harmonic proportions
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2020 ◽  
Vol 1 ◽  
pp. 145-169
Author(s):  
Galanti Tommaso

The essay aims to highlight aspects related to thoughts and works of Florentine neo-humanistic culture of the late seventeenth century. We analyze two episodes of Giovan Battista Foggini’s early activity, which was strongly conditioned and determined by the mathematician Vincenzo Viviani. The first case is the facade of Viviani’s private palace, where the scagliola reliefs give shape to the message of the epigraphs on the cartouches. Stoic ethical principles, combined with the adherence to the Jesuit thought, are used to enhance Galileo Galilei and his discoveries, generating a modern mythology aimed at exalting the figure of the great scientist. The second commission that Foggini receives from the Viviani family by the end of the seventeenth century is the palace of the grand-ducal auditor Donato Viviani della Robbia. The architectural solutions adopted by Foggini stem from the legacy of Raphael’s thought concerning geometry and harmonic proportions. At the same time, the internal plastic and pic- torial decoration provides a behavioral model based on the canons of measure and aims at the search for truth: following this vocation, man will be in a position to gain awareness of the universal harmony and to spread it through beauty and pleasure. These concepts, taken from the thought of the Jesuit Sforza Pallavicino, come to Florence through Gottfried Wilhelm Leibniz, with whom Viviani entertained a lively intellectual exchange.


2019 ◽  
Vol 16 (1) ◽  
pp. 362-368
Author(s):  
Michael A. Sherbon

The golden ratio is found to be related to the fine-structure constant, which determines the strength of the electromagnetic interaction. The golden ratio and classical harmonic proportions with quartic equations give an approximate value for the inverse fine-structure constant the same as that discovered previously in the geometry of the hydrogen atom. With the former golden ratio results, relationships are also shown between the four fundamental forces of nature: electromagnetism, the weak force, the strong force, and the force of gravitation.


Author(s):  
James Kirk Irwin

Abstract: This paper will evaluate Le Corbusier’s notion of ratio as expressed in his Modulor and Modulor 2. Particular emphasis will be placed on the dialogue (or polemical exchange) between Rudolf Wittkower and Le Corbusier contained within Modulor 2 concerning the nature of the Divine Proporzione. The historiography of this area of art and architecture includes a vigorous debate from the mid-twentieth century among Modernist architects and art historians over the nature of the Divine Proportions. It is in this context that the dialogue between Le Corbusier and Wittkower occurs. Le Corbusier describes human form with a Fibonacci-based number system expressed through a universally applied system of measure, Le Modulor. Wittkower describes a set of harmonic proportions, conceptually universal, that describe the essence of Renaissance Architecture. Both influenced the course of Modern Architecture in the late twentieth-century.  Keywords: Le Modulor, Wittkower. DOI: http://dx.doi.org/10.4995/LC2015.2015.743


2000 ◽  
Vol 28 (01) ◽  
pp. 41-55 ◽  
Author(s):  
Wei Kung Wang ◽  
Tse Lin Hsu ◽  
Hsi Chan Chang ◽  
Yuh Yin Lin Wang

We investigated the pulse spectrum variation of the human radial artery when Hsien-Ku (St 43), an acupoint on the stomach meridian, was needled and compared the results with the acupuncture effects of two other acupoints, Tsu-San-Li (St-36) and Tai-Shih (K-3), reported previously. For Hsien-Ku, the harmonic proportions were redistributed: the second harmonic (C2) decreased, C3, C5, C6, C7, C8 and C9 increased, C3, C6 and C9 became the relative peaks to their neighboring harmonics and C2, C4 became the relative minimums. The phase angles of the 2nd harmonic (P2) and 5th harmonic (P5) decreased, propagating faster. These effects were similar to that of Tsu-San-Li which is also on the stomach meridian. A totally different pattern was found for Tai-Shih on the kidney meridian. These results strengthen the theory that a meridian can be classified according to its effects on the pulse spectrum, and that all the meridian related effects such as those caused by acupuncture or meridian specific herbs are frequency specific.


1997 ◽  
Vol 25 (03n04) ◽  
pp. 357-366 ◽  
Author(s):  
Wei Kung Wang ◽  
Tse Lin Hsu ◽  
Yi Chiang ◽  
Yuh Yin Lin Wang

Extracts of the traditional Chinese fomlula Sie-Zie-Tang as well as one of its main components, Radix Aconiti were injected into rats intraperitoneally to observe pressure wave spectrum changes at the caudate artery. We found that Radix Aconiti decreased the C0 (DC term of the pulse), C5 and C6 (the harmonic proportions of the 5th and the 6th harmonic), but increased C2 and C3 (the harmonic proportions of the second and the third harmonic) significantly. For Sie-Zie-Tang, the increases of C2, C3, and C4 were accompanied by the decreasing of C0. The decreases of C5, C6 were small and not significant. The additional ingredients in the formula reduce toxic side effects (arrhythmia or heart failure caused by faster and stronger heart beat) due to Radix Aconiti. For human subjects, low dose Sie-Zie-Tang tends to normalize the Fourier components of the pressure wave. Orally taking the formula elevates the harmonic proportion of the harmonic that is lower than normal, but suppresses the higher one. Our result provides a possible mechanism for heart meridian related herbs. It strengthens heart beats, and normalizes energy distribution to different meridians. The study on Sie-Zie-Tang reveals another formula construction to reduce toxic side effects.


1996 ◽  
Vol 24 (01) ◽  
pp. 93-98 ◽  
Author(s):  
Wei Kung Wang ◽  
Tse Lin Hsu ◽  
Yi Chiang ◽  
Yuh Yin Lin Wang

The prandial effect on the pulse spectrum of the radial artery was studied. Ingestion greatly affected the spectrum of the pressure pulse. For most of the tested subjects, the harmonic proportions of the 2nd and the 4th harmonic increased significantly after ingestion, however a decreasing effect was found on the 5th, 6th, 7th, 8th, 9th harmonics. The spectrum became stable from half hour after ingestion and last 3 to 4 hours. From these results, a reliable pulse diagnosis is therefore suggested to be done in the period when the pulse spectrum is stable; physiological significance of these postprandial phenomena is also discussed.


1996 ◽  
Vol 24 (03n04) ◽  
pp. 305-313 ◽  
Author(s):  
Wei Kung Wang ◽  
Tse Lin Hsu ◽  
Hsi Chan Chang ◽  
Yuh Yin Lin Wang

The frequency specific acupuncture effect on Tai-Tsih (K-3) was examined by investigating pulse variations at the radial artery. The harmonic proportions of the 2nd, 3rd and the 4th harmonics were increased but the 5th, 6th and 9th harmonics were decreased significantly. The phase angles of all except the 2nd harmonic were increased (wave propagated slower). These results are compared with the frequency specific acupuncture effect on Tsu-San-Li (St-36) which we reported previously (Wang et al., 1995a). This study solidified the weak coupling resonance theory, which successfully explains these frequency specific effects as well as the acupuncture mechanism.


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