Dominant seventh chord: Difference between revisions
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The name of the chord derives from the {{w|Dominant (music)|dominant}} scale degree, which is the only degree of a [[diatonic scale]] on which it is found. However, in many musical genres, “dominant seventh chord” informally refers to any chord with this general structure, regardless of where it appears in the overall scale. | The name of the chord derives from the {{w|Dominant (music)|dominant}} scale degree, which is the only degree of a [[diatonic scale]] on which it is found. However, in many musical genres, “dominant seventh chord” informally refers to any chord with this general structure, regardless of where it appears in the overall scale. | ||
== In | == In temperaments == | ||
In [[meantone]] (including [[12edo]]), on which traditional tonal harmony is built, the dominant seventh chord has an [[intervallic odd limit]] of 25: | In [[meantone]] (including [[12edo]]), on which traditional tonal harmony is built, the dominant seventh chord has an [[intervallic odd limit]] of 25: | ||
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Note the ~9/5 is simultaneously ~[[16/9]], and the interval between the ~5/4 and ~9/5 is [[36/25]]~[[64/45]]. | Note the ~9/5 is simultaneously ~[[16/9]], and the interval between the ~5/4 and ~9/5 is [[36/25]]~[[64/45]]. | ||
In [[septimal meantone]] | In [[septimal meantone]] (which is well-represented by the historically prevalent [[quarter-comma meantone]]), that ~[[36/25]]~[[64/45]] is tempered to ~[[10/7]], making the chord an [[essentially tempered chord]] in the [[9-odd-limit]]. (→ [[Didymic chords #Dominant seventh chord]]) | ||
<!-- TODO: There are two temperings happening in two different interpretations of this chord: starling takes ~36/25 to ~10/7, and marvel takes ~64/45 to ~10/7. Septimal meantone equates both of those preimages, but we should describe them separately. --> | |||
== In just intonation == | == In just intonation == | ||
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In the [[5-limit]]: | In the [[5-limit]]: | ||
* [[36:45:54:64]] | * [[36:45:54:64]] is found on the dominant scale degree (V or {{Frac|3|2}}) of Ptolemy's intense diatonic scale ([[Zarlino]]), perhaps the most common 5-limit diatonic. | ||
* [[20:25:30:36]], the ''major-minor seventh chord'', combines a major third with the [[consonant]] seventh that would be found in a [[Ptolemaic minor seventh chord]] built on the same root. It is found rooted at the I ({{Frac|1|1}}) and IV ({{Frac|4|3}}) of the [[duodene]]. | * [[20:25:30:36]], the ''major-minor seventh chord'', combines a major third with the [[consonant]] seventh that would be found in a [[Ptolemaic minor seventh chord]] built on the same root. It is found rooted at the I ({{Frac|1|1}}) and IV ({{Frac|4|3}}) of the [[duodene]]. | ||
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* [[108:135:160:192]] is found on the dominant scale degree (V or {{Frac|3|2}}) of a diatonic scale with the second degree tuned a comma lower than in Zarlino ([[10/9]] instead of [[9/8]]), such as in left-handed [[nicetone]]. | * [[108:135:160:192]] is found on the dominant scale degree (V or {{Frac|3|2}}) of a diatonic scale with the second degree tuned a comma lower than in Zarlino ([[10/9]] instead of [[9/8]]), such as in left-handed [[nicetone]]. | ||
* [[128:160:192:225]], a 5-limit interpretation of an inversion of the {{w|Neapolitan chord|''Neapolitan''}} or {{w|Augmented sixth chord #German sixth|''German sixth chord''}}, is found rooted at the ♭II ({{Frac|16|15}}) and ♭VI ({{Frac|8|5}}) of the [[duodene]]. ([[225/128]] is often considered an augmented sixth rather than a minor seventh, but in | * [[128:160:192:225]], a 5-limit interpretation of an inversion of the {{w|Neapolitan chord|''Neapolitan''}} or {{w|Augmented sixth chord #German sixth|''German sixth chord''}}, is found rooted at the ♭II ({{Frac|16|15}}) and ♭VI ({{Frac|8|5}}) of the [[duodene]]. ([[225/128]] is often considered an augmented sixth rather than a minor seventh, but in septimal meantone and [[marvel]] temperament this chord is tuned identically to 4:5:6:7, and in [[12edo]] and its multiples it is tuned identically to 36:45:54:64 and 20:25:30:36.) | ||
In the [[3-limit]]: | In the [[3-limit]]: | ||
* [[576:729:864:1024]] | * [[576:729:864:1024]] is found on the dominant scale degree (V or {{Frac|3|2}}) of the [[Pythagorean tuning|Pythagorean]] diatonic scale. | ||
== See also == | == See also == | ||