Absolute Scale Degree


degree – absolute scale degree representation


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

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

Scale degree tokens are encoded as a combination of degree values, degree alterations, and octave designations. 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-.

A second integer value is used to indicate the octave following the ANSI standard pitch designations. For example, the pitch A4 lies in octave 4. (Octaves begin at C and end at B.) In order to avoid confusing scale degrees with octave indications the slash character is used as a sub-token separator. For example, the pitch C4 in the key of C major is represented as 1/4, while the pitch A#4 in the key of G major is represented as 2+/4.

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 F4 in the key of A minor is represented as the submediant (6/4) while F#4 is represented as the raised submediant (6+/4). In the same key, G4 is represented as the lowered seventh (7-/4) while G#4 is the normal leading-tone (7/4). In the key of A major, F4 is represented as the lowered submediant (6-/4).

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 degree data should be given names with the distinguishing `.dgr' extension.


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

0-9 scale degrees, octave designations, or measure numbers / scale-degree / octave number separator - scale degree lowered + scale degree raised r rest = barline; == double barline —– ——————————————————–

Summary of degree 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 degree encoding.


!! J.S. Bach, Fugue 2 WTC Book I
**kern **degree *M4/4 *M4/4 *c: *c: =1 =1 8r r 16cc 1/5 16bn 7/4 8cc 1/5 8g 5/4 8a- 6/4 16cc 1/5 16b 7/4 8cc 1/5 8dd 2/5 =2 =2 8g 5/4 16cc 1/5 16bn 7/4 8cc 1/5 8dd 2/5 16f 4/4 16g 5/4 4a- 6/4 *- *- ———————————- ————


The following Humdrum commands accept degree encoded data as inputs:

kern translates degree to kern pitch translates degree to pitch solfg translates degree to solfg tonh translates degree to Tonh vox determine active and inactive voices in a Humdrum file

The following Humdrum command produces degree data as output:

degree translates kern, pitch, solfg, Tonh, to degree – ————————————— —————————————————————————————-


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

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

Tandem interpretations for degree


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