Following out his system, he applied the newly acquired syllables to each of the hexachords—for instance, the lowest hexachord, G A B C D E, which was called hard, became ut re mi fa sol la; the second, which was called natural, C D E F G A, also became ut re mi fa sol la; and the third, which was called soft, F G A B♭ C D, became likewise ut re mi fa sol la. The next three hexachords were treated in the same manner; the last or seventh hexachord was merely a repetition of the first and the fourth.
Before leaving the hexachordal system, it may be as well to explain the mode of procedure when the voice had to go beyond the interval of the sixth. We know that the first of every set of six notes was called ut, the second, re, the third, mi, etc. When the voice had to go beyond la, the sixth note, to B♮, that sixth note was always called re, and was considered the second note of a new hexachord. If, on the other hand, the voice had to go beyond a, to B♭, the fifth note was called re, since the syllables mi fa must always come on the half-tone.
An explanation of the modern German names for notes will be easily understood in this connection. In the German nomenclature the letters of the alphabet stand for the notes of the scale as in the English, with the exception of B. This B, or “round” B, in the German system stands for B♭, which is more logical than our English usage, since our flat is merely a slightly modified form of b. The German B natural is our letter h, which is merely a corruption of the square b, [illustration], which by the addition of a line in time became our ♮. The Germans have carried the flatting and sharping of tones to a logical conclusion in their present nomenclature, for by “sharping” the sound of a single letter it is raised a semitone from its normal diapason, thus F becomes Fis, G Gis. On the other hand, in order to lower a tone, the letter representing it is “flatted,” and F is called Fes, G Ges, the only exception to these rules being the B which we have already considered.
And now we have to speak of notation and its development. Thus far we have found only two ways in which musical sounds were indicated by the ancients. First, we remember the invention of Aristophanes of Alexandria, his accents, high, low, and circumflex. Then we know from Ptolemy, Bœthius, and Alypius that letters were used to designate the different tones; but as there is no music extant in this notation to prove the theory, we need not trouble ourselves with it.
In the period now under consideration (from the third to the tenth century), music was noted in this way: an upstroke of the pen meant a raising of the voice, a downstroke lowered it, a flat stroke meant a repetition of the same note, thus / \ - [G: c' g' c' c']. Gradually it became necessary to indicate the contour of the melodies with more accuracy; therefore the circumflex was added [Over-slur] [G: g' c'' g'] and reversed [Under-slur] [G: g' e' g']. Still later a sign for two steps was invented [Step] [G: e' g' b'] and when the progression was to be diatonically stepwise the strokes were thicker [Thick Step] [G: g' a' b']. So this notation developed, and by combining the many signs together, simple non-rhythmic melodies could be indicated with comparative clearness and simplicity. The flat stroke for a single note -, indicating [G: b'], eventually became smaller and thicker, thus [Thick -]. By combining these different signs, a skip of a third and back came to be noted [Crenellation], and if the note came down on a second instead of the original note it became [Podium] [G: g' b' a']. The quilisma ([Upper Mordent]) indicated a repetition of two notes, one above the other, and we still use much the same sign for our trill. Also the two forms of the circumflex, [Over-slur] [Under-slur], were joined ([Turn]) and thus we have the modern turn, so much used by Wagner.
/ \ -\[Step][G: e' g' b'][Thick Step][G: g' a' b'].-,[G: b'],[Thick -].[Crenellation],[Podium][G: g' b' a'].([Upper Mordent])[Over-slur] [Under-slur],([Turn])Now while this notation was ingenious, it still left much to be desired as to pitch. To remedy this a red line was drawn before writing these signs or neumes, as they were called. This line represented a given pitch, generally E; above and below it were then written the signs for the notes, their pitch being determined by the relative position they held in regard to the line. Thus [Podium, Turn, Upper Mordent] was the equivalent of [G: c' e' d' e' d' c' d' e' d' e' d' e' d'], considering the line as being middle C pitch, a fourth higher F. This was the condition of musical notation in 1000 A.D.
To Guido d'Arezzo is ascribed its development up to some semblance of our present system, although the claim has often been denied. It is certain, however, that the innovations were made at this period. In the first place Guido made the red line always stand for the pitch of F, and at a little distance above it he added another line, this time yellow, which was to indicate the pitch of C. Thus the signs began to take very definite meaning as regards pitch; for, given a sign extending from one line to the other, the reader could see at a glance that the music progressed a fifth, from F to C, or vice-versa. And now the copyists, seeing the value of these lines in determining the pitch of the different signs, of their own account added two more in black ink, one of which they drew between the F and the C line, and the other above the C line, thus [illustration]. By doing this they accurately decided the pitch of every note, for the lowest line, being F, the line between that and the C line must stand for A, and the two spaces for G and B; the top line would stand for E, and the space between it and the yellow line for D. Little by little these copyists grew careless about making the lines in yellow, red, and black, and sometimes drew them all in black or red, thereby losing the distinguishing mark of the F and C lines. In order to remedy this, Guido placed the letters F and C before the lines representing these notes, thus [illustration]. In this way our modern clefs (clavis or key) originated, for the C clef, as it is called, gradually changed its shape to [illustration] and [illustration], and the F clef changed to [illustration], which is our bass clef in a rudimentary form.
Later, still another line was added to the set, thus giving us our modern staff, and another clef, [illustration], was added on the next to the lowest line. This, in turn, became our present treble clef, [G:]. In the course of time the signs themselves underwent many changes, until at last from [Podium], etc., they became our modern signs.
B = S S]).[illustration].[illustration],