Humdrum Representation for Relative Scale Degree

REPRESENTATION
**deg -- relative scale degree representation

DESCRIPTION

The **deg representation can be used to represent key-dependent scale-degree information for music in major or minor keys. The **deg representation differs from the related **degree representation in that it encodes relative rather than absolute pitch-height information.

Three types of data tokens are distinguished by **deg: scale degree tokens, rest tokens, and barlines.

Scale degree tokens are encoded as a combination of melodic approach, degree value, and degree alteration. The caret (^) denotes an ascending melodic approach to the current note, whereas the lower-case letter v denotes a descending melodic approach. Repeated pitches carry no melodic approach signifier. The scale degree values are indicated by the numbers 1 (tonic) to 7 (leading-tone). These values may be chromatically altered by raising (+) or lowering (-). The amount of chromatic alteration is not indicated; for example, a raised super-tonic is represented as 2+ whereas a doubly-raised super-tonic is also represented as 2+. A lowered submediant is represented as 6-.

Scale degree tokens are always represented with respect to a prevailing major or minor key. In the case of minor keys, scale degrees are characterized with respect to the harmonic minor scale only. By way of example, the pitch F in the key of A minor is represented as the submediant (6) while F# is represented as the raised submediant (6+). In the same key, G is represented as the lowered seventh (7-) while G#4 is the normal leading-tone (7). In the key of A major, F is represented as the lowered submediant (6-). If this pitch was approached from below, it would be encoded as ^6- -- whereas if it was approached from above, it would be encoded as v6-.

Rests are represented by the single letter `r'.

Barlines are represented using the "common system" for barlines -- see barlines.

FILE TYPE

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

SIGNIFIERS

The following table summarizes the **deg mappings of signifiers and signifieds.
0-9scale degrees, or measure numbers
^ascending melodic approach
vdescending melodic approach
-scale degree lowered by one -tone
--scale degree lowered by two -tones
+scale degree raised by one semitone
rrest
=barline; == double barline
Summary of **deg Signifiers

EXAMPLES
The sample document given below shows the opening subject of the Fugue in C minor in the second volume of Bach's Well Tempered Clavier. The left spine shows a **kern encoding while the right spine shows a corresponding **deg encoding.
!! J.S. Bach, Fugue 2 WTC Book I
**kern**deg
*M4/4*M4/4
*c:*c:
=1=1
8rr
16cc1
16bnv7
8cc^1
8gv5
8a-^6
16cc^1
16bv7
8cc^1
8dd^2
=2=2
8gv5
16cc^1
16bnv7
8cc^1
8dd^2
16fv4
16g^5
4a-^6
*-*-

PERTINENT COMMANDS

The following Humdrum command accepts **deg encoded data as inputs:
voxdetermine active and inactive voices in a Humdrum file
The following Humdrum command produces **deg data as output:
degtranslates **kern, **pitch, **Tonh, **solfg, to **deg

TANDEM INTERPRETATIONS
The following tandem interpretations can be used in conjunction with **deg:
key signatures*k[f#c#]
key*c#:
Tandem interpretations for **deg

SEE ALSO
barlines, deg, **degree, degree, **kern, **pitch, **solfg, **Tonh