5-limit: Difference between revisions

Line 16:

Recently, composers [[Catherine Lamb]] and [[Marc Sabat]] have adopted ''quintal'' for the [[harmonic class]] 5{{citation needed}} since 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. ''Pental'' is less consistent due to its Greek origins. However, that creates a conflict of usage as ''quintal'' has been 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.) [[User:Lériendil|Lériendil]] suggests the term ''quinary'' as opposed to ''quintal'' (seeing as the pent- root is still overloaded with various terms referring to fifths and pentatonic scales), though there is a minor conflict in naming with [[Arity|quinary]] scales.

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.

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://masa.plainsound.org/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.

The term '''ptolemaic''' could also refer to the 5-limit<ref>[https://marsbat.space/pdfs/JI.pdf ''Fundamental Principles of Just Intonation and Microtonal Composition''] by Thomas Nicholson and Marc Sabat —"'Ptolemaic' refers to intervals combining only the primes 2, 3, and 5."</ref>. On this wiki it is part of the [[2.3-equivalent class and Pythagorean-commatic interval naming system|Pythagorean-commatic interval naming system]], and refers specifically to intervals that contain a single factor of harmonic 5. We distinguish multi-order 5-limit intervals by ''diptolemaic'', ''triptolemaic'', and so on.

@@ Line 16: / Line 16: @@
 Recently, composers [[Catherine Lamb]] and [[Marc Sabat]] have adopted ''quintal'' for the [[harmonic class]] 5{{citation needed}} since 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. ''Pental'' is less consistent due to its Greek origins. However, that creates a conflict of usage as ''quintal'' has been 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.) [[User:Lériendil|Lériendil]] suggests the term ''quinary'' as opposed to ''quintal'' (seeing as the pent- root is still overloaded with various terms referring to fifths and pentatonic scales), though there is a minor conflict in naming with [[Arity|quinary]] scales.
-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.
+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://masa.plainsound.org/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.
 The term '''ptolemaic''' could also refer to the 5-limit<ref>[https://marsbat.space/pdfs/JI.pdf ''Fundamental Principles of Just Intonation and Microtonal Composition''] by Thomas Nicholson and Marc Sabat —"'Ptolemaic' refers to intervals combining only the primes 2, 3, and 5."</ref>. On this wiki it is part of the [[2.3-equivalent class and Pythagorean-commatic interval naming system|Pythagorean-commatic interval naming system]], and refers specifically to intervals that contain a single factor of harmonic 5. We distinguish multi-order 5-limit intervals by ''diptolemaic'', ''triptolemaic'', and so on.