5 limit.txt

// HEJI (2020) notation
// https://marsbat.space/pdfs/HEJI2_legend+series.pdf
//
// C4 is 1/1, with A4 tuned to 440 Hz.
//
// Tuning space comprises:
// 3 flats to 3 sharps
// 3 comma downs to 3 comma ups
//
// Higher limit accidentals available as secondary accidentals.

C4: 440*16/27 // Tune C4 to 16/27 of A4 = 440, setting C4 as the first nominal.


// Nominals are a chain of pure fifths from F to B
// C D   E     F   G   A     B       C (1200c equave)
   0 9/8 81/64 4/3 3/2 27/16 243/128 2/1


// Here we declare two accidental chains

// Chain 1: 3-limit accidentals from bbb to #x
// This is declared using irregular step sizes as we want to also include
// the enharmonically equivalent ~#v and ~b^ schisma-altered accidentals.

// Put the ~#v and ~b^ accidentals at the end of the chain so that the plugin
// will prefer not to use them. Lower accidental degrees are always preferred
// by the plugin.
~.b^(243/256) bbb(-113.685*3c) bb(-113.685*2c) b(-113.685c) (0) #(113.685c) x(113.685*2c) #x(113.685*3c) ~.#v(256/243)

// Chain 2: 5-limit acc from -3 to +3
v3 v2 v (81/80) ^ ^2 ^3

// First we declare a weak important ligature for the special schisma-altered
// enharmonics that we declared at deg. -4 and 4 of the 1st chain
//
// - We declare it as important (!) so that it is still accessible via the
// enharmonic cycle operation, 
// - We declare it as weak (?) so that during
// up/down operations, the plugin will prefer to use standard sharps and flats
// rather than the schisma-enharmonic variants.
//
// ⚠️ We must declare this ligature before the one below, as this ligature
// contains shares similar symbols as the one below.
//
// If we flip the order of declaration, the 'b^' and '#v' symbols will be 
// parsed & eaten up by the other ligature, leaving a stray '~' symbol, which
// is not parseable.
lig(1,2)!?
-4 0 ~.b^
4 0 ~.#v

// We declare a ligature between the 1st and 2nd chain
// In HEJI, syntonic commas can merge with sharp/flat/natural
// accidentals into a single ligatured symbol.
//
// The "!" denotes an important ligature because we don't want the plugin
// to suggest a multi-symbol spelling natural arrows + sharp/flat.
//
// This means we must declare every symbol that we want to the plugin
// to use for all permutations of the 1st and 2nd accidental chains.
lig(1,2)!
-2 -3 bbv3 // bb and 3 downs become a single double flat with 3 down arrows HEJI symbol
-2 -2 bbv2
-2 -1 bbv
-2 1 bb^
-2 2 bb^2
-2 3 bb^3
-1 -3 bv3
-1 -2 bv2
-1 -1 bv
-1 1 b^
-1 2 b^2
-1 3 b^3
1 -3 #v3
1 -2 #v2
1 -1 #v
1 1 #^
1 2 #^2
1 3 #^3
2 -3 xv3
2 -2 xv2
2 -1 xv
2 1 x^
2 2 x^2
2 3 x^3

// Here we also declare basic "non-ligatured symbols" as ligatures
// because we need the enharmonic cycling operation to work for
// these as well.
-2 0 bb
-1 0 b
0 -3 v3
0 -2 v2
0 -1 v
0 1 ^
0 2 ^2
0 3 ^3
1 0 #
2 0 x

// Here we declare 4 auxiliary up/down operations.
// These will be accessible as the aux1, aux2, aux3, aux4 up/down operations
// respectively. You can look up/modify the keyboard shortcuts to these
// operations in the "xen tuner.qml" file.
aux(0) // aux1 will modify nominals only, without modifying accidentals
aux(1) // aux2 will modify flats/sharps only, without modifying nominals or other accs
aux(2) // aux3 will modify syntonic comas only
aux(0,1) // aux4 will modify both nominals and flats/sharps.


// Now we declare secondary accidentals & text representations

// Secondary accidentals tell the plugin how to tune 'left-over' accidentals
// that don't fit into the accidental chains declared above.

// These also tell the plugin how to parse fingering text into
// accidental symbols, so you can enter both primary and secondary
// accidentals using fingerings.

// E.g. If you attach the fingering 'bbbbb' on to a note,
// the plugin will convert & render it into a triple-flat symbol
// and a double-flat symbol bbb.bb.

// The triple-flat will match as degree -3 of the first chain (sharps/flats)
// and the double-flat will match as a secondary accidental.

sec()
'~b^' ~.b^ 243/256
'b^~' ~.b^ 243/256
'bbb' bbb Math.pow(2187/2048,-3) // converts fingering 'bbb' into triple-flat symbol
'bb' bb Math.pow(2187/2048,-2)
'b' b 2048/2187

// The order of which text representations are declared matters,
// as it affects the precedence of which text strings are parsed
// first.

// E.g. we need to declare 'bbb' before 'b'.
// Otherwise, 'bbb' will match as 3 individual 'b's instead of
// one single 'bbb'.
// Even though both b.b.b and bbb will evaluate to the same interval
// offset, we rather use the correct symbol for triple flats.

'~#v' ~.#v 256/243
'#v~' ~.#v 256/243
'###' #x Math.pow(2187/2048,3)
'#x' #x Math.pow(2187/2048,3)
'x#' #x Math.pow(2187/2048,3)
'##' x Math.pow(2187/2048,2)
'x' x Math.pow(2187/2048,2)
'#' # 2187/2048

'^^^' ^3 Math.pow(81/80,3)
'^^' ^2 Math.pow(81/80,2)
'^' ^ 81/80

'vvv' v3 Math.pow(80/81,3)
'vv' v2 Math.pow(80/81,2)
'v' v 80/81

// The rest below are not part of the 5-limit accidental chains.
// You can access them by adding fingerings with the text representations.

// E.g. 'ttl#^' will render into 33/32 * 33/32 * 63/64 * 81/80 * 2187/2048

'/77' u77 Math.pow(64/63,2)
'/7' u7 64/63
'\\77' d77 Math.pow(63/64,2)
'\\7' d7 63/64

't' t 33/32
'/11' t 33/32
'd' d 32/33
'\\11' d 32/33

'/13' tt 27/26
'\\13' d| 26/27 // '\\' represents a single backslash. To enter this
                // accidental, use \13, not \\13

// When referring to SMuFL symbols or text-based accidentals,
// the backslash (\), two slashes (//), and quote (') symbols 
// need to be escaped with a backslash like so:
// \\, \/\/, \'

'/17' \'\' 2187/2176 // \'\' escapes to '' (SymbolCode 78)
'\\17' `` 2176/2187

'/19' \' 513/512 // \' escapes to ' (SymbolCode 77)
'\\19' ` 512/513

'/23' / 736/729
'\\23' \\ 729/736 // \\ escapes to \ (SymbolCode 43)

// For 29-limit, MuseScore hasn't included the HEJI supplement
// symbols yet, so we're using sagittal sharp/flat which looks alike
'/29' /||\\ 261/256
'\\29' \\!!/ 256/261

'/31' 84 32/31
'\\31' 85 31/32

// For 37-limit, we don't have the inverted 3/12ths flat
// Wyschnegradsky symbol for the 37-up accidental, so we're using
// the actual 3/12ths sharp Wyschnegradsky symbol which is the
// semi-sharp.
'/37' + 37/36
'\\37' 128 36/37

// Use standard Johnston +/- for 41-limit
'/41' j+ 82/81
'\\41' j- 81/82

// Sadly the higher-limit HEJI accidentals aren't yet available
// in MuseScore.
// Awaiting this supplement:
// https://w3c.github.io/smufl/latest/tables/extended-helmholtz-ellis-accidentals-just-intonation-supplement.html