View source for User:Xenllium/Xenllium's microtonal notation

Here is a microtonal [[Musical notation|notation]] proposed by [[User:Xenllium|Xenllium]] on 15 June 2022.

[[File:Xenllium's_microtonal_notation.png]]

This notation is valid for any tuning system in which chromatic semitone is represented by between 1 and 16 steps. Alternatively, [[EDO]]s with [[sharpness]] value between 1 and 16 can apply this notation. Not only for EDOs, this notation can be used for some [[Regular temperament|regular tunings]] which have 7-tone MOS or 1/7-octave period.

== Symbol set ==
[[File:Xenllium's_microtonal_notation_2.png]]

The symbol set comprises traditional accidentals (sharps, flats, and naturals), Stein-Zimmermann quartertone accidentals (semisharps and semiflats), and additional symbols to represent microtone intervals. Some accidentals in this notation are borrowed from [[Helmholtz-Ellis notation]] and arranged to represent microtone intervals including quarter-tone, sixth-tone, eighth-tone, tenth-tone, twelfth-tone, fourteenth-tone and sixteenth-tone.

1) The traditional accidentals, as specified in this microtonal notation, modify the note by a chromatic semitone (apotome, [[2187/2048]]).

2) The Stein-Zimmermann quartertone accidentals modify the note by half of a chromatic semitone.

3) To modify the note by a quarter of a chromatic semitone, use symbols for septimal comma in Helmholtz-Ellis notation, but also combining to quartertone accidentals.

4) To modify the note by around 1/5 or 1/6 of a chromatic semitone, use symbols for syntonic comma in Helmholtz-Ellis notation, but also combining to quartertone accidentals.

5) To modify the note by around 1/7, 1/8, 1/9 or 1/10 of a chromatic semitone, use symbols for vicesimotertial comma (left-combining up/down arrow) in Helmholtz-Ellis notation, but also combining to quartertone accidentals.

6) To modify the note by around 1/16 of a chromatic semitone, use symbols for undevicesimal comma, tridecimal third-tone or raising undecimal quartertone in Helmholtz-Ellis notation.

== Usage guide ==
A usage guide for each sharpness value will be provided here.

=== Sharp-1 and sharp-2 ===
In sharp-1 EDOs ({{EDOs|12, 19, 26, 33, 40}} and [[47edo|47]] EDOs) and regular tunings which have [[5L 2s]] scale (eg. [[Pythagorean tuning|Pythagorean]], [[Meantone family|meantone]], [[Schismatic family|schismic]] and [[Archytas clan|superpyth]]), traditional notation can be used.

In sharp-2 EDOs ({{EDOs|17, 24, 31, 38, 45}} and [[52edo|52]] EDOs) and regular tunings which have [[3L 4s]] scale (i.e. [[neutral third scales]]), the Stein-Zimmermann quartertone accidentals can be used.

=== Sharp-3 and sharp-6 ===
[[File:Xenllium's_notation_for_sharp3_and_sharp6.png]]

In sharp-3 EDOs ({{EDOs|22, 29, 36, 43, 50, 57}} and [[64edo|64]] EDOs) and sharp-6 EDOs ({{EDOs|37, 44, 51, 58, 65, 72, 79, 86, 93}} and [[100edo|100]] EDOs), quartertone accidentals with combined arrow are used for modifying the note by 1/6 of a chromatic semitone. This accidentals can also be used for regular tunings which have [[1L 6s]] scale (eg. [[Porcupine family|porcupine]] and [[Schismatic family #Squirrel|squirrel]]) or [[2L 5s]] scale (eg. [[Gravity family|gravity]]).

=== Sharp-4 and sharp-8 ===
[[File:Xenllium's_notation_for_sharp4_and_sharp8.png]]

In sharp-4 EDOs ({{EDOs|27, 34, 41, 48, 55, 62, 69}} and [[76edo|76]] EDOs) and regular tunings which have [[6L 1s]] scale (eg. [[Tetracot family|tetracot]]), accidentals for 1/8-tone are used for modifying the note by a quarter of a chromatic semitone. This accidentals are used for modifying the note by a septimal comma in Helmholtz-Ellis notation.

In sharp-8 EDOs ({{EDOs|54, 61, 68, 75, 82, 89, 96, 103, 110}} and [[117edo|117]] EDOs) and regular tunings which have pseudo-equalized 5L 2s scale, accidentals for 1/16-tone are used for modifying the note by a 1/8 of a chromatic semitone. This accidentals are used for modifying the note by a vicesimotertial comma in Helmholtz-Ellis notation.

=== Sharp-5 and sharp-10 ===
[[File:Xenllium's_notation_for_sharp5_and_sharp10.png]]

In sharp-5 EDOs ({{EDOs|32, 39, 46, 53, 60, 67, 74, 81}} and [[88edo|88]] EDOs) and sharp-10 EDOs ({{EDOs|71, 78, 85, 92, 99, 106, 113, 120, 127, 134}} and [[141edo|141]] EDOs), quartertone accidentals with combined arrow are used for modifying the note by 1/10 or 1/5 of a chromatic semitone. Combining a small up/down arrow to the left of a quartertone accidental modifies the note by a 1/10 of a chromatic semitone, and combining an arrow to the top/bottom of a quartertone accidental modifies the note by 1/5 of a chromatic semitone. This accidentals can also be used for regular tunings which have [[4L 3s]] scale (eg. [[Archytas clan #Sixix|sixix]] and [[Amity family|amity]]) or pseudo-equalized 1L 6s scale.

=== Sharp-7 ===
[[File:Xenllium's_notation_for_sharp7.png]]

In sharp-7 EDOs ({{EDOs|42, 49, 56, 63, 70, 77, 84, 91, 98}} and [[105edo|105]] EDOs) and regular tunings which have 1/7-octave period (eg. [[Keemic temperaments #Sevond|sevond]] and [[Porwell temperaments #Absurdity|absurdity]]), accidentals for 1/14-tone are used for modifying the note by a 1/7 of a chromatic semitone. These accidentals include small arrows (combined with the left of natural, sharp, flat, double-sharp or double-flat, or the top/bottom of semisharp, semiflat, sesquisharp or sesquiflat), semiflat with a stroke, Helmholtz-Ellis accidentals for undecimal quartertone and tridecimal third tone (except lowering by one undecimal quartertone, which is the same shape as Stein-Zimmermann semiflat symbol).

=== Sharp-9 ===
[[File:Xenllium's_notation_for_sharp9.png]]

In sharp-9 EDOs ({{EDOs|59, 66, 73, 80, 87, 94, 101, 108, 115, 122}} and [[129edo|129]] EDOs) and regular tunings which have pseudo-equalized 3L 4s scale (eg. [[Hemifamity temperaments #Artoneutral|artoneutral]]), accidentals for 1/18-tone are used for modifying the note by a 1/9 of a chromatic semitone. These accidentals include small arrows (combined with the left of natural, sharp, flat, double-sharp or double-flat, or the top/bottom of semisharp, semiflat, sesquisharp or sesquiflat), semiflat with a stroke, Helmholtz-Ellis accidentals for septimal comma, undecimal quartertone and tridecimal third tone (except lowering by one undecimal quartertone).

=== Sharp-11 ===
[[File:Xenllium's_notation_for_sharp11.png]]

In sharp-11 EDOs ({{EDOs|83, 90, 97, 104, 111, 118, 125, 132, 139, 146}} and [[153edo|153]] EDOs) and regular tunings which have pseudo-equalized 6L 1s scale (eg. [[Hemimean clan #Undetrita|undetrita]]), accidentals for 1/22-tone are used for modifying the note by a 1/11 of a chromatic semitone. These accidentals include small arrows (combined with the left of semisharp, semiflat, sesquisharp or sesquiflat, or the top/bottom of natural, sharp, flat, double-sharp or double-flat), combining stroke with the top/bottom of natural, sharp, flat, double-sharp, double-flat, semiflat and sesquiflat, Helmholtz-Ellis accidentals for septimal comma, undecimal quartertone and tridecimal third tone (except lowering by one undecimal quartertone).

=== Sharp-12 ===
[[File:Xenllium's_notation_for_sharp12.png]]

In sharp-12 EDOs ({{EDOs|95, 102, 109, 116, 123, 130, 137, 144, 151}} and [[158edo|158]] EDOs) and regular tunings which have pseudo-equalized 4L 3s scale, accidentals for 1/24-tone are used for modifying the note by a 1/12 of a chromatic semitone. These accidentals include small arrows (combined with the top/bottom of quartertone accidentals), combining stroke with the top/bottom of natural, sharp, flat, double-sharp, double-flat, semiflat and sesquiflat, Helmholtz-Ellis accidentals for septimal comma, undecimal quartertone and tridecimal third tone.

=== Sharp-13 ===
[[File:Xenllium's_notation_for_sharp13.png]]

In sharp-13 EDOs ({{EDOs|107, 114, 121, 128, 135, 142, 149, 156, 163}} and [[170edo|170]] EDOs) and regular tunings which have pseudo-equalized 2L 5s scale, accidentals for 1/26-tone are used for modifying the note by a 1/13 of a chromatic semitone. These accidentals include small arrows (combined with the left or the top/bottom of quartertone accidentals), combining stroke with the top/bottom of natural, sharp, flat, double-sharp, double-flat, semiflat and sesquiflat, Helmholtz-Ellis accidentals for septimal comma, undecimal quartertone and tridecimal third tone (except lowering by one undecimal quartertone).

=== Sharp-14 ===
[[File:Xenllium's_notation_for_sharp14.png]]

In sharp-14 EDOs ({{EDOs|112, 119, 126, 133, 140, 147, 154, 161, 168, 175}} and [[182edo|182]] EDOs) and regular tunings which have 1/7-octave period, accidentals for 1/28-tone are used for modifying the note by a 1/14 of a chromatic semitone. These accidentals include small arrows (combined with the left or the top/bottom of quartertone accidentals), combining stroke with the top/bottom of natural, sharp, flat, double-sharp, double-flat, semiflat and sesquiflat, Helmholtz-Ellis accidentals for undecimal quartertone and tridecimal third tone.

=== Sharp-15 ===
[[File:Xenllium's_notation_for_sharp15.png]]

In sharp-15 EDOs ({{EDOs|124, 131, 138, 145, 152, 159, 166, 173, 180, 187}} and [[194edo|194]] EDOs) and regular tunings which have pseudo-equalized 5L 2s scale (eg. [[Amity family #Trinity|trinity]]), accidentals for 1/30-tone are used for modifying the note by a 1/15 of a chromatic semitone. These accidentals include small arrows (combined with the left or the top/bottom of quartertone accidentals), combining stroke with the top/bottom of natural, sharp, flat, double-sharp, double-flat, semiflat and sesquiflat, Helmholtz-Ellis accidentals for septimal comma, undecimal quartertone and tridecimal third tone (except lowering by one undecimal quartertone).

=== Sharp-16 ===
[[File:Xenllium's_notation_for_sharp16.png]]

In sharp-16 EDOs ({{EDOs|136, 143, 150, 157, 164, 171, 178, 185, 192}} and [[199edo|199]] EDOs) and regular tunings which have pseudo-equalized 3L 4s scale, accidentals for 1/32-tone are used for modifying the note by a 1/16 of a chromatic semitone. These accidentals include small arrows (combined with the left or the top/bottom of quartertone accidentals), combining stroke with the top/bottom of natural, sharp, flat, double-sharp, double-flat, semiflat and sesquiflat, Helmholtz-Ellis accidentals for septimal comma, undecimal quartertone and tridecimal third tone.

[[Category:Notation]]