Relative Scale Degree


deg — relative scale degree representation


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.


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


The following table summarizes the deg mappings of signifiers and signifieds.

0-9 scale degrees, or measure numbers \^ ascending melodic approach v descending melodic approach - scale degree lowered by one -tone — scale degree lowered by two -tones + scale degree raised by one semitone r rest = barline; == double barline —– ————————————-

Summary of deg Signifiers


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 8r r 16cc 1 16bn v7 8cc \^1 8g v5 8a- \^6 16cc \^1 16b v7 8cc \^1 8dd \^2 =2 =2 8g v5 16cc \^1 16bn v7 8cc \^1 8dd \^2 16f v4 16g \^5 4a- \^6 *- *- ———————————- ———


The following Humdrum command accepts deg encoded data as inputs:

vox determine active and inactive voices in a Humdrum file

The following Humdrum command produces deg data as output:

deg translates **kern, **pitch, **Tonh, **solfg, to deg – ——————————— ————————————————————————-


The following tandem interpretations can be used in conjunction with deg:

key signatures *k[f#c#] key *c#: —————- ————

Tandem interpretations for deg


` barlines, deg, **degree, degree, **kern, **pitch, **solfg, **Tonh`