# step

noun: an amount equal to two half steps by which a musical note is higher or lower than another note
noun: a musical interval of two semitones

Ramsay
Nature has not finished when she has given us the Diatonic Scale of notes as first generated. In the diatonic scale, in ascending from C, the root of the tonic, the first step is an interval of 9 commas, supposing that we adopt the common division of the octave into 53 commas, which is the nearest practical measuring rule; the second step has 8 commas; the third has 5; the fourth has 9; the fifth has 8; the sixth has 9; and the seventh and last has 5 commas. So we have three steps of 9 commas, two steps of 8, and two of 5. The order of the steps in the major is 9, 8, 5, 9, 8, 9, 5. In the minor the magnitudes are the same, but the order is 9, 5, 8, 9, 5, 9, 8. So there are three magnitudes.1 But Nature has an equalizing process in the course of her musical marshallings, in which these greater ones get cut down, and have to change places with the lesser, when her purpose requires them so to do. [Scientific Basis and Build of Music, page 47]

that Nature has done so.1 And in every new key into which we modulate Nature performs the same operation, till in the course of the twelve scales she has cut every greater note into two, and made the notes of the scale into twelve instead of seven. These we, as a matter of convenience, call semitones; though they are really as much tones as are the small intervals which Nature gave us in the genesis of the first scale between B-C and E-F. She only repeats the operation for every new key which she had performed at the very first. It is a new key, indeed, but exactly like the first. The 5 and 9 commas interval between E and G becomes a 9 and 5 comma interval; and this Nature does by the rule which rests in the ear, and is uttered in the obedient voice, and not by any mathematical authority from without. She cuts the 9-comma step F to G into two, and leaving 5 commas as the last interval of the new key of G, precisely as she had made 5 commas between B and C as the last interval of the key of C, she adds the other 4 commas to the 5-comma step E to F, which makes this second-last step a 9-comma step, precisely as she had made it in the key of C.2 [Scientific Basis and Build of Music, page 48]

In the progression - that is, the going on from one to another - of these triplets in harmonizing the octave scale ascending, Nature goes on normally till we come to the passage from the sixth to the seventh note of the scale, whose two chords have no note in common, and a new step has to be taken to link them together. And here the true way is to follow the method of Nature in the birthplace of chords.1 The root of the subdominant chord, to which the sixth of the octave scale belongs, which then becomes a 4-note chord, and is called the dominant seventh; F, the root of the subdominant F, A, C, is added to G, B, D, the notes of the dominant, which then becomes G, B, D, F; the two chords have now a note in common, and can pass on to the end of the octave scale normally. In going down the octave scale with harmony, the passage from the seventh to the sixth, where this break exists, meets us at the very second step; but following Nature's method again, the top of the dominant goes over to the root of the subdominant, and F, A, C, which has no note in common with G, B, D, becomes D, F, A, C, and is called the subdominant sixth; and continuity being thus established, the harmony then passes on normally to the bottom of the scale, every successive chord being linked to the preceding note by a note in common. [Scientific Basis and Build of Music, page 49]

The scales march on following each other methodically, whether they be written with sharps or flats, and

"Not a step is out of tune, as the tides obey the moon."

The most natural, because the genetic, way to write the scales is to make the major scales all in sharps, after C, because the major genesis is upward in ratios ascending; and to make the minor scales all in flats, after A, because the minor genesis is downward in ratios descending. Let the young student, however, always keep in mind that the sharps and flats are simply marks to show how Nature, at whatever pitch we are taking the scales, is securely keeping them in the same form as when they are first generated; and in their birthplace no sharps or flats are needed. [Scientific Basis and Build of Music, page 90]