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A little more history and notation
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In music, '''19 equal temperament''', called 19-TET, 19-[[EDO|EDO]], or 19-ET, is the scale derived by dividing the [[Octave|octave]] into 19 [[Equal|equal]]ly large steps. Each step represents a frequency ratio of the 19th root of 2, or 63.16 [[cent|cents]]. It is the 8th [[prime_numbers|prime]] edo, following [[17edo|17edo]] and coming before [[23edo|23edo]].
In music, '''19 equal temperament''', called 19-TET, 19-[[EDO|EDO]], or 19-ET, is the scale derived by dividing the [[Octave|octave]] into 19 [[Equal|equal]]ly large steps. Each step represents a frequency ratio of the 19th root of 2, or 63.16 [[cent|cents]]. It is the 8th [[prime_numbers|prime]] edo, following [[17edo|17edo]] and coming before [[23edo|23edo]].


Interest in this tuning system goes back to the sixteenth century, when composer Guillaume Costeley used it in his chanson [[Seigneur_Dieu_ta_pitié|Seigneur Dieu ta pitié]] of 1558. Costeley understood and desired the circulating aspect of this tuning; in 1577 music theorist Francisco de Salinas in effect proposed it. Salinas discussed [[1-3_Syntonic_Comma_Meantone|1/3-comma meantone]], in which the fifth is of size 694.786 cents; the fifth of 19-et is 694.737, which is only a twentieth of a cent flatter. Salinas suggested tuning nineteen tones to the octave to this tuning, which fails to close by less than a cent, so that his suggestion is effectively 19-et. In the nineteenth century mathematician and music theorist Wesley Woolhouse proposed it as a more practical alternative to meantone tunings he regarded as better, such as [[50edo|50 equal temperament]] ([http://sonic-arts.org/monzo/woolhouse/essay.htm summary of Woolhouse's essay]).
== History ==
Interest in this tuning system goes back to the sixteenth century, when composer Guillaume Costeley used it in his chanson [[Seigneur_Dieu_ta_pitié|Seigneur Dieu ta pitié]] of 1558. Costeley understood and desired the circulating aspect of this tuning, which he defined as dividing the just major second into three approximately equal parts.  Costeley had other compositions that made use of intervals, such as the diminished third, which have a meaningful context in 19edo, but not in other tuning systems contemporary with the work.
 
In 1577 music theorist Francisco de Salinas proposed [[1-3_Syntonic_Comma_Meantone|1/3-comma meantone]], in which the fifth is of size 694.786 cents; the fifth of 19-et is 694.737, which is only a twentieth of a cent flatter. Salinas suggested tuning nineteen tones to the octave to this tuning, which fails to close by less than a cent, so that his suggestion is effectively 19edo.  
 
In 1835, mathematician and music theorist Wesley Woolhouse proposed it as a more practical alternative to meantone tunings he regarded as better, such as [[50edo|50 equal temperament]] ([http://sonic-arts.org/monzo/woolhouse/essay.htm summary of Woolhouse's essay]).


==As an approximation of other temperaments==
==As an approximation of other temperaments==
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| style="text-align:center;" | 9/7, 12/7
| style="text-align:center;" | 9/7, 12/7
|}
|}
== Notation ==
Looking at 19edo as an extension of 12edo, standard notation can be used, whether it is staff notation (with five lines), letter notation (with standard accidentals), solfege, or sargam.  Notes with enharmonic equivalents are different than they are in 12edo, though.
=== Letter Notation (anglophonic standard) ===
Using the letters A-G and "accidentals" b to lower a tone and # to raise a tone, with also bb to lower a tone two degrees and x to raise a tone two degrees, the notes and enharmonic equivalents are shown in the table below:
{| class="wikitable"
|+A Basic Look at Letter Notation in 19edo
!Degree
!Interval with A
!Alternative Interval with A
!Name in the key of A
!Letter(s)
!Enharmonic Equivalents
|-
|1
|Unison
|
|Tonic
|A
|
|-
|2
|
|Diminished Second
|
|A#
|Bbb
|-
|3
|Minor Second
|
|
|Bb (*)
|Ax
|-
|4
|Major Second
|
|Supertonic
|B (*)
|Cbb
|-
|5
|
|Augmented Second, Diminished Third
|
|B# or Cb
|
|-
|6
|Minor Third
|
|
|C
|Bx
|-
|7
|Major Third
|
|Mediant
|C#
|Dbb
|-
|8
|
|Augmented Third, Diminished Fourth
|
|Db
|Cx
|-
|9
|Perfect Fourth
|
|Subdominant
|D
|
|-
|10
|Augmented Fourth
|
|
|D#
|Ebb
|-
|11
|Diminished Fifth
|
|
|Eb
|Dx
|-
|12
|Perfect Fifth
|
|Dominant
|E
|Fbb
|-
|13
|Augmented Fifth
|
|
|E# or Fb
|
|-
|14
|Minor Sixth
|
|
|F
|Ex
|-
|15
|Major Sixth
|
|Submediant
|F#
|Gbb
|-
|16
|Diminished Seventh
|Augmented Sixth
|
|Gb
|Fx
|-
|17
|Minor Seventh
|
|
|G
|
|-
|18
|Major Seventh
|
|Subtonic
|G#
|Abb
|-
|19
|
|Augmented Seventh
|
|Ab
|Gx
|}
<nowiki>*</nowiki>Some cultures use letter notation, but there is a common variation to replace Bb from the table with B and then replace B from the table with H.
Chords would follow the same spelling as with standard 12edo notation, just be careful with spelling.  For example, Bb chord would be spelled Bb D F, and A# chord would be A# Cx E#; but the two are different chords, one degree apart from each other.
Key signatures are the same, but again, with the extra notes and different enharmonic equivalents, some key signatures can get messy.  For example, the key of Bbb would have bb's on B and E, and b's on C, D, F, G, and A.  Thinking of rewriting this key as A# might seem better, but then the key signature would contain x's on C, F, and G, and #'s on A, B, D, and E, which is actually worse.


==Chord Names==
==Chord Names==
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*[[Strictly_proper_19edo_scales|Strictly proper 19edo scales]]
*[[Strictly_proper_19edo_scales|Strictly proper 19edo scales]]
*[[How_to_tune_a_19edo_guitar_by_ear|How to tune a 19edo guitar by ear]]
*[[How_to_tune_a_19edo_guitar_by_ear|How to tune a 19edo guitar by ear]]
*[[Chord_progressions_in_19edo-family_scales|Chord progressions in 19edo-family scales]]
*[[Primer for 19edo]]
*[[Mason Green's New Common Practice Notation]]


==Articles==
==Articles==
Retrieved from "https://en.xen.wiki/w/19edo"