Major and minor triads: Difference between revisions
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** A more conventional interpretation labels the 300{{c}} third as "minor" and 375{{c}} as major, which is more sensible in terms of interval size and sound, despite technically not following Pythagorean notation. | ** A more conventional interpretation labels the 300{{c}} third as "minor" and 375{{c}} as major, which is more sensible in terms of interval size and sound, despite technically not following Pythagorean notation. | ||
The triads closer to the middle of the respective ranges correspond to simple [[5-limit|classical]] or [[7-limit|septimal]] intervals. More extreme than major and minor are [[Extraclassical tonality|tendo and arto]], corresponding to [[interseptimal]] and [[13-limit|tridecimal]] intervals, and ultimately suspended, corresponding to simple [[3-limit]] intervals; less extreme than major and minor are neutral triads. | |||
As interval regions, [[Minor third (interval region)|minor thirds]] and [[Major third (interval region)|major thirds]] range from, at the widest, 240-340c and 360-460c, although people tend to restrict this further, such as to roughly 260-330c and 370-440c. And as an interval region, [[Perfect fifth | As interval regions, [[Minor third (interval region)|minor thirds]] and [[Major third (interval region)|major thirds]] range from, at the widest, 240-340c and 360-460c, although people tend to restrict this further, such as to roughly 260-330c and 370-440c. And as an interval region, [[Perfect fifth]]s range from around 660 to 740 cents at the widest, often being restricted to 680-720 cents. | ||
== In just intonation == | == In just intonation == | ||
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A '''major triad''' is a [[triad]] comprising a root, [[major]] third, and [[perfect]] fifth. | A '''major triad''' is a [[triad]] comprising a root, [[major]] third, and [[perfect]] fifth. | ||
In the | In the 3-limit: | ||
* [[ | * [[64:81:96]] is found on the I, IV, and V of the Pythagorean [[5L 2s|diatonic scale]]. | ||
In the 5-limit: | In the 5-limit: | ||
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* [[4:5:6]] is found on the I ({{Frac|1|1}}), IV ({{Frac|4|3}}), and V ({{Frac|3|2}}) of Ptolemy's intense diatonic scale ([[Zarlino]]). | * [[4:5:6]] is found on the I ({{Frac|1|1}}), IV ({{Frac|4|3}}), and V ({{Frac|3|2}}) of Ptolemy's intense diatonic scale ([[Zarlino]]). | ||
In the | In the 7-limit: | ||
* [[ | * [[14:18:21]], a ''supermajor triad'', is a [[9-odd-limit]] chord that tunes the third sharper than the 5-limit major. | ||
=== Simple minor triads === | === Simple minor triads === | ||
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A '''minor triad''' is a [[triad]] comprising a root, [[minor]] third, and fifth. | A '''minor triad''' is a [[triad]] comprising a root, [[minor]] third, and fifth. | ||
In the [[ | In the [[3-limit]]: | ||
* [[ | * [[54:64:81]] is found on the ii ({{Frac|9|8}}), iii ({{Frac|81|64}}), and vi ({{Frac|27|16}}) of the Pythagorean diatonic scale. | ||
In the [[5-limit]]: | In the [[5-limit]]: | ||
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* [[27:32:40]] is found on the ii ({{Frac|9|8}}) of Ptolemy's intense diatonic scale. | * [[27:32:40]] is found on the ii ({{Frac|9|8}}) of Ptolemy's intense diatonic scale. | ||
In the [[ | In the [[7-limit]]: | ||
* [[ | * [[6:7:9]], a ''subminor triad'', is a [[9-odd-limit]] chord that tunes the third flatter than the 5-limit minor. | ||
== SCL files == | == SCL files == | ||