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Pythagoras 
The
Pythagorean Harmonic Scale 
Who
is located near Pythagoras? 
Pythagoras
Bio 



Raphael
Santi
Pythagoras
and Musical Proportion
on the fresco "The School
of Athens"
(enlarged)
15091511
Vaticano, Stanza della Segnatura, Rome 



Youth
holds at the feet of Pythagoras a panel on which is inscribed his
consonances of song. Pythagoras saw in the geometry of musical harmony
a key to the order of the cosmos ("harmony of the spheres").
Notice the tablet. It shows: the words diatessaron, diapente, diapason.
The roman numerals for 6, 8, 9, and 12, showing the ratio of the
intervals, same as in the music book frontispiece. Under the tablet
is a triangular number 10 called the sacred tetractys.
Pythagoras
is represented by his theory of mathematical harmony on the left,
Euclid by the perfection of Geometry on the right  and the elaborate
perspective design of the architectural setting seems to embody
both. Pythagoras [and not the Evangelist Matthew according to Vasari
in the 16th c. Pythagoras, representing Arithmetic, is sitting in
the foreground. The two men who are jostling to look over his shoulder
recall figures in Leonardo da Vinci's unfinished Adoration of the
Magi in the Uffizi. Raphael had occasion to study Leonardo's picture
during his stay in Florence. Probably Raphael used two Groups (one
around Pythagoras) to show some early Philosophers with the somehow
mysterious Pythagoras and the other group around Euclid (or Archimedes),
Ptolemy etc. who represent more the clear true Science. A closer
look at Pythagoras text, we recognize his most important discovery
of harmony theory (music) and the numbers 1, 2, 3 and 4 which added
together give the sacred number 10 (X). Epogdoon is a natural number
which is 1/8 larger than a given number for example 18 is the Epogdoon
of 16. 




The
Pythagorean Harmonic Scale, tone, diatessaron, diapente, diapason
Take
four pieces of string 6", 8", 9", 12", of equal
consistency, and vibrate them under equal tension
interval between VI (6) and XII (12)
= octave
interval between VI (6), IX (9), and between VIII (8) and XII (12)
= fifth
interval between VI (6) and VIII (8), and between IX (9) and XII
(12)
= fourth
interval between VIII (8) and IX (9)
= major tone




Under
Raphael's musical diagram is a representation a triangular figure
composed of 4 rows of 10 points: I, II, III, IIII, called the tetractys,
which is the Pythagorean perfect number 10. The sum of the first four
figures constitutes all musical harmonies. Moreover, the Pythagorean
number 10 comprises all numbers, and thus was regarded as sacred and
as the "mother of the universe."
As can be seen from the tablet, 10 is the sum of
the first four figures (1, 2, 3, 4) which constitutes all musical
harmonies and can be associated with the philosophical concept of
the Harmony of the Spheres.
In harmony, diapason is the ratio of 2:1 between
a pair of frequencies . The diapason is also called octave. The
diatessaron is a ratio of 4:3 between a pair of frequencies. It
is the harmonic mean of unison and diapason: Diapente is the ratio
3:2 between a pair of frequencies or, equivalently, the ratio 2:3
between a pair of wavelengths. It is the arithmetic mean of diapason
and unison. In a diagrammatic representation of a lyra the strings
are tuned in the relative proportions VI, VIII, VIIII, XII giving
the intervals of an octave (diapason) between VI and XII, fifths
(diapente) between VI, VIIII and VII, XII and fourths (diatessaron)
between VI, VIII and VIIII, XII. The interval of a tone is present
between VIII and VIIII. In contrast to the group around Euclid (or
Archimedes) persons around Pythagoras stretch their head to see
what Pythagoras is writing.






Who
is located near Pythagoras?
Who
is the old man who copies the words of Pythagoras? Probably Boethius
[Anicius Manlius Severinus Boethius (480 Rome – c. 524526
execution of Boethius)], a person who with his work was influential
in the Medieval times, with books such as Consolatio Philosophiae
(The Consolation of Philosophy) written when he was in prison before
his execution. Due to his knowledge of Greek he translated various
astronomical and mathematical Greek texts which were important for
the advance of Science in Europe.
Some say it is Empedocles, Zeno, Archytas of Tarentum, Iamblichus.
But maybe also Anaximander (611  547 BC) (there are some similarities
of this image with a sculpture of Anaximander), Terpander or Nicomachus
or another musician and follower of Pythagoras.
The
philosopher of Cordoba Averroës [Abu AlWalid Muhammad Ibn
Ahmad Ibn Muhammad Ibn Ahmad Ibn Ahmad Ibn Rushd (1126 Cordoba 
10.12.1198 Marrakech /Morocco)] identified by his turban. He was
an author with commentaries to Aristotle's Metaphysics and On The
Soul, Commentaries to Plato's Republic and many more other books
about Philosophy, Astronomy, Medicine. 




Pythagoras
Greek philosopher and mathematician
Pythagoras,
(born c. 570 bce, Samos, Ionia [Greece]—died c. 500–490
bce, Metapontum, Lucanium [Italy]) Greek philosopher, mathematician,
and founder of the Pythagorean brotherhood that, although
religious in nature, formulated principles that influenced
the thought of Plato and Aristotle and contributed to the
development of mathematics and Western rational philosophy.
(For a fuller treatment of Pythagoras and Pythagorean thought,
see Pythagoreanism).
Pythagoras
emigrated to southern Italy about 532 bce, apparently to escape
Samos’s tyrannical rule, and established his ethicopolitical
academy at Croton (now Crotone, Italy). It is difficult to
distinguish Pythagoras’s teachings from those of his
disciples. None of his writings have survived, and Pythagoreans
invariably supported their doctrines by indiscriminately citing
their master’s authority. Pythagoras, however, is generally
credited with the theory of the functional significance of
numbers in the objective world and in music.
Other
discoveries often attributed to him (the incommensurability
of the side and diagonal of a square, for example, and the
Pythagorean theorem for right triangles) were probably developed
only later by the Pythagorean school. More probably, the bulk
of the intellectual tradition originating with Pythagoras
himself belongs to mystical wisdom rather than to scientific
scholarship.
Encyclopædia
Britannica, Inc.







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