History of Harmonics

In the following, we take a little journey through time of the presence of the harmonics, over Hans Kayser, Victor Goldschmidt, Albert von Thimus, Johannes Kepler, Robert Fludd to the antiquity to Plato and the League of Pythagoreans.

Hans Kayser - der Gründer der harmonikalen Lehre vom Klang der Welt

Hans Kayser (1891-1964)

Born April 1, 1891 in Buchau, Württemberg, † April 14, 1964 in Bern, was a German art and music theorist and founder of modern harmonic basic research in the 20th century.

"First and foremost, harmonics is a whole doctrine, that is, it seeks to grasp the world and mankind under holistic facial and auditory points, and the scientific instrument for this is the primordial phenomenon of the tone - ..."

Kayser, for example, sees Max Planck's quantum theory, with its discontinuously increasing discrete energy levels and the overtone series of music theory, realize similar principles of natural law.
He also sees parallels to the harmonic ratios of the tones in the proportions  of crystalline bodies. Kayser refers to writings of the crystallographers Victor Mordechai Goldschmidt and Christian Samuel Weiss, which draw analogies between their science and music theory.

Life and work of Hans Kayser will be discussed in more detail elsewhere on this site.

Victor Goldschmidt - der Entdecker der Harmonie der Kristallstrukturen

Victor Goldschmidt (1853-1933)

Born February 10, 1853 in Mainz; † May 8, 1933 in Salzburg, was a German mineralogist, crystallographer, natural philosopher, mineral collector and patron.

"Harmony is the key to understanding nature, choosing what is contained in our individual senses and the regressive unifier of sensory perceptions, the mind, adapted to the external world, but only from this is the nature accessible to our knowledge." Epistemology is therefore the summary of those laws that are common to the mind and the outside world .... " Heidelberg, December 1900. See an elaboration "World Sound of Metals" HERE. In this way he goes the opposite way as later Hans Kayser, who, starting from the music, goes on the search for correspondences in the forms and structures of nature.

See an elaboration "Weltklang der Metalle"  (world sound of crystals) HERE.

In this way he goes the opposite way as later Hans Kayser, who, starting from music, goes on the search for correspondences in the forms and structures of nature.

Albert von Thimus - der Wiederentdecker der Harmonik

Albert von Thimus (1806-1876)

Albert von Thimus set a decisive course in the 19th century in order to establish harmonics. He understood harmonis as a theory of proportion based on numbers, expressing itself in music, architecture, art, culture, etc. Music is based on numbers and their relationships to each other. The same laws of music are reflected in people and in the world. Thimus built by his research a bridge that mediated between the 17th and the 20th century. He understood his work as a reconstruction of original Pythagorean wisdom.

Thimus's task was to deduce the Pythagorean school from harmonic roots and thus contribute to a unified and holistic worldview. He incorporated the Sefer Jezira, the
I Ching, Egyptian, Oriental, Greek, Latin texts, etc. into his book, which he interpreted in a harmonic way. "The Harmonic Symbolism of Antiquity"

Johannes Kepler, Entdecker der Harmonie der Planetenbahnen

Johannes Kepler (1571-1613)

The astronomer, astrologer and mathematician Johannes Kepler writes in the 17th century:

"Geometry is as eternal as the spirit of God before the creation of things, and has given "Our sculptor has added the mind to the senses, not merely for the sake of the human being's livelihood - many kinds of living things with their irrational soul can do that much more skillfully. But also to the fact that we penetrate from the being of things, which we look with eyes, to the causes of their being and becoming, although obviously no benefit is connected with it.

"Geometry is as eternal as the spirit of God before the creation of things, and has given in it the archetypes of the creation of the world."

Harmonices Mundi, 1619

Robert Fludd, ein englischer Philosoph, Theosoph und Mediziner

Robert Fludd (1574-1637) 

was an English philosopher, theosophist and physician.
The astronomer Johannes Kepler attacked Fludd because of the pictures and hieroglyphs used in his books. Kepler compared his truly mathematical diagrams with the numbers hermetically used by Fludd.

"Monochordium Mundi symphoniacum"

Pythagoras eine Figur iam Westportal der Kathedrale Chartres

The School of Chartres (11th / 12th century AD)


The cathedral school to Chartres reached in the 11./12. Century European celebrity. It was created by Fulbertus of Chartres (* 950, † 1028) in the Platonic sense as "Academy". Decisive for the philosophical work was a new Platonism, in particular Plato's idea of ​​a world soul as a cosmological principle. Of the writings of Plato, the Latin translation of the Timaios was known. This writing has played a special role in the interpretation. It ensured that the basic ideas of harmonics were taken seriously.
This explains how, with the construction of the Cathedral of Chartres from 1194 to 1260 AD, the Pythagorean harmonics were able to achieve the formative and proportionate ideas of form and proportion that are still overwhelming today. And that is why the visitor in the central west portal of the cathedral still encounters a figure representing Pythagoras (see picture on the left).

The New Platonists (3rd-6th century AD)

By Neoplatonism we mean today the most recent and last significant current of Greek philosophy. It originated before the middle of the 3rd century from Rome, where the philosopher Plotinus († 270) had founded a new school of philosophy. It spread from there over the Roman Empire. As the last representative of ancient Greek philosophy, it resulted in an examination of Christianity, which had already become the Roman state religion.

The spread of this school to the east in particular led to the doctrine of Iamblichos of Chalkis († 320/325), which deviated significantly from the original Roman school of Plotinus. This development finally led back to Rome with the scholar Boethius (480/485 - 524/526 AD). Both are of particular importance for the transmission of the Pythagorean harmony through history.


Boethius Neuplatoniker

Boethius (480/485 - 524/526 n. Chr.)

Iamblichos verfasste in griechischer Sprache eine Gesamtdarstellung der pythagoreischen Lehre. Von den insgesamt zehn Büchern sind nur die Bücher 1 bis 4 erhalten. Für die Weitergabe der pythagoreischen Harmonik ist insbesondere das zweite Buch, Protreptikos (Aufruf) zur Philosophie von Bedeutung. Viele für das weiterführende Verständnis der Harmonik-Ideen von Pythagoras sind offensichtlich in den verloren gegangenen Büchern nicht mehr verfügbar.

Iamblichos Neuplatoniker

Iamblichos (240/245 - 320/325 AD)

Iamblichos wrote in Greek an overall presentation of the Pythagorean doctrine. Of the 10 books, only books 1 to 4 are preserved. For the passing on of the Pythagorean harmonics the second book, Protreptikos (Calling) to the philosophy is particularly important. Many of the advanced understanding of Pythagoras' harmonic ideas are obviously no longer available in the lost books.

Platon Förderer der Harmonik

Plato (428 / 427- 348/347 BC)

He was a disciple of Socrates, whose thinking and method he described in many of his works. The versatility of his talents and the originality of his groundbreaking achievements as a thinker and writer made Plato one of the most famous and influential figures in intellectual history.

Particularly in "Timaios" an intensively discussed research topic are the mixing processes in the creation of the world soul by the creator god, the demiurge, and the individual souls by the gods subordinate to him. The role of the mean values ​​(geometric, harmonic and arithmetic mean) in the presentation of the mathematical basis of the creation of the world soul is emphasized.

It is probable that Plato, in his information on the structure of the world soul, has taken into account the mathematical relations underlying musical harmony. However, he did not address the music-theoretical interpretation of the given numerical relationships but left the corresponding conclusions to the knowledgeable Reader.

Pythagoras der Vater der Harmonik

Pythagoras (circa 570-490 BC)

The philosopher and scientist Pythagoras, as well as the Covenant of Pythagoreans can be considered as the founding fathers of the harmonical philosophy of the West. We know very little about Pythagoras himself, that's because he did not leave us any writings.
What we know about him with certainty - apart from a few fragments of some pre-Socratics - goes back to isolated messages from Herodotus (about 490 - 420 BC) and Plato (427 - 347 BC).
In addition there are some relatively probable traditions of Aristotle (384 BC) and his disciples Eudemos and Aristoxenos, who still knew Philip's last eyewitnesses to Pythagoras.
The only direct traditions of Pythagorean thought, especially in relation to the Pythagorean Tetraktys, can be found in the fragments of the Pythagorean Philolaos (around 450 BC).

Ancient source material for Tetraktys.

Die einzigen direkten Überlieferungen pythagoreischen Gedankenguts, insbesondere auch in Bezug auf die Pythagoreische Tetraktys finden sich in den Fragmenten des Pythagoreers Philolaos (um 450 v.Chr.):

Antikes Quellmaterial zur Tetraktys