Parry (Grove's Dictionary, article _chromatic_) recommends writing the scale with such accidentals as can occur in chromatic chords without changing the key in which the passage occurs. Thus, taking C as a type, "the first accidental will be D[flat], as the upper note of the minor ninth on the tonic; the next will be E[flat], the minor third of the key; the next F[sharp], the major third of the super-tonic--all of which can occur without causing modulation--and the remaining two will be A[flat] and B[flat], the minor sixth and seventh of the key." According to this plan the chromatic scale beginning with C would be spelled--C, D[flat], D, E[flat], E, F, F[sharp], G, A[flat], A, B[flat], B, C--the form being the same both ascending and descending. This is of course written exclusively from a harmonic standpoint and the advantage of such a form is its definiteness.
94. For _sight-singing purposes_ the chromatic scale[20] is usually written by representing the intermediate tones in ascending by sharps, (in some cases naturals and double-sharps), and the intermediate tones in descending by flats (sometimes naturals and double-flats). The chromatic scale in nine different positions, written from this standpoint, follows, and the syllables most commonly applied in sight-singing have also been added. In the first two scales the student of harmony is asked to note that because of the very common practice of modulating to the dominant and sub-dominant keys, the intermediate tones [sharp]4 and [flat]7 are quite universally used in both ascending and descending melody passages. In other words the scales that follow would more nearly represent actual usage if in each case [sharp]4 (FI) were substituted for [flat]5 (SE) in the descending scale; and if [flat]7 (TE) were substituted for [sharp]6 (LI) in the ascending form.
[Footnote 20: The word _chromatic_ means literally _colored_ and was first applied to the intermediate tones because by using them the singer could get smoother and more diversely-shaded progressions, _i.e._, could get more _color_ than by using only the diatonic tones. Composers were not long discovering the peculiar value of these additional tones and soon found that these same tones were exceedingly valuable also in modulating, hence the two uses of intermediate tones at the present time--first, to embellish a melody; second, to modulate to another key.]