triads in JI]] |
| | * [[:File:Ji-13-11-csound-foscil-220hz.mp3]] – another sound example |
| | |
| | == External links == |
| | * [http://dkeenan.com/Music/NobleMediant.txt ''The Noble Mediant''] by Margo Schulter and David Keenan, the earliest description of 13/11 as the "neo-Gothic" minor third |
| | |
| | == Notes == |
| | <references group="note"/> |
| | |
| | [[Category:Third]] |
| | [[Category:Minor third]] |
| | [[Category:Over-11 intervals]] |
| | [[Category:Major minthmic]] |
| | [[Category:Gentle]] |
| | [[Category:Neo-gothic]] |
| | [[Category:Taxicab-2 intervals]] |