Mozart's 1782-1786
Revolution in Music

by
Lyndon H. LaRouche, Jr.

Illustrations

These graphics are reprinted with permission from the Fidelio Magazine, Volume I, No. 4, 1992. To read the complete article, click here.

For Other Articles on Music, visit the Revolution in Music Page

Figure 1

The six species of the human singing voice, and their registers

* * Click here for a Printable Version of the Chart * *

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Figure 2

The violin family of instruments was developed in order to imitate, and then extend, the principles of the bel canto singing voice. Each member of the violin family has four strings, with each string turned at the musical interval of a fifth above or below the adjacent string or strings. (a) In the simplest case, each open (unfingered) string of the violin can be used as the lowest tone of a new surrogate “vocal” register. The succeeding higher tones fingered on that string remain in the same “register,” until the player changes to the next-higher string. For example, a register shift is simulated by moving from the C♯ played on the G string, up to the open D string—simulating, for instance, the contralto’s shift from first to second register. (b) The same principle applies to the open strings of the viola—C, G, D, and A. Because the viola’s range straddles the usual treble and bass clefs, for clarity the same four strings are shown here using four different clefs; the treble clef, the modern tenor clef (sounds one octave lower than the treble clef), the alto clef (in which most viola music is written), and the bass clef. (c)The violoncello’s open strings.

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Figure 3

The violin plays the passage sung by the soprano, but as a displacement one octave lower. The octave displacement enables the violinist to imitate the II-III register shift by changing form the G string to the D string, and then the III-IV shift by switching to the A string.

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Figure 4

By the nature of their construction, the woodwing instruments have registrations which are essentially fixed, even thought they can be modified to some degree by choosing altgernate fingerings for the same note. The wind instruments therefore tended to be designed and produced in sets or “chest,” whose member mostly corresponded to a particular species of singing voice. Above: a woodcut diagram of various wind instruments in use in the early seventeenth century.

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Figure 5

“Squaring the circle”: Estimating the area of a square approximately equal to that of a given circle, as the average area of two regular polygons.

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Figure 6

An incribed polygon of 2¹⁶ (65,536) sides may seem to closely approach a circl. but the perimeter of the polygon nca never become congruent with the circle’s perimter.

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Figure 7

In his 1673 On the Pendulum clock, Huygens demonstrated that a pendulum made to follow the path of a cycloid (curve MPI) will have the same period, no matter what the amplitude of the swing—that is, the cycloid is “tautochronic.”

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Figure 8



		Positive and negative curvature. (a) The figures derived by rolling a circle on the interior of a larger circle (hypocycloids) are of a differenc species than those produced bgy rolling it on the exterior of the same circle (epicycloids). (b) Packing of spheres, as illustated in Kepler’s “On the Six-Cornered Snowflake.”

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Figure 9

In 1697, Johann Bernoulli demonstrated that cycloid AMK had both the “tautochronic” property shown by Huygens, and the property of a “brachistochrone”—that is, it is the least-action, least-time pathway of descent.

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Figure 10

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Figure 11

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Figure 12

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Figure 13

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Table 1


(a)		Soprano register shifts on violin
(b)		Mezzosoprano register shifts on violin
(c)		Tenor register shifts on viola
(d)		Bass register shifts on violoncello
	Each member of the violin family can be fingered in such a way that it can imitate the register shifts of any voice singing within that instrument’s range. Here, the violin is shown imitating (a) the soprano, and (b) the mezzosoprano vocal register shifts. For example, the soprano’s I-II register shift is imitated by shifting from a fingered F on the G string, to a fingered F♯ on the next-higher D string. The viola is shown imitating the tenor voice species, and the violoncello (’cello) the bass voice. Because these shifts can be made in various places, there are many other possible imitations; also, the four “benchmark” examples shown here are not necessarily the most frequently used. The reader is encouraged to find other possible imitations.
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Mozart's 1782-1786 Revolution in Music

by Lyndon H. LaRouche, Jr.

Illustrations

Join the Schiller Institute, and help make a new, golden Renaissance!

Mozart's 1782-1786
Revolution in Music

by
Lyndon H. LaRouche, Jr.

Join the Schiller Institute,
and help make a new, golden Renaissance!