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 - 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.


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


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