The beautiful necessity; seven essays on theosophy and architecture . use it is neither too obvious nor too ratio of 4 :y is important for the reasonthat it expresses the angle of sixty degrees,that is, the numbers 4 and 7 represent (verynearly) the ratio between one-half the baseand the altitude of an equilateral triangle;also because they form part of the numericalseries i, 4, 7, 10, etc. Both are mysticnumbers, and in Gothic architecture, particu-larly, proportions were frequently determinedby numbers to which a mystic value was at-tached. According to Gwilt, the Gothicchapels o
The beautiful necessity; seven essays on theosophy and architecture . use it is neither too obvious nor too ratio of 4 :y is important for the reasonthat it expresses the angle of sixty degrees,that is, the numbers 4 and 7 represent (verynearly) the ratio between one-half the baseand the altitude of an equilateral triangle;also because they form part of the numericalseries i, 4, 7, 10, etc. Both are mysticnumbers, and in Gothic architecture, particu-larly, proportions were frequently determinedby numbers to which a mystic value was at-tached. According to Gwilt, the Gothicchapels of Windsor and Oxford are dividedlongitudinally by four, and transversely byseven equal parts. The arcade above theroses in the fagade of the cathedral of Tours shows seven principal units across the front of the nave, and four in each of the towers. A distinguishing characteristic of the series of ratios which represent the consonant intervals within the compass of an octave is that it advances by the addition of i to both terms: 1:2, 2:3, 3 4, 4:5, and 5:6. Such a. H0U5E IN RDM£ 90 VII FROZEN MUSIC 89 series always approaches unity, just as, represented graphically by means of paral-lelograms, it tends towards a square. Ac-cording to W. Watkins Lloyd—in an article published in The American Architect of March 31, 1888—the scale of ratios which determined all the important proportions of the Parthenon is of this order, advancing by consecutive differences of 5. The author has no means of verifying the truth of this statement, but gives it here for what it is worth (Illustration 92). Alberti in his book presents a design for a tower showing his idea for its general proportions. It consists of six stories, in a sequence of orders. The lowest story is a perfect cube and each of the other stories is 11-12 of the story below, or diminishing practically in the proportion of 8, 7, 6, 5, 4, 3, allowing in each case for the amount hidden by the projection of the cornice below; each
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