Claudius Ptolemy (130) rectified this error, and in the so-called syntonous or intense diatonic scale reduced the proportions of his tetrachord to s, iii, f, -i.
The brilliant success of Humperdinck's Hansel and Gretel, in which Wagnerian technique is applied to the diatonic style of nursery songs with a humorous accuracy undreamed of by Wagner's imitators, points a moral which would have charmed Wagner himself; but until the revival of some rudiments of musical common sense becomes widespread, there is little prospect of the influence of Wagner's harmonic style being productive of anything better than nonsense.
Now suppose we take G as the key-note and form its diatonic scale.
It is evident that for exact diatonic scales for even a limited number of key-notes, key-board instruments would have to be provided with a great number of separate strings or pipes, and the corresponding keys would be required.
The term usually excludes the ringing of the bells according to the diatonic scale in which they are hung (see Bell).
The frequency ratios in the diatonic scale are all expressible either as fractions, with i, 2, 3 or 5 as numerator and denominator, or as products of such fractions; and it may be shown that for a given note the numerator and denominator are smaller than any other numbers which would give us a note in the immediate neighbourhood.
The greater tone, lesser tone, and diatonic semitone of modern music. 2 Ptolemy set forth this system as one of eight possible forms of the diatonic scale.
We shall treat only of the diatonic scale, which is the basis of European music, and is approximated to as closely as is consistent with convenience of construction in key-board instruments, such as the piano, where the eight white notes beginning with C and ending with C an octave higher may be taken as representing the scale with C as the key-note.
But Zarlino uncompromisingly declared that the syntonous or intense diatonic scale was the only form that could reasonably be sung; and in proof of its perfection he exhibited the exact arrangement of its various diatonic intervals, to the fifth inclusive, in every part of the diapason or octave.