|
| |
Leon Battista Alberti
Music with Arithmetic, Geometry and Astronomy,
made up the Quadrivium, the four ways, or liberal arts, advocated in the Middle
Ages as essential for the education of the human being, (together with their
outward expression in Grammar, Rhetoric and Logic; the Trivium). Although the
educated person would often have learnt to master a musical instrument, it was
the mathematical and proportional aspect of music which was held to be of most
relevance. Actually playing music, and even composing, because in the creative
moment instinctive faculties seemed to have the upper hand, were, at least up to
the end of the Middle Ages, seen as inferior to the purity of theory alone.
From The Ten Books of Architecture, continued...
In Chapter VI, Alberti develops the relationship between the proportions of
numbers and the measuring of areas.
Methodically, he lists three types of area;
short, middle, and long.
The shortest of all is the square, and in this category of short areas he
includes, sesquialteria, or fifths, or diapente, and sesquitertia, or fourths,
or diatessaron:
"These three Proportions therefore, which we may also call simple, are," he
says, "proper for the smaller Platforms."
Then he lists three further Proportions "Proper for middling Platforms":
First the Double, which he says is best;
second, the Sesqialtera Doubled;
and third, the Sesquitertian Doubled.
The first is a straightforward:
The second is found by taking a square, finding its fifth or sesquialtera,
and extending the area by that amount, and then, in turn, extending that area by
its fifth:
"Thus the Length will exceed the Breadth by a double Proportion plus one Tone
more"
The third Proportion is found by doing the same with the square and its
Fourth
"Here the longer Line contains the shorter twice, excluding one Tone of that
shorter Line."
For his category of "long" areas he lists three: Double Sesquialtera, Double
Sesqitertia, and Quadruple.
Alberti's own summary:
Short: 1:1, 2:3, 3:4
Middling: 2:4. 4:9, 9:16
Long:1:3, 3:8, 1:4
"By the help of these Mediocrates the Architects have discovered many
excellent Things, as well as with Relation to the whole Structure, as to its
several Parts; which we have not Time here to particularize. But the most common
Use they have made of these Mediocrates, has been however for their Elevations."
(p, 200, 1775, Leoni Edition.)
(Note: 18th Nov. 1997: I hope soon to add the sound files
which correspond to these areas.)
Title Page:Introduction
Plato: The Timaeus
Pythagoras: Music and
Space
Alberti: Harmony and Proportion
Palladio: The
Proportion of Rooms-
The Arithmetic Mean
The Geometric Mean-
The Harmonic Mean
Summary: The Square
Root of 2
This page from:
www.aboutscotland.com/harmony/prop2.html
| |
ENQUIRY PAGE
ORDER YOUR CD
|
