Humdrum Representation for Basic Notated Music

REPRESENTATION

**kern -- core pitch/duration representation for common practice music notation

DESCRIPTION

The **kern scheme can be used to represent basic or core information for period-of-common-practice Western music. The **kern representation allows pitch and canonical duration information to be encoded. In addition, **kern also provides limited capabilities for representing accidentals, articulation, ornamentation, ties, slurs, phrasing, barlines, stem-direction and beaming. In general, **kern is intended to represent the underlying semantic information implied by a musical score rather than the visual or orthographic information embodied by a given printed rendition; **kern is designed to facilitate analytic applications rather than music printing or sound generation. Other Humdrum representations should be used for these latter purposes.

Three types of data tokens are distinguished in **kern: notes, rests, and barlines.

Notes can encode a variety of attributes including absolute pitch, accidental, canonical duration, articulation, ornamentation, ties, slurs, phrasing, stem-direction and beaming.

Pitches in **kern are encoded as "nominally" equally-tempered values. Transposing instruments are represented at concert pitch with a tandem interpretation indicating the nature of the transposition. Pitch information is encoded through a scheme of upper- and lower-case letters. Middle C (C4) is represented using the single lower-case letter c. Successive octaves are designated by letter repetition, thus C5 is represented by cc, C6 by ccc and so on. For pitches below C4, upper-case letters are used: C for C3, CC for C2, and so on. This same scheme is used for other pitch letter-names. Changes of octave are deemed to occur between B and C. Thus the B below middle c is represented as B; the B below CC is represented as BBB, and so on.

Accidentals are encoded using the octothorpe (#) for sharps, the minus sign (-) for flats, and the lower-case letter n for naturals. Accidentals are encoded immediately following the diatonic pitch information. Double-sharps and double-flats have no special representations in **kern and are simply denoted by repetition (##) and (--). Triple- and quadruple accidentals are similarly encoded by repetition. Sharps, flats, and naturals are mutually exclusive in **kern, so tokens such as cc#n and GG-# are illegal. In addition, natural signs may not be repeated (i.e. nn).

In **kern, all pitches are encoded as contextually independent absolute values. Pitches must be encoded with the appropriate accidental, even if the accidental is specified in a key-signature, or is present earlier in the same measure. Transposing instruments must be notated at (sounding) concert pitch (although see the tandem interpretation transposition (3)).

Note tokens may be modified by the presence of additional signifiers.

The **kern representation provides no generic means for representing "curved lines" found in printed scores. Lines must be explicitly interpreted as ties, slurs or phrases. The open brace { denotes the beginning of a phrase. The closed brace } denotes the end of a phrase. The open parenthesis ( and closed parenthesis ) signify the beginning and end of a slur respectively. The semicolon ; denotes a pause. The open square bracket [ denotes the first note of a tie. The closed square bracket ] denotes the last note of a tie. The underscore character _ denotes middle notes of a tie.

Additional signifiers are provided for denoting articulation marks and ornaments. The letters T and t are used to signify whole-tone and semitone trills, respectively. Whole-tone and semitone mordents are signified by the letters M and m. Inverted mordents are signified by W (whole-tone) and w (semitone). (Note that trills, mordents, and inverted mordents wider than two semitones in size are also denoted by the upper-case signifier.) The letter S signifies a turn, whereas the dollar sign ($) signifies an inverted (or Wagnerian) turn. When a concluding turn is appended to the end of an ornament (such as a trill), the upper-case letter R is added to the ornament signifier (as in tR and TR). In addition to these ornaments, **kern provides a signifier for (multi-note) arpeggiation (:). The presence of ornaments other than trills, mordents, inverted mordents, and turns types can be indicated by the generic ornament symbol (O).

Articulation marks include the apostrophe (') for staccato, the double-quote (") for pizzicato, the greve (`) for staccatissimo or attacca, the tilde (~) for tenuto, and the caret (^) for all note-related accents (including < and >). In addition, **kern provides signifiers for up-bow (v) and down-bow (u). The presence of other articulation types can be indicated by the generic articulation symbol (I).

As noted, the **kern scheme is intended for analytic applications rather than as a means for representing visual renderings of notation. Nevertheless, **kern distinguishes up-stems, down-stems, and beamings in order to assist in analytic tasks such as the determination of voicings and in order to facilitate the parsing of note-groupings. Up-stems and down-stems are indicated by the slash (/) and backslash characters (\) respectively. The beginning and ends of beams are signified by the upper-case letters L and J. Multiple beams are indicated via letter repetition, e.g. LL <--> JJ and LLL <--> JJJ for double- and triple-beams respectively. Partial beams may extend to the right (K) or left (k). Again, multiple partial beams are indicated via letter repetition. By way of example, a doubly-dotted sixteenth note beamed to a thirty-second note can be represented as:

16..LL
32JJkk
Slurs and phrase markings can be nested (e.g. slurs within slurs) and may also be elided (e.g. overlapping phrases). Nested markings mean that one slur or phrase is entirely subsumed under another slur or phrase. For example: ( ( ) ) means that a short slur has occurred within a longer slur. Elisions are overlaps, for example, where an existing phrase fails to end while a new phrase begins. In **kern the ampersand character is used to mark elided slurs or phrases. For example: { &{ } &} means that two phrases overlap -- the initial phrase ending after second phrase has begun. Multiple levels of elisions are indicated by repeating the ampersand character. Both the beginning and ending must be marked by the same number of ampersands. For example, the following coding represents a series of elided phrases where three separate phrases begin before any of the phrases is terminated: { &{ &&{ } &&} &} Notice that the second elided phrase terminates after third phrase has ended.

Durations are encoded in a manner identical to the **recip representation. Durations are encoded as nominal proportions using integer numbers and the period character. With the exception of the value zero, durations are represented by reciprocal numerical values corresponding to the American duration names: 1 for whole note, 8 for eighth, 32 for thirty-second, etc. The number zero (0) is reserved for the breve duration (i.e. a duration of twice the length of a whole note). Dotted durations are indicated by adding the period character (.) immediately following the numerical value -- hence 8. signifies a dotted-eighth note and 2.. signifies a doubly-dotted half note. Any number of augmentation dots may follow the duration integer.

Triplet and other irregular durations are represented using the same reciprocal logic. Three quarter triplets in the time of four quarters (a whole duration) are signified by the value 3 (i.e. "third notes"). Eighth-note quintuplets (5 in the time of 4) are represented by the value 10 (a half duration divided by 5). See **recip for further details.

The **kern representation also allows for the encoding of acciaccaturas, non-canonical groupettos, and appoggiaturas. Depending on the expected analytic application, one way to handle these notational devices is to encode the notes according to the manner in which they are typically performed. Alternatively, since these notes are viewed as embellishment notes and hold potentially less analytic status, a special designation for these notes can be useful for certain types of studies.

Acciaccaturas (grace notes) are visually represented as minature notes denoted by a slash mark through the stem. In **kern these notes are treated as "durationless" notes and are designated by the lower-case letter q. Hence, the token G#q denotes a G#3 acciaccatura. Non-canonical groupettos are minature (non-cue) notes (typically in groups) whose stems do not contain a slash, and whose notated durations cause the total notated duration for the measure to exceed the prevailing meter. These groupetto notes are encoded as notes having their notated durations, but are also designated by the upper-case letter Q. Hence, a minature sixteenth-note middle C would be encoded as 16cQ. Depending on the analytic task, these notes may be treated as equivalent to their notated durations, or they may be discarded. For example, the timebase command eliminates these notes. Note that data records containing acciaccaturas or groupettos notes must not include normal notes.

In the case of appoggiaturas, **kern requires that they be encoded as performed. An appropriate duration is assigned to the appoggiatura according to common performance practice. The duration of the subsequent note is reduced by a corresponding amount. The status of the two notes forming the appoggiatura is nevertheless marked. The appoggiatura itself is designated by the upper-case letter P, whereas the subsequent note (whose notated duration has been shorted) is designated by the lower-case letter p.

Rest tokens are denoted by the lower-case letter r along with a numerical duration signifier. Rests may also have the attributes of stem-direction, beaming, slur, and phrase, but rests cannot be assigned articulation or ornamentation attributes. In many meters, a full measure of rest is indicated by a whole rest, even if the actual duration of the measure differs from four quarters. The actual duration of the rest is encoded, however, repetition of the r is used to indicate that the visual rendering of the rest is as a whole rest.

Barlines are represented using the "common system" for barlines -- see barlines. A barline is denoted by the occurrence of an equals sign (=) at the beginning of the token -- followed by an optional measure number (integer) followed by an optional letter (single lower-case alphabetic character), followed by an optional pause marking (;). Double-barlines are represented by the occurrence of two or more equals signs (==) at the beginning of the token -- followed by an optional pause marking (;).

In representing any work, editorial interpretations are inevitable. It may be necessary to make explicit certain implicit information in a score (such as expanding abbreviations), or it may be necessary to estimate missing or unreadable information. Interpreting the voicings (that is, making explicit the degree of connectedness between successive pitches) is an important editorial function in **kern representations. The **kern representation provides several special-purpose signifiers to help make explicit various classes of editorial amendments, interpretations, or commentaries. Five types of editorial signifiers are made available: (1) sic (information is encoded literally, but is questionable) signified by Y; (2) invisible symbol (unprinted note, rest or barline, but logically implied) signified by y; (3) editorial interpretation, (a "modest" editorial act of interpretation -- such as the interpretation of accidentals in musica ficta) signified by x; (4) editorial intervention (a "significant" editorial intervention) signified by X; (5) footnote (accompanying local or global comment provides a text commentary pertaining to a specified data token) signified by ?.

FILE TYPE

It is recommended that files containing predominantly **kern data should be given names with the distinguishing `.krn' extension.

SIGNIFIERS

The following table summarizes the **kern mappings of signifiers and signifieds.
0breve duration
1whole duration
2half duration
3half-note triplet duration
4quarter duration
6quarter-note triplet duration
8eighth duration
12eighth-note triplet duration
16sixteenth duration
24sixteenth-note triplet duration
32thirty-second duration
64sixty-fourth duration
128one-hundred and twenty-eighth duration
.duration augmentation dot
(must follow a number)
-flat sign-nus character)
- -double-flat (two successiv-nus characters)
a-gabsolute pitches above middle C
A-Gabsolute pitches below middle C
#sharp
##double sharp
hend glissando
iundefined; user assignable
jundefined; user assignable
kpartial beam extending leftward
kktwo partial beams extending leftward
lundefined; user assignable
mmordent (semitone)
nnatural sign
oharmonic
pdesignator of a note subsequent to an appoggiatura
qacciaccatura (grace note signifier; in lieu of duration)
rrest
rrany duration rest that is visually rendered as whole duration
ttrill (semitone)
udown-bow
vup-bow
winverted mordent (semitone)
xeditorial interpretation; immediately preceding signifier is interpreted
xxeditorial interpretation; entire data token is interpreted
yeditorial mark: invisible symbol; unprinted note, rest, or
zsforzando
barline, but logically implied
Hbegin glissando
Igeneric articulation (unspecified articulation)
Jend beam
JJend two beams
Kpartial beam extending rightward
KKtwo partial beams extending rightward
Lstart beam
LLstart two beams
Mmordent (whole tone)
Nundefined; user assignable
Ogeneric ornament (unspecified ornament)
Pappoggiatura note designator
Qgroupetto note designator
Rsignified ornament ends with a turn
Sturn
$Wagnerian turn
Ttrill (whole tone)
Ucon sordino; muted note
Vundefined; user assignable
Winverted mordent (whole tone)
Xeditorial intervention; immediately preceding signifier is an
editorial addition; see also x
XXeditorial intervention; entire data token is an editorial addition
Yeditorial mark: sic marking; information is encoded
Zundefined; user assignable
literally, but is questionable
(space character) multiple-stop conjunction -- indicates
joint note-tokens
=barline; == double barline
[first note of a tie
]last note of a tie
_middle note(s) of a tie (underscore)
(slur start
)slur end
{phrase mark (start)
}phrase mark (end)
;pause sign
'staccato mark
sspiccato
"pizzicato mark
`staccatissimo mark; attacca mark; martellato mark, (heavy wedge)
~tenuto mark
^accent mark
:arpeggiation (of multi-note chord)
|in barline -- thin line designator
!in barline -- thick line designator
,breath mark
/up-stem
\down-stem
&elision marker (for slurs or phrases)
?editorial mark: immediately preceding signifier has accompanying
editorial footnote in an ensuing comment
??editorial mark: entire preceding data token has accompanying
editorial footnote in an ensuing comment
@ % + | < >undefined; user assignable
Summary of **kern Signifiers

CONTEXT DEPENDENCIES

In general, signifiers in the **kern representation are intended to be context independent. This means, for example, that the data tokens {(16ff#/' and /ff#16'({ are equivalent. A few exceptions to this principle are necessary in order to maintain the meaning of multiple-character signifiers.

Numbers encoding a duration must be contiguous. That is, a sixteenth note may be encoded as 16ff# or ff#16 but not as 1ff#6. Augmentation dots (signified by the period) must follow immediately after the associated duration numerals. Thus 16.ff# is acceptable, but not 16ff#. or .16ff#. Sharps, flats, and naturals must follow immediately after the corresponding alphabetic pitch signifiers (16ff# but not 16#ff). Signifiers that can be repeated must be contiguous. This include pp, PP, LL, JJ, XX, xx, ??, ##, --, and ..

The elision marker (&) must immediately precede the associated slur (&{ ... &}) or slur (&( ... &)).

Barlines follow a strict contextual syntax. Barlines must begin with one or more equals-signs, followed by an optional measure number, followed by an optional lower-case letter, followed by an optional pause signifier.

In certain applications, it may be necessary to have a canonical ordering of the signifiers within **kern data tokens. For example, when comparing two ostensibly identical **kern files, trivial differences of signifier orderings will cause UNIX commands such as cmp and diff to declare the files to be "different." In this case, it is useful to adopt a standard order of signifiers so that direct file comparisons may be made. Similarly, differences in signifier orderings can cause problems for pattern matching tasks. For example, in searching for a sixteenth-note F-sharp, it is convenient to define a simple regular expression -- such as 16f# rather than having to define a regular expression that handles all possible contextual orderings -- such as (16.*f#)|(f#.*16). For this reason, a canonical ordering of the **kern signifiers is given in the following table.
signifiedsignifier(s)comments
1. open phrase elision indicator&must precede {
2. open phrase mark{
3. open slur elision indicator&must precede (
4. open slur(
5. open tie[
6. duration0123456789any combination; signifiers
may be repeated
7. augmentation dot(s).signifier may be repeated
8. pitch or restabcdefgrABCDEFGonly one of; signifier may
be repeated
9. accidental- or # or n- and # may be repeated
10. glissandoh or H
11. harmonico
12. pause;
13. ornamentMmS$TtWwR or OO precludes others; no
repetition of a given signifier;
must appear in order given
14. appoggiatura designatorp or P
15. acciaccatura designatorq
16. groupetto designatorQ
17. articulationUsz ' " ` ~ ^ : or II precludes others; no
repetition of a given signifier;
must appear in order given
18. bowingu or vonly one of
19. stem-direction/ or \ only one of
20. beamingL or Jsignifiers may be repeated
21. partial beamingk or Ksignifiers may be repeated
22. user-defined marksijlone or more of;
NVZmay be repeated but
@ % + | < > must be in order given
23. closed or continuing tie] or _
24. closed slur elision indicator&must precede )
25. closed slur)
26. closed phrase elision indicator&must precede }
27. closed phrase mark}
28. breath mark,
29. editorial marksxx or XX

Canonical Ordering of Signifiers in **kern Note Tokens


Note that the editorial signifiers ?, y, and Y, as well as the single editorial signifiers x and X (as opposed to xx and XX) can appear anywhere in a data token, except as the first character.

EXAMPLES

A sample document is given below:
!! J.S. Bach, Fugue 2 WTC Book I
!! (3 parts), in c minor; BWV 847b
**kern**kern**kern
*M4/4*M4/4*M4/4
*MM72*MM72*MM72
*k[b-e-a-]*k[b-e-a-]*k[b-e-a-]
*c:*c:*c:
=1=1=1
1r8r1r
.16cc.
.16bn.
.8cc.
.8g.
.8a-.
.16cc.
.16b.
.8cc.
.8dd.
=2=2=2
1r8g1r
.16cc.
.16bn.
.8cc.
.8dd.
.16f.
.16g.
.4a-.
.16g.
.16f.
=3=3=3
1r16e-8r
.16cc.
.16bn16gg
.16an16ff#
.16g8gg
.16fn.
.16e-8cc
.16d.
.8c8ee-
.8ee-16gg
..16ff#
.8dd8gg
.8cc8aan
=4=4=4
*-*-*-

PERTINENT COMMANDS

The following Humdrum commands accept **kern encoded data as inputs:
census -kdetermine general characteristics of a **kern file
centstranslates **kern to **cents
degtranslates **kern to **deg
degreetranslates **kern to **degree
freqtranslates **kern to **freq
hintcalculate harmonic intervals from **kern input
keyestimate the key of a **kern input
mintcalculate melodic intervals from **kern input
pctranslates **kern to **pc
pitchtranslates **kern to **pitch
proofcheck for errors in **kern encoded file
semitstranslate **kern to numerical **semits
solfatranslate **kern to numerical **solfa
solfgtranslate **kern to numerical **solfg
syncomeasure degree of metric syncopation
timebasereformat **kern score with constant timebase
tonhtranslate **kern to numerical **Tonh
transtranspose **kern score
urrhythmcharacterize the rhythmic prototypes in a passage
voxdetermine active and inactive voices in a Humdrum file
The following Humdrum commands produce **kern data as outputs:
kerntranslates **cents, **degree, **freq, **fret, **MIDI, **pitch, **semits, **solfg, **specC, and **Tonh to **kern
timebasereformat **kern score with constant timebase
transtranspose **kern score

TANDEM INTERPRETATIONS

The following tandem interpretations can be used in conjunction with **kern:
clef*clefG2
instrument*I
instrument class*IC
key signatures*k[f#c#]
key*c#:
meter signatures*M6/8
tempo*MM96.3
timebase*tb32
transposing instrument*ITr
Tandem interpretations for **kern

SEE ALSO

barlines, **cents, **degree, **freq, **fret, **MIDI, **mint, **pc, **pitch, **recip, **semits, **solfg, **specC, **Tonh