Pythagorean Harmony

When I hear the word harmonize, I immediately think about Pythagoras.  Many great philosophers consider harmony to be a state which is a prerequisite for something to be considered beautiful.  They often said that things are considered to be beautiful only when its contents are harmonious in nature. These philosophers said that our world was beautiful, because our Creator had designed it to be Good and then they seemed to go on and on about the universe, souls, conformity, nature, good and evil, harmony and beauty, trying to link all of these items together.

Pythagoras who lived in the 6th century BC is considered the ‘Father of Harmonics’.  There is a well known myth that tells how he developed his harmonic theory.  The story starts of with him contemplating about harmony, and he is distracted when he passes by a blacksmith shop where the workers were pounding on a piece of metal placed on an anvil.  Pythagoras noted the variances in pitch between the sounds being made by large hammers and those made by smaller implements.  He started estimating the harmonies (combination of simultaneously sounded musical notes to produce chords and chord progressions having a pleasing effect) and discords (lack of harmony between notes sounding together) resulting from combinations of these sounds.  Pythagoras discovered harmonic progression of simple whole numbers and he gained his first clue about the musical intervals of the diatonic scale.

He entered the shop, and carefully examined the tools then he made note of their weights, and when he returned to his own house, Pythagoras constructed an arm of wood so that extended out from the wall of his room.  He made stringed instruments that could be tuned, so that they would consistently produce layered consonant musical intervals.  At regular intervals along this arm he attached four cords (three or more notes that combine harmoniously), all of like composition, size, and weight.  He attached a twelve-pound weight to the first of these arms, to the second a nine-pound weight, to the third an eight-pound weight, and to the fourth a six-pound weight.  These different weights corresponded to the sizes of the blacksmith’s hammers.

Pythagoras is said to have discovered the fact that two similar strings under the same tension and differing only in length, when sounded together give an effect that is pleasant to the ear, if the lengths of the strings are in the ratio of two small integers.  If the lengths are as one is to two, they then correspond to the octave in music.  If the lengths are as two is to three, they correspond to the interval between C and G, which is called a fifth.  These intervals are generally accepted as ‘pleasant’ sounding chords.  He discovered that the first and fourth strings produced the harmonic interval of the octave when sounded together, and Pythagoras learned that doubling the weight had the same effect as halving the string.  The tension of the first string being twice that of the fourth string, their ratio was said to be 2:1, or duple.

Pythagoras discovered the musical intervals and he also taught that people could be healed using sound and harmonic frequencies and he became the first person to prescribe music as medicine.  He applied the principles of harmonics to everything from music, art and architecture to running governments, raising a family, friendship, and personal development.

Pythagoras taught that music should never be approached simply as a form of entertainment, saying that it was much more, being an expression of ‘HARMONIA’, the Divine principle that brings order to chaos and discord.  Thus music contained a dual value similar to that of  mathematics, as it could enable men and women to see into the structures of nature.  His discovery of harmonic musical intervals containing the ability to be expressed by perfect numerical ratios, led him to the realization that all sensible phenomena follow the pattern of number.  Pythagoras thought that numbers were sacred and harmony was a path to the soul.

20 thoughts on “Pythagorean Harmony

      1. I had trouble with math in school. That said, I love numbers and their definitive nature. Just give me an Excel spreadsheet and I will let the numbers sing out in a most harmonious way.

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      2. It is wonderful when you develop the confidence to do thing. I have been known to dabble with Excel on occasions and I once wrote a nested IF statement that is sort of complex, so I explained it below
        =IF(I2=0,IF(F2>0,J2-F2,IF(G2>0,J2-G2,IF(F2+G2=0,J2-H2))),IF(I2>0,J2-I2))
        a) Formula 1 looks at column I to see IF it is zero [IF(I2=0] and if it does, then either steps b, or c, or d will apply.
        b) Formula 1 then looks at column F to see IF it is greater than zero [IF(F2>0] and if it is, then F is subtracted from J [J2-F2]
        c) Formula 1 then looks at column G to see IF it is greater than zero [IF(G2>0] and if it is, then G is subtracted from J [J2-G2]
        d) Formula 1 then looks at the sum of columns F and G to see IF it equals zero [IF(F2+G2=0] and if it is, then H is subtracted from J [J2-H2]
        e) Now Formula 1 looks at column I to see IF it is greater than zero and if it is, then I is subtracted from J [J2-I2]

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      1. To be honest, I must agree with what you said, because I’m not a great fan of mathematics. However, knowing your articles usually tend to carry out amusing ‘googlies’, I continued and was impressed as always!

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  1. Hey, I again missed this post. Again See Jim that’s why I called you a writer. Not a fan of Arithmetic or Algebra, strangely Trigonometry came naturally to me..

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    1. Trig is really just an extension of geometry (which is the study of shapes located in space) and I think that it is the easiest of all the maths, unless you go beyond classical elementary or Euclidean Geometry, which involves size, shape, and measurement and is split up into Plane Geometry, which is two-dimensional and Solid Geometry, which is three-dimensional. Once you begin to delve into the more complex types such as algebraic geometry, analytical geometry, contemporary geometry also known as topology, continuous geometry, differential geometry, Kähler geometry, Lobachevski geometry which later became known as hyperbolic geometry, projective geometry, Poisson geometry, Riemannian Geometry, Sophus Lie’s Contact Geometry, symplectic geometry, tropical geometry things do get more difficult.

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