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HARMONY is a state recognized by great philosophers as the immediate prerequisite of beauty. A compound is termed beautiful only when its parts are in harmonious combination. The world is called beautiful and its Creator is designated the Good because good perforce must act in conformity with its own nature; and good acting according to its own nature is harmony, because the good which it accomplishes is harmonious with the good which it is. Beauty, therefore, is harmony manifesting its own intrinsic nature in the world of form. The universe is made up of successive gradations of good, these gradations ascending from matter (which is the least degree of good) to spirit (which is the greatest degree of good). In man, his superior nature is the summum bonum .
Secret Teachings of All Ages: The Pythagorean Theory of Music and Color
The magical mathematics of music | plus.maths.org
May 2005 The astronomer Galileo Galilei observed in 1623 that the entire universe "is written in the language of mathematics", and indeed it is remarkable the extent to which science and society are governed by mathematical ideas. It is perhaps even more surprising that music, with all its passion and emotion, is also based upon mathematical relationships. Such musical notions as octaves, chords, scales, and keys can all be demystified and understood logically using simple mathematics. Pitch: Wave frequenciesDiminished Chords - Understanding Diminished Chords
A diminished chord’s character is best described as ambiguous. When heard alone, diminished chords can be perceived as eerie, goofy, or even annoying. When heard within music, diminished chords often create the desire for tonal resolution; they tend to “leave the listener hanging.”Mathematics and music have a strange connection. Music is the only art form, where the form and the medium are the same. Mathematics is the only science where the methods and the subject are the same.
Math and Music
Symmetry is a well-known phenomenon, both in nature, whose existence does not depend on persons, and in culture, the person- and people-made part of reality. It is found in the physical world of atoms and molecules, in the geometrical world of ellipses and spheres and in the biological world of plants and animals, including human bodies (at least as far as their outward appearance is concerned). It is found in the domestic world of chairs and tables, in the architectural world of buildings and towns and in the artistic world of paintings and jewelry. We find symmetry everywhere, in nature because of some principle of conservation or maximum entropy , and in culture because of the sense of beauty it evokes or, perhaps, for some other reason. A sober person who values truth, and hopefully also relevance, is bound to rejoin that asymmetry too is found everywhere, and not only because every so-called 'symmetry' is probably in practice merely an approximation of it.

