# Representation: **deg¶

## 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.

 0-9 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*

### 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 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 *- *-

### PERTINENT COMMANDS¶

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

### TANDEM INTERPRETATIONS¶

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