Quarter-comma meantone: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 307608164 - Original comment: **
Modern renderings: Add John Bull's ''Fantasia «Ut Re Mi Fa Sol La»'' (late 1500s/early 1600s, from ''Fitzwilliam Virginal Book Vol.1 No.51'') – performed on Cembalo Universale (harpsichord having 19 notes per octave for extended meantone) by Robert Hill (2015)
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{interwiki
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| de = Viertelkomma-mitteltönig
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-03-04 15:16:36 UTC</tt>.<br>
| en = Quarter-comma meantone
: The original revision id was <tt>307608164</tt>.<br>
| es =
: The revision comment was: <tt></tt><br>
| ja =
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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<h4>Original Wikitext content:</h4>
{{Wikipedia}}
<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">Quarter comma meantone is the tuning of [[Meantone family|meantone temperament]] which makes the fifth the fourth root of 5, or in other words 696.578 cents. This means the fifth is flattened by 1/4 of the syntonic comma (81/80 ratio) of 21.506 cents, which is to say by 5.377 cents, hence the name quarter-comma or 1/4-comma meantone. It is also the tuning where the major tone is the exact geometric mean between the greater tone of 9/8 and the lesser tone of 10/9, and hence it can be argued it is the only tuning which is strictly "mean tone". It is the minimax tuning for 5-limit meantone, meaning the maximum error on the 5-limit [[Diamonds|diamond]] is minimized. It is also the minimax tuning for septimal meantone in the 7- and 9-limit odd limits, and for meanpop, the version of 11-limit meantone which tunes 11/8 to the doubly diminished fifth, C-Gbb. Moreover, historically it was the predominant tuning of Western common-practice music in the latter part of the Renaissance and the early modern (17th century) era.
'''Quarter-comma meantone''' is the tuning of [[meantone]] temperament which makes the perfect fifth ([[3/2]]) the fourth root of 5, or in other words 696.578&nbsp;[[cent]]s. This means the fifth is flattened by {{frac|1|4}} of the syntonic comma ([[81/80]] ratio) of 21.506{{cent}}, which is to say by 5.377{{cent}}, hence the name.  


Because of all of these features, it has a certain claim to be considered the canonical meantone tuning and often "meantone" is taken to mean quarter-comma specifically. The traditional interval names, listed below, may be considered to have their older traditional tuning in the quarter-comma meantone tunings listed below. However, other tunings (besides [[12edo]] which is ubiquitous but not an especially good tuning for meantone) may be preferred. Note, for instance, that the doubly augmented second and the doubly diminished fourth are both neutral thirds, about six cents apart. If we want a tuning which will equate the two, we need to use [[31edo]] instead.
Quarter-comma meantone is the tuning where the major third ([[5/4]]) is tuned pure, and the minor third ([[6/5]]) and the fifth are equally flat by {{frac|1|4}} syntonic comma. It is also the tuning where the whole tone is the exact [[geometric mean]] between the greater tone of [[9/8]] and the lesser tone of [[10/9]] (the "semiptolemaic major second" sqrt(5/4)), from which the term "meantone" is derived, and many argue that it is the only tuning which is strictly "mean tone". It is the minimax tuning for 5-limit meantone, meaning the maximum error on the [[5-odd-limit]] [[tonality diamond]] is minimized. It is also the minimax tuning for septimal meantone in the [[7-odd-limit|7-]] and [[9-odd-limit]], and for meanpop (the version of 11-limit meantone which tunes 11/8 to the doubly diminished fifth, C–G𝄫) in the [[11-odd-limit]]. Moreover, historically it was the predominant tuning of Western common-practice music in the latter part of the Renaissance and the early modern (17th century) era.


=Intervals of quarter-comma meantone=
Because of all of these features, it has a certain claim to be considered the canonical meantone tuning and often "meantone" is taken to mean quarter-comma specifically. The traditional interval names, listed below, may be considered to have their older traditional tuning in the quarter-comma meantone tunings listed below. However, other tunings (besides [[12edo]] which is ubiquitous but not an especially good tuning for meantone) may be preferred. Note, for instance, that the doubly augmented second and the doubly diminished fourth are both neutral thirds, about 6{{c}} apart. In [[31edo]], these two intervals are enharmonically equivalent.
Below is a table listing 36 of the notes of quarter-comma meantone, giving the size in cents, the number of fifths up or down on the [[chain of fifths]], the [[http://en.wikipedia.org/wiki/Letter_notation|letter notation]] for the interval relative to C as the tonic, the traditional name for the interval, a shorthand form of the name, and the size of the interval in [[Fractional monzos|fractional monzo]] notation.


||~ Size
== Tuning profile ==
in [[cent]]s ||~ Fifths
[[Projection map]]:  
dist. ||~ Note
C-based ||~ Traditional
Interval name ||~ Int.
(short) ||~ Fract.
[[Fractional monzos|Monzo]] ||
||= 0 ||= 0 || C || Unison ||= P1 || [0 0 0&gt; ||
|| 41.0590 ||= -12 || Dbb || Diminished second, diesis ||= d2 || [7 0 -3&gt; ||
|| 76.0490 ||= 7 || C# || Augmented unison, chromatic semitone ||= A1 || [-4 0 7/4&gt; ||
|| 117.108 ||= -5 || Db || Minor second, diatonic semitone ||= m2 || [3 0 -5/4&gt; ||
|| 152.098 ||= 14 || C## || Augmented chromatic semitone ||  || [-8 0 7/2&gt; ||
|| 158.167 ||= -17 || Ebbb || Doubly diminished third ||  || [10 0 -17/4&gt; ||
|| 193.157 ||= 2 || D || Major second ||= M2 || [-1 0 1/2&gt; ||
|| 234.216 ||= -10 || Ebb || Diminished third ||= d3 || [6 0 -5/2&gt; ||
|| 269.206 ||= 9 || D# || Augmented second ||= A2 || [-5 0 9/4&gt; ||
|| 310.265 ||= -3 || Eb || Minor third ||= m3 || [2 0 -3/4&gt; ||
|| 345.255 ||= 16 || D## || Doubly augmented second ||  || [-9 0 4&gt; ||
|| 351.324 ||= -15 || Fbb || Doubly diminished fourth ||  || [9 0 -15/4&gt; ||
|| 386.314 ||= 4 || E || Major third ||= M3 || [-2 0 1&gt; ||
|| 427.373 ||= -8 || Fb || Diminished fourth ||= d4 || [5 0 -2&gt; ||
|| 462.363 ||= 11 || E# || Augmented third ||= A3 || [-6 0 11/4&gt; ||
|| 503.422 ||= -1 || F || "Perfect" fourth ||= P4 || [1 0 -1/4&gt; ||
|| 544.480 ||= -13 || Gbb || Doubly diminished fifth ||  || [8 0 -13/4&gt; ||
|| 579.471 ||= 6 || F# || Augmented fourth ||= A4 || [-3 0 3/2&gt; ||
|| 620.529 ||= -6 || Gb || Diminished fifth ||= d5 || [4 0 -3/2&gt; ||
|| 655.520 ||= 13 || F## || Doubly augmented fourth ||  || [-7 0 13/4&gt; ||
|| 696.578 ||= 1 || G || "Perfect" fifth ||= P5 || [0 0 1/4&gt; ||
|| 737.637 ||= -11 || Abb || Diminshed sixth ||= d6 || [7 0 -11/4&gt; ||
|| 772.627 ||= 8 || G# || Augmented fifth ||= A5 || [-4 0 2&gt; ||
|| 813.686 ||= -4 || Ab || Minor sixth ||= m6 || [3 0 -1&gt; ||
|| 848.676 ||= 15 || G## || Doubly augmented fifth ||  || [-8 0 15/4&gt; ||
|| 854.745 ||= -16 || Bbbb || Doubly diminished seventh ||  || [10 0 -4&gt; ||
|| 889.735 ||= 3 || A || Major sixth ||= M6 || [-1 0 3/4&gt; ||
|| 930.794 ||= -9 || Bbb || Diminished seventh ||= d7 || [6 0 -9/4&gt; ||
|| 965.784 ||= 10 || A# || Augmented sixth ||= A6 || [-5 0 5/2&gt; ||
|| 1006.84 ||= -2 || Bb || Minor seventh ||= m7 || [2 0 -1/2&gt; ||
|| 1041.83 ||= 17 || A## || Doubly augmented sixth ||  || [-9 0 17/4&gt; ||
|| 1047.90 ||= -14 || C'bb || Doubly diminished octave ||  || [9 0 -7/2&gt; ||
|| 1082.89 ||= 5 || B || Major seventh ||= M7 || [-2 0 5/4&gt; ||
|| 1123.95 ||= -7 || C'b || Diminished octave ||= d8 || [5 0 -7/4&gt; ||
|| 1158.94 ||= 12 || B# || Augmented seventh ||= A7 || [-6 0 3&gt; ||
||= 1200 ||= 0 || C' || Perfect octave ||= P8 || [1 0 0&gt; ||
[[media type="custom" key="11601270"]]
See [[http://en.wikipedia.org/wiki/Quarter-comma_meantone|Quarter-comma meantone]]


==Music==
{| class="right-all"
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/reelrock.mp3|Reelin' and Rockin']] by [[http://en.wikipedia.org/wiki/Chuck_Berry|Chuck Berry]]
|-
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/Le%20Tic-Toc%20Choc.mp3|Le Tic-Toc Choc]] by [[http://en.wikipedia.org/wiki/Fran%C3%A7ois_Couperin|François Couperin]]
| [⟨ || 1 || 1 || 0 || -3 || ]
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/Prelude%20in%20g%20Op%2023%20%235.mp3|Prelude in g minor Op 23 #5]] by [[http://en.wikipedia.org/wiki/Sergei_Rachmaninoff|Sergei Rachmaninoff]]
|-
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/At%20the%20Hop.mp3|At the Hop]] by [[http://en.wikipedia.org/wiki/Arthur_Singer|Singer]], [[http://en.wikipedia.org/wiki/John_Medora|Medora]] and [[http://en.wikipedia.org/wiki/David_White_%28musician%29|White]]
| ⟨ || 0 || 0 || 0 || 0 || ]
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/Meistersinger%20Prelude.mp3|Prelude to Die Meistersinger von Nürnberg]] by [[http://en.wikipedia.org/wiki/Richard_Wagner|Richard Wagner]]
|-
[[http://www.youtube.com/watch?v=b68Ek5hDgDo|Laura che il verde lauro]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/Nicola%20Vicentino%20%281511-%20c.1576%29%20-%20Laura%20che%20il%20verde%20lauro.mp3|play]] by [[http://en.wikipedia.org/wiki/Nicola_Vicentino|Nicola Vicentino]]
| || 0 || 1/4 || 1 || 5/2 || ]
[[http://youtu.be/6t5PdeC1Trw|Country Bumpkin]] by [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/Country%20Bumpkin%20Live%20At%20The%20Turks%2023,9,2010ce.mp3|play]] [[Mark Allan Barnes]]
|-
Five canons by [[Claudi Meneghin]]:
| ⟨ || 0 || 0 || 0 || 0 || ]]
[[http://www.youtube.com/watch?v=AyEpCWkxSsM|Canon 2 in 1 in F at the octave]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Claudi%20Meneghin_%20Canon%202%20in%201%20in%20F%20at%20the%20octave.mp3|play]]
|}
[[http://www.youtube.com/watch?v=IwE9scGcU90|Canon 2 in 1 in A- upon a ground]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Claudi%20Meneghin_%20Canon%202%20in%201%20in%20A-%20upon%20a%20ground.mp3|play]]
[[http://www.youtube.com/watch?v=zwKeFLgbngY|Canon 2 in 1 in G- at the major seventh]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Claudi%20Meneghin_%20Canon%202%20in%201%20in%20G-%20at%20the%20major%20seventh.mp3|play]]
[[http://www.youtube.com/watch?v=mEeKltGny04|Canon at the minor second on an ancient Padanian folk theme]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Claudi%20Meneghin_%20Canon%20at%20the%20minor%20second%20on%20an%20ancient%20Pad.mp3|play]]
[[http://www.youtube.com/watch?v=6_YVhwArGTI|Canon 2 in 1 on "Ah! vous dirai-je, maman" at the diminished fifth]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Claudi%20Meneghin_%20Canon%202%20in%201%20on%20_Ah_%20vous%20dirai-je,%20maman_%20.mp3|play]]
[[http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Ricercar%20a%206/Quarter-comma-meantone.mp3|Bach's Ricercar a 6 from A Musical Offering]] rendered by Claudi Meneghin
[[http://micro.soonlabel.com/quarter-comma-meantone/its-a-quarter-of-a-mean-tone.mp3|A Quarter of a Mean Tone]] by [[Chris Vaisvil]]</pre></div>
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Quarter-comma meantone&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Quarter comma meantone is the tuning of &lt;a class="wiki_link" href="/Meantone%20family"&gt;meantone temperament&lt;/a&gt; which makes the fifth the fourth root of 5, or in other words 696.578 cents. This means the fifth is flattened by 1/4 of the syntonic comma (81/80 ratio) of 21.506 cents, which is to say by 5.377 cents, hence the name quarter-comma or 1/4-comma meantone. It is also the tuning where the major tone is the exact geometric mean between the greater tone of 9/8 and the lesser tone of 10/9, and hence it can be argued it is the only tuning which is strictly &amp;quot;mean tone&amp;quot;. It is the minimax tuning for 5-limit meantone, meaning the maximum error on the 5-limit &lt;a class="wiki_link" href="/Diamonds"&gt;diamond&lt;/a&gt; is minimized. It is also the minimax tuning for septimal meantone in the 7- and 9-limit odd limits, and for meanpop, the version of 11-limit meantone which tunes 11/8 to the doubly diminished fifth, C-Gbb. Moreover, historically it was the predominant tuning of Western common-practice music in the latter part of the Renaissance and the early modern (17th century) era.&lt;br /&gt;
&lt;br /&gt;
Because of all of these features, it has a certain claim to be considered the canonical meantone tuning and often &amp;quot;meantone&amp;quot; is taken to mean quarter-comma specifically. The traditional interval names, listed below, may be considered to have their older traditional tuning in the quarter-comma meantone tunings listed below. However, other tunings (besides &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; which is ubiquitous but not an especially good tuning for meantone) may be preferred. Note, for instance, that the doubly augmented second and the doubly diminished fourth are both neutral thirds, about six cents apart. If we want a tuning which will equate the two, we need to use &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; instead.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Intervals of quarter-comma meantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;Intervals of quarter-comma meantone&lt;/h1&gt;
Below is a table listing 36 of the notes of quarter-comma meantone, giving the size in cents, the number of fifths up or down on the &lt;a class="wiki_link" href="/chain%20of%20fifths"&gt;chain of fifths&lt;/a&gt;, the &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Letter_notation" rel="nofollow"&gt;letter notation&lt;/a&gt; for the interval relative to C as the tonic, the traditional name for the interval, a shorthand form of the name, and the size of the interval in &lt;a class="wiki_link" href="/Fractional%20monzos"&gt;fractional monzo&lt;/a&gt; notation.&lt;br /&gt;
&lt;br /&gt;


[[Tuning map]]: {{val| 1200 1896.5784 2786.3137 3365.7843 }}


&lt;table class="wiki_table"&gt;
[[Error map]]: {{val| 0 -5.3766 0 -3.0416 }}
    &lt;tr&gt;
        &lt;th&gt;Size&lt;br /&gt;
in &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Fifths&lt;br /&gt;
dist.&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Note&lt;br /&gt;
C-based&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Traditional&lt;br /&gt;
Interval name&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Int.&lt;br /&gt;
(short)&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Fract.&lt;br /&gt;
&lt;a class="wiki_link" href="/Fractional%20monzos"&gt;Monzo&lt;/a&gt;&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Unison&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;P1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[0 0 0&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;41.0590&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;-12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Dbb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Diminished second, diesis&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;d2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[7 0 -3&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;76.0490&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Augmented unison, chromatic semitone&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[-4 0 7/4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;117.108&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;-5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Db&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Minor second, diatonic semitone&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;m2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[3 0 -5/4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;152.098&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C##&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Augmented chromatic semitone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[-8 0 7/2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;158.167&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;-17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ebbb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Doubly diminished third&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[10 0 -17/4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;193.157&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;D&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Major second&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;M2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[-1 0 1/2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;234.216&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;-10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ebb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Diminished third&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;d3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[6 0 -5/2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;269.206&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;D#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Augmented second&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[-5 0 9/4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;310.265&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;-3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Eb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Minor third&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;m3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[2 0 -3/4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;345.255&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;D##&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Doubly augmented second&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[-9 0 4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;351.324&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;-15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Fbb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Doubly diminished fourth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9 0 -15/4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;386.314&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;E&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Major third&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;M3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[-2 0 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;427.373&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;-8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Fb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Diminished fourth&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;d4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[5 0 -2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;462.363&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;E#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Augmented third&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[-6 0 11/4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;503.422&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;-1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;F&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;quot;Perfect&amp;quot; fourth&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[1 0 -1/4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;544.480&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;-13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gbb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Doubly diminished fifth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[8 0 -13/4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;579.471&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;F#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Augmented fourth&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[-3 0 3/2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;620.529&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;-6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Diminished fifth&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;d5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[4 0 -3/2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;655.520&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;F##&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Doubly augmented fourth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[-7 0 13/4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;696.578&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;quot;Perfect&amp;quot; fifth&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;P5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[0 0 1/4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;737.637&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;-11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Abb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Diminshed sixth&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;d6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[7 0 -11/4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;772.627&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Augmented fifth&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[-4 0 2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;813.686&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;-4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ab&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Minor sixth&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;m6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[3 0 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;848.676&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G##&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Doubly augmented fifth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[-8 0 15/4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;854.745&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;-16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Bbbb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Doubly diminished seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[10 0 -4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;889.735&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Major sixth&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;M6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[-1 0 3/4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;930.794&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;-9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Bbb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Diminished seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;d7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[6 0 -9/4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;965.784&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Augmented sixth&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[-5 0 5/2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1006.84&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;-2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Bb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Minor seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;m7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[2 0 -1/2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1041.83&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A##&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Doubly augmented sixth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[-9 0 17/4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1047.90&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;-14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C'bb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Doubly diminished octave&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[9 0 -7/2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1082.89&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;B&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Major seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;M7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[-2 0 5/4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1123.95&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;-7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C'b&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Diminished octave&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;d8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[5 0 -7/4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1158.94&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;B#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Augmented seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[-6 0 3&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;1200&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C'&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Perfect octave&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;P8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;[1 0 0&amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/11601270?h=0&amp;amp;w=0&amp;quot; class=&amp;quot;WikiMedia WikiMediaCustom&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;custom&amp;amp;quot; key=&amp;amp;quot;11601270&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;script type="text/javascript" src="http://mediaplayer.yahoo.com/js"&gt;
== Intervals of quarter-comma meantone ==
&lt;/script&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;&lt;br /&gt;
Below is a table listing 36 of the notes of quarter-comma meantone, giving the size in cents, the number of fifths up or down on the [[chain of fifths]], the {{w|letter notation}} for the interval relative to C as the tonic, the traditional name for the interval, a shorthand form of the name, and the size of the interval in [[fractional monzo]] notation.
See &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Quarter-comma_meantone" rel="nofollow"&gt;Quarter-comma meantone&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
{| class="wikitable right-1 center-2 center-5"
&lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Intervals of quarter-comma meantone-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;Music&lt;/h2&gt;
|-
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/reelrock.mp3" rel="nofollow"&gt;Reelin' and Rockin'&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Chuck_Berry" rel="nofollow"&gt;Chuck Berry&lt;/a&gt;&lt;br /&gt;
! Size<br />in [[cent]]s
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/Le%20Tic-Toc%20Choc.mp3" rel="nofollow"&gt;Le Tic-Toc Choc&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Fran%C3%A7ois_Couperin" rel="nofollow"&gt;François Couperin&lt;/a&gt;&lt;br /&gt;
! Fifths<br />dist.
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/Prelude%20in%20g%20Op%2023%20%235.mp3" rel="nofollow"&gt;Prelude in g minor Op 23 #5&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Sergei_Rachmaninoff" rel="nofollow"&gt;Sergei Rachmaninoff&lt;/a&gt;&lt;br /&gt;
! Note<br />C-based
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/At%20the%20Hop.mp3" rel="nofollow"&gt;At the Hop&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Arthur_Singer" rel="nofollow"&gt;Singer&lt;/a&gt;, &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/John_Medora" rel="nofollow"&gt;Medora&lt;/a&gt; and &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/David_White_%28musician%29" rel="nofollow"&gt;White&lt;/a&gt;&lt;br /&gt;
! Traditional<br />interval name
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/Meistersinger%20Prelude.mp3" rel="nofollow"&gt;Prelude to Die Meistersinger von Nürnberg&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Richard_Wagner" rel="nofollow"&gt;Richard Wagner&lt;/a&gt;&lt;br /&gt;
! Int.<br />(short)
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=b68Ek5hDgDo" rel="nofollow"&gt;Laura che il verde lauro&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/Nicola%20Vicentino%20%281511-%20c.1576%29%20-%20Laura%20che%20il%20verde%20lauro.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Nicola_Vicentino" rel="nofollow"&gt;Nicola Vicentino&lt;/a&gt;&lt;br /&gt;
! [[Fractional monzo|Fract.<br />monzo]]
&lt;a class="wiki_link_ext" href="http://youtu.be/6t5PdeC1Trw" rel="nofollow"&gt;Country Bumpkin&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/Country%20Bumpkin%20Live%20At%20The%20Turks%2023,9,2010ce.mp3" rel="nofollow"&gt;play&lt;/a&gt; &lt;a class="wiki_link" href="/Mark%20Allan%20Barnes"&gt;Mark Allan Barnes&lt;/a&gt;&lt;br /&gt;
|-
Five canons by &lt;a class="wiki_link" href="/Claudi%20Meneghin"&gt;Claudi Meneghin&lt;/a&gt;:&lt;br /&gt;
| 0.00000
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=AyEpCWkxSsM" rel="nofollow"&gt;Canon 2 in 1 in F at the octave&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Claudi%20Meneghin_%20Canon%202%20in%201%20in%20F%20at%20the%20octave.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;br /&gt;
| 0
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=IwE9scGcU90" rel="nofollow"&gt;Canon 2 in 1 in A- upon a ground&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Claudi%20Meneghin_%20Canon%202%20in%201%20in%20A-%20upon%20a%20ground.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;br /&gt;
| C
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=zwKeFLgbngY" rel="nofollow"&gt;Canon 2 in 1 in G- at the major seventh&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Claudi%20Meneghin_%20Canon%202%20in%201%20in%20G-%20at%20the%20major%20seventh.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;br /&gt;
| Unison
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=mEeKltGny04" rel="nofollow"&gt;Canon at the minor second on an ancient Padanian folk theme&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Claudi%20Meneghin_%20Canon%20at%20the%20minor%20second%20on%20an%20ancient%20Pad.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;br /&gt;
| P1
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=6_YVhwArGTI" rel="nofollow"&gt;Canon 2 in 1 on &amp;quot;Ah! vous dirai-je, maman&amp;quot; at the diminished fifth&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Claudi%20Meneghin_%20Canon%202%20in%201%20on%20_Ah_%20vous%20dirai-je,%20maman_%20.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;br /&gt;
| {{monzo| 0 0 0 }}
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Ricercar%20a%206/Quarter-comma-meantone.mp3" rel="nofollow"&gt;Bach's Ricercar a 6 from A Musical Offering&lt;/a&gt; rendered by Claudi Meneghin&lt;br /&gt;
|-
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/quarter-comma-meantone/its-a-quarter-of-a-mean-tone.mp3" rel="nofollow"&gt;A Quarter of a Mean Tone&lt;/a&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
| 41.0590
| −12
| Dbb
| Diminished second, diesis
| d2
| {{monzo| 7 0 -3 }}
|-
| 76.0490
| 7
| C#
| Augmented unison, chromatic semitone
| A1
| {{monzo| -4 0 7/4 }}
|-
| 117.108
| -5
| Db
| Minor second, diatonic semitone
| m2
| {{monzo| 3 0 -5/4 }}
|-
| 152.098
| 14
| Cx
| Doubly augmented unison, augmented chromatic semitone
| AA1
| {{monzo| -8 0 7/2 }}
|-
| 158.167
| −17
| Ebbb
| Doubly diminished third
| dd3
| {{monzo| 10 0 -17/4 }}
|-
| 193.157
| 2
| D
| Major second
| M2
| {{monzo| -1 0 1/2 }}
|-
| 234.216
| −10
| Ebb
| Diminished third
| d3
| {{monzo| 6 0 -5/2 }}
|-
| 269.206
| 9
| D#
| Augmented second
| A2
| {{monzo| -5 0 9/4 }}
|-
| 310.265
| −3
| Eb
| Minor third
| m3
| {{monzo| 2 0 -3/4 }}
|-
| 345.255
| 16
| Dx
| Doubly augmented second
| AA2
| {{monzo| -9 0 4 }}
|-
| 351.324
| −15
| Fbb
| Doubly diminished fourth
| dd4
| {{monzo| 9 0 -15/4 }}
|-
| 386.314
| 4
| E
| Major third
| M3
| {{monzo| -2 0 1 }}
|-
| 427.373
| −8
| Fb
| Diminished fourth
| d4
| {{monzo| 5 0 -2 }}
|-
| 462.363
| 11
| E#
| Augmented third
| A3
| {{monzo| -6 0 11/4 }}
|-
| 503.422
| −1
| F
| Perfect fourth
| P4
| {{monzo| 1 0 -1/4 }}
|-
| 544.480
| −13
| Gbb
| Doubly diminished fifth
| dd5
| {{monzo| 8 0 -13/4 }}
|-
| 579.471
| 6
| F#
| Augmented fourth
| A4
| {{monzo| -3 0 3/2 }}
|-
| 620.529
| −6
| Gb
| Diminished fifth
| d5
| {{monzo| 4 0 -3/2 }}
|-
| 655.520
| 13
| Fx
| Doubly augmented fourth
| AA4
| {{monzo| -7 0 13/4 }}
|-
| 696.578
| 1
| G
| Perfect fifth
| P5
| {{monzo| 0 0 1/4 }}
|-
| 737.637
| −11
| Abb
| Diminished sixth
| d6
| {{monzo| 7 0 -11/4 }}
|-
| 772.627
| 8
| G#
| Augmented fifth
| A5
| {{monzo| -4 0 2 }}
|-
| 813.686
| −4
| Ab
| Minor sixth
| m6
| {{monzo| 3 0 -1 }}
|-
| 848.676
| 15
| Gx
| Doubly augmented fifth
| AA5
| {{monzo| -8 0 15/4 }}
|-
| 854.745
| −16
| Bbbb
| Doubly diminished seventh
| dd7
| {{monzo| 10 0 -4 }}
|-
| 889.735
| 3
| A
| Major sixth
| M6
| {{monzo| -1 0 3/4 }}
|-
| 930.794
| -9
| Bbb
| Diminished seventh
| d7
| {{monzo| 6 0 -9/4 }}
|-
| 965.784
| 10
| A#
| Augmented sixth
| A6
| {{monzo| -5 0 5/2 }}
|-
| 1006.84
| −2
| Bb
| Minor seventh
| m7
| {{monzo| 2 0 -1/2 }}
|-
| 1041.83
| 17
| Ax
| Doubly augmented sixth
| AA6
| {{monzo| -9 0 17/4 }}
|-
| 1047.90
| −14
| C'bb
| Doubly diminished octave
| dd8
| {{monzo| 9 0 -7/2 }}
|-
| 1082.89
| 5
| B
| Major seventh
| M7
| {{monzo| -2 0 5/4 }}
|-
| 1123.95
| −7
| C'b
| Diminished octave
| d8
| {{monzo| 5 0 -7/4 }}
|-
| 1158.94
| 12
| B#
| Augmented seventh
| A7
| {{monzo| -6 0 3 }}
|-
| 1200.00
| 0
| C'
| Perfect octave
| P8
| {{monzo| 1 0 0 }}
|}
 
== Music ==
=== Modern renderings ===
; {{W|Johann Sebastian Bach}}
* [https://web.archive.org/web/20201127013537/http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Ricercar%20a%206/Quarter-comma-meantone.mp3 ''Bach's Ricercar a 6 from A Musical Offering''] rendered by Claudi Meneghin
* [https://www.youtube.com/watch?v=2osCf4AQ_0k ''Praeludium et fuga in G, BWV 541'' - J S Bach, in meantone temperament] (late 1500s &ndash; early 1600s; performed on quarter-comma meantone pipe organ by Helena Holmlund, recorded 2013)
 
; {{W|Chuck Berry}}
* [https://web.archive.org/web/20201127012202/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/reelrock.mp3 ''Reelin' and Rockin'''] (1957)
 
; {{W|John Bull (composer)|John Bull}}
* [https://www.youtube.com/watch?v=hpDkbRpxwKw ''Fantasia «Ut Re Mi Fa Sol La»''] (late 1500s/early 1600s, from ''Fitzwilliam Virginal Book Vol.1 No.51'') – performed on Cembalo Universale (harpsichord having 19 notes per octave for extended meantone) by {{W|Robert_Hill_(musician)|Robert Hill}} (2015)
 
; [[Giovanni Pietro Del Buono]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/quartercomma/Giovanni%20Pietro%20Del%20Buono-%20Tre%20Sonate%20Sopra%20Ave%20Maris%20Stella%20(V,%20VI,%20VII).mp3 ''Tre Sonate Sopra Ave Maris Stella'' (V, VI, VII)] (''c''. 1641–1644)
 
; {{W|Dieterich Buxtehude}}
* [https://www.youtube.com/watch?v=SR0gWBjdzsA ''Magnificat primi toni'' BuxWv 203] (c. 1690; performed on quarter-comma meantone pipe organ by Helena Holmlund, recorded 2013)
 
; {{W|François Couperin}}
* [https://web.archive.org/web/20201127015607/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/Le%20Tic-Toc%20Choc.mp3 ''Le Tic-Toc Choc''] (1722)
 
; {{W|Ferenc Farkas}}
* [https://www.youtube.com/watch?v=SkZ2FDXMzlA ''The 1699 Meantone Organ from Rupea at the Black Church in Brasov | Farkas Ferenc Hungarian Dances''] (1961; performed in 2024 by {{W|Bálint Karosi}})
 
; {{W|Sergei Rachmaninoff}}
* [https://web.archive.org/web/20201127014732/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/Prelude%20in%20g%20Op%2023%20%235.mp3 ''Prelude in g minor'' Op. 23 #5] (1901)
 
; {{W|Arthur Singer}}, {{w|John Medora}} and {{w|David White %28musician%29|David White}}
* [https://web.archive.org/web/20201127014551/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/At%20the%20Hop.mp3 ''At the Hop''] (1957)
 
; {{W|Jan Pieterszoon Sweelinck}}
* [https://www.youtube.com/watch?v=-_z6lhgLNJI&list=WL&index=238 ''Fantasia chromatica by Sweelinck'', in meantone temperament] (late 1500s &ndash; early 1600s; performed on quarter-comma meantone pipe organ by Helena Holmlund, recorded 2013)
 
; {{W|Richard Wagner}}
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/Meistersinger%20Prelude.mp3 "Prelude" to ''Die Meistersinger von Nürnberg''] (1868)
 
; {{W|Nicola Vicentino}}
* [https://www.youtube.com/watch?v=b68Ek5hDgDo ''Laura che il verde lauro'']{{dead link}} [https://web.archive.org/web/20201127014948/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/Nicola%20Vicentino%20(1511-%20c.1576)%20-%20Laura%20che%20il%20verde%20lauro.mp3 play]
 
=== 21st century ===
; [[Mark Allan Barnes]]
* [https://youtu.be/6t5PdeC1Trw ''Country Bumpkin''] (2010) [https://web.archive.org/web/20201127012811/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/quartercomma/Country%20Bumpkin%20Live%20At%20The%20Turks%2023,9,2010ce.mp3 play]
* [https://www.youtube.com/watch?v=HVwXUwK5_Vg ''Ozone Layer''] (2012) [https://web.archive.org/web/20201127013628/http://micro.soonlabel.com/gene_ward_smith/Others/quartercomma/Ozone%20Layer.mp3 play]
 
; [[Eufalesio]]
* [https://soundcloud.com/eufalesio/procession-for-the-death-of-a-star?in=eufalesio/sets/microtonal-stuff "Procession for the death of a star"] from [https://soundcloud.com/eufalesio/sets/microtonal-stuff ''Microtonal stuff''] (2022)
 
; [[Francium]]
* [https://www.youtube.com/watch?v=5S3NCRNHFzc ''A Meantone Prelude''] (2023)
 
; [[Adam Freese]]
* [https://www.youtube.com/watch?v=S3gnksLkjRw ''Unnamed fugue''] (2023)
 
; [[Claudi Meneghin]]
* ''Five canons'' (2011)
** "Canon 2 in 1 in F at the octave" [https://www.youtube.com/watch?v=AyEpCWkxSsM YouTube] | [https://web.archive.org/web/20201127013925/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Claudi%20Meneghin_%20Canon%202%20in%201%20in%20F%20at%20the%20octave.mp3 play]
** "Canon 2 in 1 in A- upon a ground" [https://web.archive.org/web/20190902004518/http://soonlabel.com/xenharmonic/archives/2089/cm-canon-2-in-1-upon-a-ground-4th-version-edited blog] | [https://web.archive.org/web/20190902003004/http://soonlabel.com/xenharmonic/wp-content/uploads/2013/11/CM-Canon-2-in-1-upon-a-ground-4th-version-edited.mp3 play]
** "Canon 2 in 1 in G- at the major seventh" [https://www.youtube.com/watch?v=zwKeFLgbngY YouTube] | [https://web.archive.org/web/20201127013440/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Claudi%20Meneghin_%20Canon%202%20in%201%20in%20G-%20at%20the%20major%20seventh.mp3 play]
** "Canon at the minor second on an ancient Padanian folk theme" [https://www.youtube.com/watch?v=mEeKltGny04 YouTube] | [https://web.archive.org/web/20201127014141/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Claudi%20Meneghin_%20Canon%20at%20the%20minor%20second%20on%20an%20ancient%20Pad.mp3 play]
** "Canon 2 in 1 on "Ah! vous dirai-je, maman" at the diminished fifth" [https://www.youtube.com/watch?v=6_YVhwArGTI YouTube] | [https://web.archive.org/web/20201127013943/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Claudi%20Meneghin_%20Canon%202%20in%201%20on%20_Ah_%20vous%20dirai-je,%20maman_%20.mp3 play]
 
; [[Norokusi]]
* [https://www.youtube.com/watch?v=ZjJSa9brfSY ''Suite No.6 (2025) for Piano in Quarter-comma Meantone Temperament''] (2025)
* [https://www.youtube.com/watch?v=OZriKGVcXDM ''Ballade No.5 (2025) in C Major for Piano in Quarter-comma Meantone Temperament''] (2025)
 
; [[Juhani Nuorvala]]
* [https://soundcloud.com/juhani-nuorvala/enharmoninen-sarja-enharmonic-suite ''Enharmoninen sarja (Enharmonic Suite)''] (2017, [[Matias Häkkinen]] on harpsichord with 2 split keys per octave, tuned in quarter-comma meantone (C C♯ D D♯ Eb E F F♯ G G♯ A♭ A=415Hz B♭ B)
 
; [[Cam Taylor]]
* [https://www.youtube.com/watch?v=bQcDISy6e4M ''Free jam in 1/4-comma E♭-G♯''] (2024)
 
; [[Chris Vaisvil]]
* [http://micro.soonlabel.com/quarter-comma-meantone/its-a-quarter-of-a-mean-tone.mp3 ''A Quarter of a Mean Tone'']
* ''No Voice Leading'' (2012) [https://chrisvaisvil.com/harpsichord-in-d-minor-in-quarter-comma-meantone-tuning/ blog] | [http://micro.soonlabel.com/quarter-comma-meantone/20120704-harpsichord-quarter-meantone.mp3 play]
 
[[Category:Meantone]]
[[Category:Listen]]
[[Category:Historical]]