Dodecachordon

...sounds are distinguished by lines and spaces in songs. Although the parallel lines are drawn at equal distances to the eye, the voices themselves are not all separated by an equal interval In musical notation, the physical distance between lines doesn't change, but the musical "distance" (pitch interval) between notes can be either a whole tone or a half-step (semitone)., as will be demonstrated more extensively later when we discuss intervals.

Ancient musicians called voices phthongos original: "phthongos," a Greek term for a musical sound of a definite pitch and called keys strings. However, Guido of Arezzo A famous 11th-century monk and music theorist credited with inventing the musical staff and the "ut-re-mi" system—a man of exceptional learning whom our age still follows—arranged these keys into an order like a ladder scala. He placed the voice "ut" on the lowest parallel line, marking it with the third letter of the Greek alphabet, Gamma (Γ). He did this so that we would not be unmindful that this discipline, like all others, came from the Greeks.

Next, in the space above the first parallel line, he placed the voice "re," preceded by the letter A. Then, on the second line, he placed the voice "mi" with the letter B written before it. Some believe this "B" should be drawn with a square body so that the right side descends below the base and the left side rises above the top, in this form: ♮ This is the origin of our modern "natural" sign, used to indicate B-natural, which was called "hard B" because of its square shape.. Franchino Gaffurio original: "Franchinus Laudenis," a contemporary of Glarean and a major music theorist of the Italian Renaissance, the leader in this art in our time, taught this. He was moved by the reason that there should be a distinction between the two voices "mi" and "fa" at the eighth key, b-flat and b-natural original: "b fa ♮ mi".

Furthermore, in the space above the second line, Guido placed two voices, "fa" and "ut," marked with the letter C. This begins a new order of six voices hexachord to take over where the previous order ran out while ascending. It does not start at the very end of the previous order, but in the middle, so that voices that are similar by nature are placed in the same key. Our musicians agree there is a certain natural similarity every fourth voice: "ut" with "fa," "re" with "sol," and "mi" with "la." However, I believe the reason for this division was to ensure the semitone the smallest interval in this system always occurred in the third position, between "mi" and "fa," following the form of the diatonic genus The standard musical scale of Western music, consisting of whole tones and half-steps., which we will treat later.

I do not know on whose authority they teach that "ut" and "fa" are "soft" voices, "re" and "sol" are "natural," and "mi" and "la" are "hard," unless we prefer to look at common usage rather than the art itself. For what song is more tearful and "soft" than one where mi reigns? For example, some have composed harmonies for the Lamentations of Jeremiah and the complaint of the Holy Magdalene at the tomb of the Lord: "They have taken away my Lord" original: "Tulerunt dominum meum". Perhaps our musicians took these ideas from the nature of the Modes The "Modes" were the predecessors to our modern major and minor scales, each thought to have a specific emotional character.. For in the Lydian mode (which some see as soft, but others as grave and severe), "ut" and "fa" reign in the fourth above. In the Dorian, a grave and severe mode, "re" and "sol" reign. In the Phrygian, which is religious and "hard," "mi" and "la" reign. But these matters are too deep for this section and will be explained later.

For beginners, they teach this better: among these six voices, three are lower (ut, re, mi) and three are higher (fa, sol, la). When ascending, one should use the lower ones; when descending, the higher ones. The remaining keys arranged by Guido are as follows: D, on the third line, with the two voices "sol" and "re." E, in the space, likewise with two voices, "la" and "mi." And F, on the fourth line, with "fa" and "ut." G, in the space, with three voices: "sol," "re," and "ut." For here begins the order of six voices called disjunct original: "διεζευγμένων", which means the tetrachord of the separated voices, having "mi" in the b key; whereas the previous order, which begins as conjunct original: "συνημμένων", contains the...

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Book I.

...tetrachord of the connected voices, which has "fa" in the b key.

Up to this point, starting from A, these are the keys they call "essential": A, B, C, D, E, F, G. The remaining keys are then repeated in the same way as the first ones, though with more voices added because of the "mi" and "fa" in the b key, using lowercase letters: a, b, c, d, e, f, g. After these, five doubled letters follow: aa, bb, cc, dd, ee.

However, the two voices "mi" and "fa" in the b key are not equidistant from the lowercase a. The "mi" is separated from the a by a whole tone, but the "fa" is separated by a minor semitone. Thus, these two voices in what seems to be the same key are actually further apart from each other than "mi" is from "fa" in the small c, or "fa" from "mi" in the small a. We will demonstrate this more broadly later when we discuss the division of the tone.

If we count the b key as one location, there are twenty keys in the Guidonian scale in this order:

Thus, in musical notation, Γ (Gamma) falls on the first line, as we said, and A in the space above the first line. Then, line and space take the voices step by step in an ascent until the end is reached. This is an image of a ladder, whether you prefer to look at it ascending or descending, as will be clear in the illustration below.

Furthermore, I would like to advise the reader that it was impossible for us to completely avoid the "common speech" accepted by everyone who treats these subjects. If I had invented new names—since there was no such ancient description—I would be accused of arrogance. Alternatively, I must concede something to the usage of so many years. Finally, since this subject is in some way new, I do not know why anyone should avoid these words, which are new but accepted by use.

Among the Latin authors, why are terms like quadrans (a fourth), triens (a third), and quincunx (five-twelfths) masculine, if not because the word for a unit of weight, as, is masculine? In the same way, we say "rising" and "setting" in the masculine because of the Sun, and "continent" in the feminine because of the Earth. So, let us be permitted to use "second," "third," and "fourth," since these refer back to the consonances the intervals between musical notes. Why else do the Greeks say diapason the interval of an octave; literally "through all [the strings]" rather than "through all things"?

Ultimately, a teacher must speak clearly and strive above all to be understood. It is necessary, therefore, that he does not flee or reject everything that might be useful to the task. Let the reader remember that Cicero The Roman statesman and orator known for his perfect Latin style spoke one way when treating Philosophy and another way when he charmed his "divinity," the Roman People, with sweet oratory. But now, let us place below the General Model, in which we have placed each letter with its string, marking the designation of both the Greek and Latin keys with numbers, which we will discuss more fully in Chapter XVIII of this volume.

The Guidonian Scale ___________________ | ee | |------------------| | dd | |------------------| | cc | |------------------| | bb | |------------------| | aa | |------------------| | g | |------------------| | f | |------------------| | e | |------------------| | d | |------------------| | c | |------------------| | b | |------------------| | a | |------------------| | G | |------------------| | F | |------------------| | E | |------------------| | D | |------------------| | C | |------------------| | ♮ | |------------------| | A | |------------------| | Γ | |__________________|