Langwidge: Difference between revisions

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Since the temperament is generated by the fifth, [[chain-of-fifths notation]] can be used. Note that -17 generator steps [[octave reduction|octave-reduced]] yield [[17/16]], so that 17/16 is C–Ebbb. +9 generator steps octave-reduced yield [[19/16]], so that 19/16 is C-D#. As such, it is considered to present a challenge to the tradition of tertian harmony, since the simplest harmonic building block, the 1-19/16-3/2 triad, is C-D#-G and not C-Eb-G.

This temperament is, however, neither the first nor the most successful to raise the notational issue, and there are a number of ways to address it. First, whether 19/16 must be notated as a minor third is debatable. Western harmony mainly dealt with the [[5-limit]], and only the mapping of [[5/1|5]] is fully established. Most conceptualization systems of [[just intonation]] ([[FJS]], [[HEJI]], etc.) indeed ~~treats~~ 19/16 as a minor third, but [[Sagittal notation|Sagittal]] is a notable exception in that it is equipped with an accidental of ratio 19683/19456 besides the more common [[513/512]], so 19/16 can be an augmented second there. Otherwise, if one wants to notate 19/16 as a minor third, ~~they~~ can adopt an additional module of accidentals such as arrows to represent the comma step, allowing them to write the chord above as C-^Eb-G. There are also other temperaments known to raise the notational issue in much simpler chords, such as [[schismatic]] temperament which represents the 5-limit 10:12:15 triad as C-D#-G.

This temperament is, however, neither the first nor the most successful to raise the notational issue, and there are a number of ways to address it. First, whether 19/16 must be notated as a minor third is debatable. Western harmony mainly dealt with the [[5-limit]], and only the mapping of [[5/1|5]] is fully established. Most conceptualization systems of [[just intonation]] ([[FJS]], [[HEJI]], [[Color notation]],etc.) indeed treat 19/16 as a minor third, but [[Sagittal notation|Sagittal]] is a notable exception in that it is equipped with an accidental of ratio 19683/19456 besides the more common [[513/512]], so 19/16 can be an augmented second there. Otherwise, if one wants to notate 19/16 as a minor third, one can adopt an additional module of accidentals such as arrows to represent the comma step, allowing them to write the chord above as C-^Eb-G. (Color notation can notate 19/16 as either an ino 3rd or a noqu 2nd.) There are also other temperaments known to raise the notational issue in much simpler chords, such as [[schismatic]] temperament which represents the 5-limit 10:12:15 triad as C-D#-G.

== Temperament data ==

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 Since the temperament is generated by the fifth, [[chain-of-fifths notation]] can be used. Note that -17 generator steps [[octave reduction|octave-reduced]] yield [[17/16]], so that 17/16 is C–Ebbb. +9 generator steps octave-reduced yield [[19/16]], so that 19/16 is C-D#. As such, it is considered to present a challenge to the tradition of tertian harmony, since the simplest harmonic building block, the 1-19/16-3/2 triad, is C-D#-G and not C-Eb-G.
-This temperament is, however, neither the first nor the most successful to raise the notational issue, and there are a number of ways to address it. First, whether 19/16 must be notated as a minor third is debatable. Western harmony mainly dealt with the [[5-limit]], and only the mapping of [[5/1|5]] is fully established. Most conceptualization systems of [[just intonation]] ([[FJS]], [[HEJI]], etc.) indeed treats 19/16 as a minor third, but [[Sagittal notation|Sagittal]] is a notable exception in that it is equipped with an accidental of ratio 19683/19456 besides the more common [[513/512]], so 19/16 can be an augmented second there. Otherwise, if one wants to notate 19/16 as a minor third, they can adopt an additional module of accidentals such as arrows to represent the comma step, allowing them to write the chord above as C-^Eb-G.  There are also other temperaments known to raise the notational issue in much simpler chords, such as [[schismatic]] temperament which represents the 5-limit 10:12:15 triad as C-D#-G.
+This temperament is, however, neither the first nor the most successful to raise the notational issue, and there are a number of ways to address it. First, whether 19/16 must be notated as a minor third is debatable. Western harmony mainly dealt with the [[5-limit]], and only the mapping of [[5/1|5]] is fully established. Most conceptualization systems of [[just intonation]] ([[FJS]], [[HEJI]], [[Color notation]],etc.) indeed treat 19/16 as a minor third, but [[Sagittal notation|Sagittal]] is a notable exception in that it is equipped with an accidental of ratio 19683/19456 besides the more common [[513/512]], so 19/16 can be an augmented second there. Otherwise, if one wants to notate 19/16 as a minor third, one can adopt an additional module of accidentals such as arrows to represent the comma step, allowing them to write the chord above as C-^Eb-G. (Color notation can notate 19/16 as either an ino 3rd or a noqu 2nd.) There are also other temperaments known to raise the notational issue in much simpler chords, such as [[schismatic]] temperament which represents the 5-limit 10:12:15 triad as C-D#-G.
 == Temperament data ==