5-limit: Difference between revisions

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== Terminology ==

Due to their historical significance, 5-limit intervals go by various names, including '''classic(al)'''<ref>[https://dkeenan.com/Music/IntervalNaming.htm ''A note on the naming of musical intervals''] by [[Dave Keenan]]</ref>, '''pental'''~~{{Citation needed}}~~, or '''quinquimal'''{{Citation needed}}. Although the corresponding Latin numerals are used to refer to higher prime limits such as ''septimal'' for the 7-limit and ''undecimal'' for the 11-limit, ''quintal'' is ''never'' used to refer to the 5-limit because it is the adjective associated with the fifth [[5L 2s|diatonic]] degree. (Quintal harmony does ''not'' mean 5-limit harmony, but harmony with chords stacked by fifths – cf. secundal harmony, tertian harmony, quartal harmony.)

Due to their historical significance, 5-limit intervals go by various names, including '''classic(al)'''<ref>[https://dkeenan.com/Music/IntervalNaming.htm ''A note on the naming of musical intervals''] by [[Dave Keenan]]</ref>, '''pental'''<ref>[https://chrisvaisvil.com/microtonal-theory-pages/gallery-of-just-intervals/ Gallery of Just Intervals « Music & Techniques by Chris Vaisvil]</ref>, or '''quinquimal'''{{Citation needed}}. Although the corresponding Latin numerals are used to refer to higher prime limits such as ''septimal'' for the 7-limit and ''undecimal'' for the 11-limit, ''quintal'' is ''never'' used to refer to the 5-limit because it is the adjective associated with the fifth [[5L 2s|diatonic]] degree. (Quintal harmony does ''not'' mean 5-limit harmony, but harmony with chords stacked by fifths – cf. secundal harmony, tertian harmony, quartal harmony.)

A finite set of 5-limit intervals are labeled ''just'', especially when the interval in question is the simplest in the [[Interval category|category]]. For example, 5/4 is known as the ''just major third''<ref>[https://marsbat.space/pdfs/HEJI2_legend+series.pdf ''The Helmholtz-Ellis JI Pitch Notation (HEJI)''] by [[Marc Sabat]] and [[Thomas Nicholson]] from Plainsound Music Edition</ref>. Indeed, ''just intonation'' traditionally meant specifically the 5-limit version thereof. Even so, justness is not to be generalized to all 5-limit intervals, nor can we assume all just intervals 5-limit in contemporary usage.

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 == Terminology ==
-Due to their historical significance, 5-limit intervals go by various names, including '''classic(al)'''<ref>[https://dkeenan.com/Music/IntervalNaming.htm ''A note on the naming of musical intervals''] by [[Dave Keenan]]</ref>, '''pental'''{{Citation needed}}, or '''quinquimal'''{{Citation needed}}. Although the corresponding Latin numerals are used to refer to higher prime limits such as ''septimal'' for the 7-limit and ''undecimal'' for the 11-limit, ''quintal'' is ''never'' used to refer to the 5-limit because it is the adjective associated with the fifth [[5L 2s|diatonic]] degree. (Quintal harmony does ''not'' mean 5-limit harmony, but harmony with chords stacked by fifths – cf. secundal harmony, tertian harmony, quartal harmony.)
+Due to their historical significance, 5-limit intervals go by various names, including '''classic(al)'''<ref>[https://dkeenan.com/Music/IntervalNaming.htm ''A note on the naming of musical intervals''] by [[Dave Keenan]]</ref>, '''pental'''<ref>[https://chrisvaisvil.com/microtonal-theory-pages/gallery-of-just-intervals/ Gallery of Just Intervals « Music & Techniques by Chris Vaisvil]</ref>, or '''quinquimal'''{{Citation needed}}. Although the corresponding Latin numerals are used to refer to higher prime limits such as ''septimal'' for the 7-limit and ''undecimal'' for the 11-limit, ''quintal'' is ''never'' used to refer to the 5-limit because it is the adjective associated with the fifth [[5L 2s|diatonic]] degree. (Quintal harmony does ''not'' mean 5-limit harmony, but harmony with chords stacked by fifths – cf. secundal harmony, tertian harmony, quartal harmony.)
 A finite set of 5-limit intervals are labeled ''just'', especially when the interval in question is the simplest in the [[Interval category|category]]. For example, 5/4 is known as the ''just major third''<ref>[https://marsbat.space/pdfs/HEJI2_legend+series.pdf ''The Helmholtz-Ellis JI Pitch Notation (HEJI)''] by [[Marc Sabat]] and [[Thomas Nicholson]] from Plainsound Music Edition</ref>. Indeed, ''just intonation'' traditionally meant specifically the 5-limit version thereof. Even so, justness is not to be generalized to all 5-limit intervals, nor can we assume all just intervals 5-limit in contemporary usage.