Humdrum Representation for Melodic Intervals¶
**mint – melodic interval representation
The **mint representation provides a means for characterizing sequential (melodic) pitch distances. The **mint representation permits the encoding of four types of data tokens: interval tokens, pitch offsets, rests, and barlines.
Interval tokens consist of up to three component parts: (1) interval direction, (2) diatonic interval size, and (3) interval quality. The interval direction is signified by a leading plus sign (+) for ascending motion, or a leading minus sign (-) for descending motion. No special signifier is provided to denote unison motion. Note that interval direction information is optional, and so is not a mandatory aspect of the **mint representation.
The diatonic interval size is signified by integer values – 1 for unison, 2 for second, 3 for third, 11 for eleventh, and so on.
Interval qualities are signified as follows: the upper-case letter `M’ for major intervals, lower-case `m’ for minor intervals, upper-case `P’ for perfect, lower-case ‘d’ for diminished, upper-case `A’ for augmented. Doubly-diminished and doubly-augmented intervals are represented by `dd’ and `AA’ respectively. Triply- and quadruply- diminished or augmented intervals are similarly represented by character repetition, e.g. `AAA’. Note that interval quality information is optional, and so is not a mandatory aspect of the **mint representation.
The normal or canonical order for data elements in a **mint interval token is as follows: (1) direction of interval motion, (2) diatonic interval size, (3) interval quality. Note that more than one interval token may appear within Humdrum multiple-stops.
Pitch offsets indicate initial or starting absolute pitches from which successive pitch intervals arise. Pitch offsets are optional and need not appear in a **mint representation. Pitch offsets are distinguished by square brackets. Within the square brackets appears a pitch designation using any one of the following pitch-related representations: ****kern**, ****pitch**, ****solfg** or ****Tonh**. For example, the following **mint pitch offsets are considered equivalent: `b’ (**kern), `B5’ (**pitch), `si5’ (**solfg), `H5’ (**Tonh). Where necessary, several pitch offsets may appear as a Humdrum multiple-stop.
Rests are denoted by the lower-case letter `r’.
Barlines are represented using the “common system” for barlines – see **barlines**.
It is recommended that files containing predominantly **mint data should be given names with the distinguishing `.mnt’ extension.
The following table summarizes the **mint mappings of signifiers and signifieds.
0-9 interval size signifiers; measure numbers A augmented interval quality d diminished interval quality M major interval quality m minor interval quality P perfect interval quality r rest = barline; == double barline
ascending interval ; measure pause
Summary of ***mint** Signifiers*
The following example shows a **pitch spine on the left and a corresponding **mint spine on the right.INPUT OUTPUT !! Wagner, Tristan Prelude !! Wagner, Tristan Prelude **pitch **mint *M6/8 *M6/8 A3 [A3] =1 =1 F4 +m6 . . E4 -m2 =2 =2 F3 B3 D#4 G#4 -M7 -P4 -m2 +M3 *- *-
The following Humdrum command produces **mint data as outputs:
**mint** produces **mint output from **pitch, **kern, **solfg, or **Tonh input
The following tandem interpretations can be used in conjunction with **mint:
meter signatures *M6/8 key signatures *k[f#c#] key *c#:
Tandem interpretations for ***mint***