|
|
|
Musical Platonic analysis The importance of music for Plato (427 - 347 BC) in the formation of the population can be obtained also from critical judgment that appears on one of the dialogues about Cinesias aimed mainly to amuse viewers rather than to make them better; in fact this controversial author of music and texts written in function to be performed by choral songs for a deity has been called by some as killer of the choir, corruptor of dithyramb besides man with poor moral values. In practice the solemn songs performed during Dionysia, Panathenaea, Thargelia, Lenee festivals were accompanied by rhythmic music and briskly dance and Aristotle postulated that the tragedy might have its origin in the dithyramb. When the audience was listening to these melodic poems of choral type such was the influence on the soul to have probably some consequences in real life. e-mail: info@salutary.eu Tel: +39 338 1809310 Date: 01/01/2017 
n: 3343
 Pythagorean numerical acoustics For the Pythagoreans the secret of the acoustics could be identified with the science of numbers and then the sound is length, speed and harmony derived from precise measurements such as the ratio of three to two, that is the third part of itself, used to divide the monochord and achieve the perfect fifth (C - - - G), the best consonance after that also too obvious of octave and therefore suitable to obtain the scale of sounds, then the fractions of other notes may also be calculated with squares, cubes and then other multiplications. Galilei that made extensive studies on Pythagoras argued that harmony depended on how the frequency of the sound beats on the eardrum and he had singled in the fifth a substantial consonance because linked to sweet a tinge of bitterness. Considerations of this kind are reflected on the whole melody, since a series of sounds ordered and rhythmic should always be consonants. e-mail: info@salutary.eu Tel: +39 338 1809310 Date: 01/01/2016 n: 3033 The Pythagoreans golden section Among the most interesting discoveries of the Pythagoreans and crucial to the manufacture of musical instruments it is necessary to mention undoubtedly the so-called golden ratio of a segment (the segment average proportion among whole the segment and the remaining part) that is obtained with various calculations on polygons such as decagon or pentagon; in this latter case is double since the sides are the golden section of the two diagonals that with they form the triangle, but the same diagonal cut in average and extreme right forming minors isosceles triangles whose base is the golden section for the other two sides. Then the ratio obtained from the golden section has become a kind of definition of the beauty, many monuments are designed keeping in mind like a referral fee, and then with a secret musical link that few know. e-mail: info@salutary.eu Tel: +39 338 1809310 Date: 10/08/2015 n: 2911 Average and Pythagorean harmonics surplus For the Pythagoreans the extent of the surplus in quantities proportional is important for the musical harmony, which occurs when the parties are in excess and exceeded by the same rates that is precisely the harmonic excess verifiable in the arithmetic average; for example in the eighth the mean between 12 and 6 is the paramese of nine units (12 - 9 = 9 - 6) and the interval expressed between greater terms 12 and 9 (12/9 = 4/3, which corresponds to a fourth) is smaller than that between the minor terms 9 and 6 (9/6 = 3/2 a fifth). Instead using the formula for the harmonic mean (a - b)/a = (b - c)/c using the nete of twelve units, the mese of eight units and six for the hypate we get that eight is the average harmonic since (12 - 8)/12 = (8 - 6)/6 and in this interval the proportion expressed by the greater terms 12 and 8 (12/8 = 3/2 which corresponds to a fifth) is greater than that between minor terms 8 and 6 (8/6 = 4/3 a fourth). e-mail: info@salutary.eu Tel: +39 338 1809310 Date: 13/03/2014 n: 2468 A unique Pythagorean note For the Pythagoreans the music was based on numerical relationships that always led back to a single report or note and then to the concept of the number One, from the moment that the whole is the sum of unity and we possess the idea of unity, but at the same time supporting these arguments on a theoretical plane leads to a large number of contradictions that Plato for example tries to solve in a dialogue in which the protagonist is Parmenides (considered a Pythagorean) that had supported the stillness and eternity of being. In the works "Of the nature" Parmenides (late sixth century BC - first half of fifth) with musical and allegorical language warns the reader of not to push the research to the not be where there is no knowledge and then nothing can not give anything, and focus on being who is One, because if were to decline would be divided into parts (if the being is divisible then moves, but if it moves then no longer exists) and always was, what was is and always will be. e-mail: info@salutary.eu Tel: +39 338 1809310 Date: 19/10/2013 n: 2346 Pythagorean recognition of the numbers The stratagem of the Pythagoreans to bring everything to the numbers stemmed from the need for recognition of the various things, since if it was not possible to bring them back to points, polygons, and numerical calculations was not even possible to recognize with certainty as was the case for reports of vibrating strings in the music field and thus also humans or animals were identified in a figurative mode with points as is evident from the story of the Pythagorean Eurytus. The discovery of incommensurable magnitudes as the side and the diagonal of the square (obtainable from the Pythagorean theorem) and initially kept secret had scaled the building sorted according to the numbers and geometric figures that could be drawn on points always recognizable and precisely calculated that reflected the harmony of music, but this did not prevent that the search should proceed in the same direction more or less on numbers basis. e-mail: info@salutary.eu Tel: +39 338 1809310 Date: 01/08/2013 n: 2278 Pythagorean harmonic mean According to the Pythagorean could be found both the same harmony in solid figures that in the music, because for example the cube has twelve sides, eight corners and six floors and therefore the number of angles is between that of the average levels and that of the sides for the harmonic music mean (the mese of 8 units represents the number of corners, the nete that of the sides 12 and the hypate of 6 units the plans). By examining the three dimensions of the cube can be seen that is harmonically composed of himself once, for once and then once again, with a unique geometric harmony that has led some Pythagoreans to compare these relationships with those of the universe and of life itself starting from the cube of the first odd number in the musical sense. Simply multiplying three, which is the first odd number, for three and three more will get twenty-seven which is at an interval of tone compared to twenty-four (27-3) whereas 27/24 is equal to 9/8 (second interval). e-mail: info@salutary.eu Tel: +39 338 1809310 Date: 16/05/2013 n: 2211 Pythagorean harmonic progression Among the many studies carried out first by the Pythagoreans on numbers there were arithmetic progressions, geometric and harmonic that could be verified with musical ratios, such as the nete of twelve units, the mese of eight units and the hypate of six are in progress harmonic according to the formula (a - b) : (b - c) = a : c, which satisfies the property that three numbers are in harmonic progression if their inverses are in arithmetic progression, and then 1/b - 1/a = 1/c - 1/b (considering, however, that the numbers were expressed with segments of chord that may not have the reverse). The numbers were used to verify the harmonic balance and harmony for which only reports 1, 3/2, 4/3 were assessed as consonants corresponded to the numbers that made up the tetraktys of ten point one + two + three + four, a triangular figure of four side considered very important for the Pythagoreans. e-mail: info@salutary.eu Tel: +39 338 1809310 Date: 25/02/2013 n: 2143 The Pythagorean music lyre with eight strings The Greek musical instruments were initially fairly simple and also the lira had only four strings and for improve the harmonic combinations Terpando passed to the seven-stringed lyre, but Pythagoras and his circle to make possible agreements of octave and fifth added the eighth rope that also allowed to harmonize the concept based on the number of the Cosmos (which is a Pythagorean term), since in all things nature seemed to assimilate to the numbers. According to the story of Nicomachus of Gerasa seems that Pythagoras to avoid the monotonous effect with only the fourth tunes made from the intermediate notes of the two tetrachords joined in the seven-stringed made to vibrate along with the extreme (basically in a pattern E - - A, A - - D) added a string and in this way with the eight-sringed lyre made possible the octave tune (1 : 2) and then over to the fourth E - - A (3 : 4), also the fifth A - - - E (2 : 3). e-mail: info@salutary.eu Tel: +39 338 1809310 Date: 01/01/2013 n: 2096 Melodic scale and modal musical system The various notes of a musical scale may be taken as the basis of a new range (for example that of C) and consequently vary also the relationship between full and half tones, in the tempered system there are only two ways, which differ from the major and minor quality of the third (C-E in the major with the semitone between the third and fourth degree, A-C in the minor with the semitone between the second and the third), while in the Greek music there were so many modal as are the degrees of the scale with a wider modal system. Also the notion of the division of musical time in Pythagoreans derived from the tradition, for which there can be no rhythm without rhythmical movement, which in practice is what divides the time (distributed in parts perceptible) with which it will split the composition, since the time does not divide himself. Rhythm occurs when the division of time receives an order determined within eurythmy and harmonics music systems. e-mail: info@salutary.eu Tel: +39 338 1809310 Date: 06/11/2012 n: 2048 Music * The author doesn't assume some kind of responsibility for the bad use of the articles councils (all rights are reserved) |
 |
