Quarter-comma meantone: Difference between revisions

Latest revision as of 18:39, 4 June 2026

English Wikipedia has an article on:

Quarter-comma meantone

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 cents. This means the fifth is flattened by 1⁄4 of the syntonic comma (81/80 ratio) of 21.506 ¢, which is to say by 5.377 ¢, hence the name.

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 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- 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.

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 ¢ apart. In 31edo, these two intervals are enharmonically equivalent.

Tuning profile

Projection map:

[⟨	1	1	0	-3	]
⟨	0	0	0	0	]
⟨	0	1/4	1	5/2	]
⟨	0	0	0	0	]]

Tuning map: ⟨1200 1896.5784 2786.3137 3365.7843]

Error map: ⟨0 -5.3766 0 -3.0416]

Intervals of quarter-comma meantone

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 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.

Size in cents	Fifths dist.	Note C-based	Traditional interval name	Int. (short)	Fract. monzo
0.00000	0	C	Unison	P1	[0 0 0⟩
41.0590	−12	Dbb	Diminished second, diesis	d2	[7 0 -3⟩
76.0490	7	C#	Augmented unison, chromatic semitone	A1	[-4 0 7/4⟩
117.108	-5	Db	Minor second, diatonic semitone	m2	[3 0 -5/4⟩
152.098	14	Cx	Doubly augmented unison, augmented chromatic semitone	AA1	[-8 0 7/2⟩
158.167	−17	Ebbb	Doubly diminished third	dd3	[10 0 -17/4⟩
193.157	2	D	Major second	M2	[-1 0 1/2⟩
234.216	−10	Ebb	Diminished third	d3	[6 0 -5/2⟩
269.206	9	D#	Augmented second	A2	[-5 0 9/4⟩
310.265	−3	Eb	Minor third	m3	[2 0 -3/4⟩
345.255	16	Dx	Doubly augmented second	AA2	[-9 0 4⟩
351.324	−15	Fbb	Doubly diminished fourth	dd4	[9 0 -15/4⟩
386.314	4	E	Major third	M3	[-2 0 1⟩
427.373	−8	Fb	Diminished fourth	d4	[5 0 -2⟩
462.363	11	E#	Augmented third	A3	[-6 0 11/4⟩
503.422	−1	F	Perfect fourth	P4	[1 0 -1/4⟩
544.480	−13	Gbb	Doubly diminished fifth	dd5	[8 0 -13/4⟩
579.471	6	F#	Augmented fourth	A4	[-3 0 3/2⟩
620.529	−6	Gb	Diminished fifth	d5	[4 0 -3/2⟩
655.520	13	Fx	Doubly augmented fourth	AA4	[-7 0 13/4⟩
696.578	1	G	Perfect fifth	P5	[0 0 1/4⟩
737.637	−11	Abb	Diminished sixth	d6	[7 0 -11/4⟩
772.627	8	G#	Augmented fifth	A5	[-4 0 2⟩
813.686	−4	Ab	Minor sixth	m6	[3 0 -1⟩
848.676	15	Gx	Doubly augmented fifth	AA5	[-8 0 15/4⟩
854.745	−16	Bbbb	Doubly diminished seventh	dd7	[10 0 -4⟩
889.735	3	A	Major sixth	M6	[-1 0 3/4⟩
930.794	-9	Bbb	Diminished seventh	d7	[6 0 -9/4⟩
965.784	10	A#	Augmented sixth	A6	[-5 0 5/2⟩
1006.84	−2	Bb	Minor seventh	m7	[2 0 -1/2⟩
1041.83	17	Ax	Doubly augmented sixth	AA6	[-9 0 17/4⟩
1047.90	−14	C'bb	Doubly diminished octave	dd8	[9 0 -7/2⟩
1082.89	5	B	Major seventh	M7	[-2 0 5/4⟩
1123.95	−7	C'b	Diminished octave	d8	[5 0 -7/4⟩
1158.94	12	B#	Augmented seventh	A7	[-6 0 3⟩
1200.00	0	C'	Perfect octave	P8	[1 0 0⟩

Music

Modern renderings

Johann Sebastian Bach

Bach's Ricercar a 6 from A Musical Offering rendered by Claudi Meneghin
Praeludium et fuga in G, BWV 541 - J S Bach, in meantone temperament (late 1500s – early 1600s; performed on quarter-comma meantone pipe organ by Helena Holmlund, recorded 2013)

Chuck Berry

Reelin' and Rockin' (1957)

John Bull

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)

Giovanni Pietro Del Buono

Tre Sonate Sopra Ave Maris Stella (V, VI, VII) (c. 1641–1644)

Dieterich Buxtehude

Magnificat primi toni BuxWv 203 (c. 1690; performed on quarter-comma meantone pipe organ by Helena Holmlund, recorded 2013)

François Couperin

Le Tic-Toc Choc (1722)

Ferenc Farkas

The 1699 Meantone Organ from Rupea at the Black Church in Brasov | Farkas Ferenc Hungarian Dances (1961; performed in 2024 by Bálint Karosi)

Sergei Rachmaninoff

Prelude in g minor Op. 23 #5 (1901)

Arthur Singer, John Medora and David White

At the Hop (1957)

Jan Pieterszoon Sweelinck

Fantasia chromatica by Sweelinck, in meantone temperament (late 1500s – early 1600s; performed on quarter-comma meantone pipe organ by Helena Holmlund, recorded 2013)

Richard Wagner

"Prelude" to Die Meistersinger von Nürnberg (1868)

Nicola Vicentino

Laura che il verde lauro^{[dead link]} play

21st century

Mark Allan Barnes

Country Bumpkin (2010) play
Ozone Layer (2012) play

Eufalesio

"Procession for the death of a star" from Microtonal stuff (2022)

Francium

A Meantone Prelude (2023)

Adam Freese

Unnamed fugue (2023)

Claudi Meneghin

Five canons (2011)
- "Canon 2 in 1 in F at the octave" YouTube | play
- "Canon 2 in 1 in A- upon a ground" blog | play
- "Canon 2 in 1 in G- at the major seventh" YouTube | play
- "Canon at the minor second on an ancient Padanian folk theme" YouTube | play
- "Canon 2 in 1 on "Ah! vous dirai-je, maman" at the diminished fifth" YouTube | play

Norokusi

Juhani Nuorvala

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

Free jam in 1/4-comma E♭-G♯ (2024)

Chris Vaisvil

A Quarter of a Mean Tone
No Voice Leading (2012) blog | play

Quarter-comma meantone: Difference between revisions

Latest revision as of 18:39, 4 June 2026

Contents

Tuning profile

Intervals of quarter-comma meantone

Music

Modern renderings

21st century

Navigation menu

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{interwiki
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+| de = Viertelkomma-mitteltönig
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-12 03:05:28 UTC</tt>.<br>
+| en = Quarter-comma meantone
-: The original revision id was <tt>236015330</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>
+}}
-<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 696.478 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 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.
-|| 0. || 0 || C || Unison || P1 || [0 0 0&gt; ||
+== Tuning profile ==
-|| 41.0590 || -12 || Dbb || Diminished second, diesis || d2 || [7 0 -3&gt; ||
+[[Projection map]]:
-|| 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; ||
-|| 1006.843 || -2 || Bb || Minor seventh || m7 || [2 0 -1/2&gt; ||
-|| 1041.833 || 17 || A## || Doubly augmented sixth || || [-9 0 17/4&gt; ||
-|| 1047.902 || -14 || C'bb || Doubly diminished octave || || [9 0 -7/2&gt; ||
-|| 1082.892 || 5 || B || Major seventh || M7 || [-2 0 5/4&gt; ||
-|| 1123.951 || -7 || C'b || Diminished octave || d8 || [5 0 -7/4&gt; ||
-|| 1158.941 || 12 || B# || Augmented seventh || A7 || [-6 0 3&gt; ||
-|| 1200.000 || 0 || C' || Perfect octave || P8 || [1 0 0&gt; ||
-See [[http://en.wikipedia.org/wiki/Quarter-comma_meantone|Quarter-comma meantone]]
+{| class="right-all"
+|-
+| [⟨ || 1 || 1 || 0 || -3 || ]
+|-
+| ⟨ || 0 || 0 || 0 || 0 || ]
+|-
+| ⟨ || 0 || 1/4 || 1 || 5/2 || ]
+|-
+| ⟨ || 0 || 0 || 0 || 0 || ]]
+|}
-==Music==
+[[Tuning map]]: {{val| 1200 1896.5784 2786.3137 3365.7843 }}
-[[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]]
-[[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_(musician)|White]]
-[[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(1511-%20c.1576)%20-%20Laura%20che%20il%20verde%20lauro.mp3|play]] by [[http://en.wikipedia.org/wiki/Nicola_Vicentino|Nicola Vicentino]]
-Five canons by [[Claudi Meneghin]]:
-[[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]]</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 696.478 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 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:0:&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:0 --&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 chain of fifths, 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;
+[[Error map]]: {{val| 0 -5.3766 0 -3.0416 }}
-&lt;table class="wiki_table"&gt;
+== Intervals of quarter-comma meantone ==
-    &lt;tr&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.
-        &lt;td&gt;0.&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&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&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&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&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&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&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&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&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&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&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&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&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&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&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&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&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&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&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&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&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&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&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&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&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&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&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&gt;-1&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;F&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Perfect fourth&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&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&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&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&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&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&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&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&gt;1&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;G&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;Perfect fifth&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&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&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&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&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&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&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&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&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&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&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&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&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&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&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&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;1006.843&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&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&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;1041.833&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&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;1047.902&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&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;1082.892&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&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&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;1123.951&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&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&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;1158.941&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&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&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&gt;1200.000&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&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&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;br /&gt;
+{| class="wikitable right-1 center-2 center-5"
-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;
+! Size<br />in [[cent]]s
-&lt;!-- ws:start:WikiTextHeadingRule:2:&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:2 --&gt;Music&lt;/h2&gt;
+! Fifths<br />dist.
-&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;
+! Note<br />C-based
-&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;
+! Traditional<br />interval name
-&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;
+! Int.<br />(short)
-&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_(musician)" rel="nofollow"&gt;White&lt;/a&gt;&lt;br /&gt;
+! [[Fractional monzo|Fract.<br />monzo]]
-&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;
+|-
-&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(1511-%20c.1576)%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;
+| 0.00000
-Five canons by &lt;a class="wiki_link" href="/Claudi%20Meneghin"&gt;Claudi Meneghin&lt;/a&gt;:&lt;br /&gt;
+| 0
-&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;
+| C
-&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;
+| Unison
-&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;
+| P1
-&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;
+| {{monzo| 0 0 0 }}
-&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;/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]]

Quarter-comma meantone: Difference between revisions

Latest revision as of 18:39, 4 June 2026

Tuning profile

Intervals of quarter-comma meantone

Music

Modern renderings

21st century

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