**degree -- absolute scale degree representation

DESCRIPTION

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.

FILE TYPE

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

SIGNIFIERS

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
*-	*-

PERTINENT COMMANDS

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

• Pertinent description in the Humdrum User Guide
• Index to Humdrum Representations
• Index to Humdrum Commands
• Table for Contents for Humdrum User Guide