Two large caveats are in order (both are discussed at length in the introduction to the essay): (1) my usual warning about music for social uses (the published version is not "the piece," which would certainly involve multiple iterations, but also variations, improvisation, interludes (or "trios"), and sequences ("sets" or "medleys"); (2) a warning that the sources are of all sorts, from published commercial products to ethnographic transcriptions. The sequence, here as in the essay, must be topical; a chronological sequence by publication date would be nonsensical (to give a taste of the problem: in the large collections of Joyce and O'Neill, one repeatedly finds notes to the effect "I remember this from childhood" or "from the singing of _____ in County _____"). Related to (2): the bass-clef accompaniments are additions to commercial publications. This is historically a repertoire of song, fiddle, and flute; the most likely more complex accompaniment (before the piano in a mid-nineteenth upper-middle class household) would be a harp.
The four categories are: (1) simple examples of rising lines, with appropriate focal tones; (2) play of registers common in—and congenial to—the violin; (3) "long" cadences where the lower and upper registers are connected by a stepwise sequence; (4) modal tunes, or tunes showing a modal heritage.
To begin, then: "The Duchess of Gordon," my one example of a simple rising line. The strathspey is a slow, often highly ornamented fiddle tune making frequent use of dotted notes, including the "Scotch snap" (see beat three in bar 1). This version, where the two phrases are identical, is most likely a fragment.
The next example is "David Grady's Reel," from P. W. Joyce, Ancient Irish Music: comprising one hundred airs hitherto unpublished, many of the old popular songs, and several new songs (1873). The reel is a lively dance in common time. I can't speak to the dances, but the music for the reel and the jig are often "cousins," the one in duple, the other in triple time.
As this already demonstrates, categories (1) & (2) overlap more often than not. By far the most common registral distinctions map onto the violin's fifths layout as lower fifth and upper fourth of the octave, or G4-D5 and D5-G5, indicated with directional arrows in the first system below. In this instance, the lower register dips down still further to the open D string. The upper register easily accommodates a stepwise ascending cadence gesture, repeated in every phrase here (boxed). Two points of interest: (1) phrases 2-4 open with a gesture to a successively higher note (circled and connected); (2) the high note B5, sforzando, articulates the division between repetitions of the tune (arrow in the final bar).
