Quarter-comma meantone: Difference between revisions
why is "perfect" in quote marks? it's not distinguished from other ~700c intervals |
→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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{{Wikipedia}} | {{Wikipedia}} | ||
'''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 [[cent]]s. This means the fifth is flattened by 1 | '''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 [[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. | ||
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 | 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. | ||
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 | 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. | ||
== Tuning profile == | == Tuning profile == | ||
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== Intervals of quarter-comma meantone == | == 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 | 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. | ||
{| class="wikitable right-1 center-2 center-5" | {| class="wikitable right-1 center-2 center-5" | ||
! Size <br> in [[cent]]s | |- | ||
! Fifths <br> dist. | ! Size<br />in [[cent]]s | ||
! Note <br> C-based | ! Fifths<br />dist. | ||
! Traditional <br> interval name | ! Note<br />C-based | ||
! Int. <br> (short) | ! Traditional<br />interval name | ||
! [[Fractional monzo|Fract. <br> monzo]] | ! Int.<br />(short) | ||
! [[Fractional monzo|Fract.<br />monzo]] | |||
|- | |- | ||
| 0.00000 | | 0.00000 | ||
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|- | |- | ||
| 41.0590 | | 41.0590 | ||
| | | −12 | ||
| Dbb | | Dbb | ||
| Diminished second, diesis | | Diminished second, diesis | ||
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| 14 | | 14 | ||
| Cx | | Cx | ||
| | | Doubly augmented unison, augmented chromatic semitone | ||
| AA1 | | AA1 | ||
| {{monzo| -8 0 7/2 }} | | {{monzo| -8 0 7/2 }} | ||
|- | |- | ||
| 158.167 | | 158.167 | ||
| | | −17 | ||
| Ebbb | | Ebbb | ||
| Doubly diminished third | | Doubly diminished third | ||
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|- | |- | ||
| 234.216 | | 234.216 | ||
| | | −10 | ||
| Ebb | | Ebb | ||
| Diminished third | | Diminished third | ||
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|- | |- | ||
| 310.265 | | 310.265 | ||
| | | −3 | ||
| Eb | | Eb | ||
| Minor third | | Minor third | ||
| Line 119: | Line 120: | ||
|- | |- | ||
| 351.324 | | 351.324 | ||
| | | −15 | ||
| Fbb | | Fbb | ||
| Doubly diminished fourth | | Doubly diminished fourth | ||
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|- | |- | ||
| 427.373 | | 427.373 | ||
| | | −8 | ||
| Fb | | Fb | ||
| Diminished fourth | | Diminished fourth | ||
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|- | |- | ||
| 503.422 | | 503.422 | ||
| | | −1 | ||
| F | | F | ||
| Perfect fourth | | Perfect fourth | ||
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|- | |- | ||
| 544.480 | | 544.480 | ||
| | | −13 | ||
| Gbb | | Gbb | ||
| Doubly diminished fifth | | Doubly diminished fifth | ||
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|- | |- | ||
| 620.529 | | 620.529 | ||
| | | −6 | ||
| Gb | | Gb | ||
| Diminished fifth | | Diminished fifth | ||
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|- | |- | ||
| 737.637 | | 737.637 | ||
| | | −11 | ||
| Abb | | Abb | ||
| | | Diminished sixth | ||
| d6 | | d6 | ||
| {{monzo| 7 0 -11/4 }} | | {{monzo| 7 0 -11/4 }} | ||
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|- | |- | ||
| 813.686 | | 813.686 | ||
| | | −4 | ||
| Ab | | Ab | ||
| Minor sixth | | Minor sixth | ||
| Line 217: | Line 218: | ||
|- | |- | ||
| 854.745 | | 854.745 | ||
| | | −16 | ||
| Bbbb | | Bbbb | ||
| Doubly diminished seventh | | Doubly diminished seventh | ||
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|- | |- | ||
| 1006.84 | | 1006.84 | ||
| | | −2 | ||
| Bb | | Bb | ||
| Minor seventh | | Minor seventh | ||
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|- | |- | ||
| 1047.90 | | 1047.90 | ||
| | | −14 | ||
| C'bb | | C'bb | ||
| Doubly diminished octave | | Doubly diminished octave | ||
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|- | |- | ||
| 1123.95 | | 1123.95 | ||
| | | −7 | ||
| C'b | | C'b | ||
| Diminished octave | | Diminished octave | ||
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; {{W|Johann Sebastian Bach}} | ; {{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://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 – early 1600s; performed on quarter-comma meantone pipe organ by Helena Holmlund, recorded 2013) | |||
; {{W|Chuck Berry}} | ; {{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) | * [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]] | ; [[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) | * [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}} | ; {{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) | * [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}} | ; {{W|Sergei Rachmaninoff}} | ||
| Line 313: | Line 324: | ||
; {{W|Arthur Singer}}, {{w|John Medora}} and {{w|David White %28musician%29|David White}} | ; {{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) | * [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 – early 1600s; performed on quarter-comma meantone pipe organ by Helena Holmlund, recorded 2013) | |||
; {{W|Richard Wagner}} | ; {{W|Richard Wagner}} | ||
| Line 324: | Line 338: | ||
* [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://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] | * [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]] | ; [[Francium]] | ||
| Line 339: | Line 356: | ||
** "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] | ** "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] | ||
;[[Cam Taylor]] | ; [[Norokusi]] | ||
* [https://www.youtube.com/watch?v=bQcDISy6e4M ''Free jam in 1/4-comma | * [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]] | ; [[Chris Vaisvil]] | ||