Remember that the scale degrees are pitches that the melody uses repeatedly. There may also be pitches that the melody uses just once, or occasionally, and that therefore do not correspond with our pitch lines. The use of pitches outside of the melody’s prevailing scale will be called “extra-scalar pitch.”
The solution here is perhaps obvious: symbols for extra-scalar pitches are placed between the pitch lines. This is illustrated in the following score of the beginning of the song “Consider Yourself” from Lionel Bart’s musical Oliver!
The song is based on a major scale, which has intervals of 200, 400, 500, 700, 900, and 1100 cents above the tonic. But the title phrase also includes a pitch at 600 cents, passing between the scale degrees at 500 and 700 cents. This extra-scalar pitch appears as a symbol placed halfway between the relevant pitch lines (circled in this example, though of course it would not be circled in the actual score).
If an extra-scalar pitch is half or two-thirds of the way between adjacent scale degrees, or if its exact pitch is not considered important to specify, then the symbol can simply be placed half or two-thirds of the way between adjacent pitch lines. If the extra-scalar pitch needs to be specified more precisely, its interval in cents above the tonic can be written beneath the symbol where that pitch occurs.
Sometimes what at first appears to be an extra-scalar pitch comes to be used repeatedly, replacing what was previously one of the scale degrees. In this case, the scale has changed, and so should the pitch lines.
An important type of extra-scalar pitch occurs when a melody does not move only by discrete pitch steps (as all of our examples so far do) but instead (or as well) moves by slides or inflections of pitch. Notating such melodies will call for a different approach from the hitherto horizontal and vertical straight lines of our rotated T symbol.
Sources of audio
Lionel Bart, “Consider Yourself” from Oliver!, sung by Martin Horsey and Keith Hampshire in original 1960 London cast album, Decca CD, ASIN: B000025BD5, track 7.