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.

0-9interval size signifiers; measure numbers
Aaugmented interval quality
ddiminished interval quality
Mmajor interval quality
mminor interval quality
Pperfect interval quality
=barline; == double barline
-descending interval
+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.
!! Wagner, Tristan Prelude!! Wagner, Tristan Prelude
F3 B3 D#4 G#4-M7 -P4 -m2 +M3


The following Humdrum command produces **mint data as outputs:
mintproduces **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#]
Tandem interpretations for **mint


barlines, **hint, hint, kern, mint, **solfg, **Tonh, xdelta, ydelta