Friday March 26, 2021’s Smile of the Day: Ptolemy

On this Day:

In 127, Greek astronomer and mathematician Ptolemy begins his observations of the heavens (until 141 AD).

Claudius Ptolemy c. 100 – c. 170 AD) was a mathematician, astronomer, natural philosopher, geographer and astrologer who wrote several scientific treatises, three of which were of importance to later Byzantine, Islamic and Western European science. The first is the astronomical treatise now known as the Almagest, although it was originally entitled the Mathematical Treatise (Μαθηματικὴ Σύνταξις) and then known as The Great Treatise (Ἡ Μεγάλη Σύνταξις). The second is the Geography, which is a thorough discussion of the geographic knowledge of the Greco-Roman world. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. This is sometimes known as the Apotelesmatiká (Ἀποτελεσματικά) but more commonly known as the Tetrábiblos from the Koine Greek (Τετράβιβλος) meaning “Four Books” or by the Latin Quadripartitum.

Ptolemy lived in the city of Alexandria in the Roman province of Egypt under the rule of the Roman Empire, had a Latin name (which several historians have taken to imply he was also a Roman citizen), cited Greek philosophers, and used Babylonian observations and Babylonian lunar theory. The 14th-century astronomer Theodore Meliteniotes gave his birthplace as the prominent Greek city Ptolemais Hermiou (Πτολεμαΐς ‘Ερμείου) in the Thebaid (Θηβᾱΐς). This attestation is quite late, however, and there is no evidence to support it. He died in Alexandria around 168.

Ptolemy’s Almagest is the only surviving comprehensive ancient treatise on astronomy. Babylonian astronomers had developed arithmetical techniques for calculating astronomical phenomena; Greek astronomers such as Hipparchus had produced geometric models for calculating celestial motions. Ptolemy, however, claimed to have derived his geometrical models from selected astronomical observations by his predecessors spanning more than 800 years, though astronomers have for centuries suspected that his models’ parameters were adopted independently of observations. Ptolemy presented his astronomical models in convenient tables, which could be used to compute the future or past position of the planets. The Almagest also contains a star catalogue, which is a version of a catalogue created by Hipparchus. Its list of forty-eight constellations is ancestral to the modern system of constellations, but unlike the modern system they did not cover the whole sky (only the sky Hipparchus could see). Across Europe, the Middle East and North Africa in the Medieval period, it was the authoritative text on astronomy, with its author becoming an almost mythical figure, called Ptolemy, King of Alexandria. The Almagest was preserved, like most of extant Classical Greek science, in Arabic manuscripts (hence its familiar name). Because of its reputation, it was widely sought and was translated twice into Latin in the 12th century, once in Sicily and again in Spain. Ptolemy’s model, like those of his predecessors, was geocentric and was almost universally accepted until the appearance of simpler heliocentric models during the scientific revolution.

His Planetary Hypotheses went beyond the mathematical model of the Almagest to present a physical realization of the universe as a set of nested spheres, in which he used the epicycles of his planetary model to compute the dimensions of the universe. He estimated the Sun was at an average distance of 1,210 Earth radii, while the radius of the sphere of the fixed stars was 20,000 times the radius of the Earth.

Ptolemy presented a useful tool for astronomical calculations in his Handy Tables, which tabulated all the data needed to compute the positions of the Sun, Moon and planets, the rising and setting of the stars, and eclipses of the Sun and Moon. Ptolemy’s Handy Tables provided the model for later astronomical tables or zījes. In the Phaseis (Risings of the Fixed Stars), Ptolemy gave a parapegma, a star calendar or almanac, based on the appearances and disappearances of stars over the course of the solar year.

Ptolemy also wrote an influential work, Harmonics, on music theory and the mathematics of music. After criticizing the approaches of his predecessors, Ptolemy argued for basing musical intervals on mathematical ratios (in contrast to the followers of Aristoxenus and in agreement with the followers of Pythagoras), backed up by empirical observation (in contrast to the overly theoretical approach of the Pythagoreans). Ptolemy wrote about how musical notes could be translated into mathematical equations and vice versa in Harmonics. This is called Pythagorean tuning because it was first discovered by Pythagoras. However, Pythagoras believed that the mathematics of music should be based on the specific ratio of 3:2, whereas Ptolemy merely believed that it should just generally involve tetrachords and octaves. He presented his own divisions of the tetrachord and the octave, which he derived with the help of a monochord. His Harmonics never had the influence of his Almagest or Planetary Hypotheses, but a part of it (Book III) did encourage Kepler in his own musings on the harmony of the world (Kepler, Harmonice Mundi, Appendix to Book V). Ptolemy’s astronomical interests also appeared in a discussion of the “music of the spheres” (per Wikipedia).

First, a Story:

Why haven’t aliens visited our solar system yet? They read the reviews in The Lonely Planet: Only one star.

Second, a Song:

The musica universalis (literally universal music), also called music of the spheres or harmony of the spheres, is an ancient philosophical concept that regards proportions in the movements of celestial bodies – the Sun, Moon, and planets – as a form of music. This “music” is not thought to be audible, but rather a harmonic, mathematical or religious resonance. The idea continued to appeal to scholars until the end of the Renaissance, influencing many schools of thought, including humanists. Further scientific exploration discovered orbital resonance in specific proportions in some orbital motion.

The connection between music, mathematics, and astronomy had a profound impact on history. It resulted in music’s inclusion in the Quadrivium, the medieval curriculum that included arithmetic, geometry, music, and astronomy, and along with the Trivium (grammar, logic, and rhetoric) made up the seven liberal arts, which are still the basis for higher education today.

A small number of recent compositions either make reference to or are based on the concepts of Musica Universalis or Harmony of the Spheres. Among these are Elegy by Diego Cobian, Music of the Spheres by Mike Oldfield, Om by the Moody Blues, The Earth Sings Mi Fa Mi album by The Receiving End of Sirens, Music of the Spheres by Ian Brown, and Björk’s single Cosmogony, included in her 2011 album Biophilia. Earlier, in the 1910s, Danish composer Rued Langgaard composed a pioneering orchestral work titled Music of the Spheres. Music of the Spheres was also the title chosen for the musical foundation of the video game Destiny, and was composed by Martin O’Donnell, Michael Salvatori, and Paul McCartney. The game features an 8-part musical companion also called Music of the Spheres, officially released in 2018.

Paul Hindemith wrote an Opera (1957), and a Symphony using the same music, called Die Harmonie der Welt (“The harmony of the world”) based upon the life of the Astronomer Johannes Kepler. 

Rush percussionist and lyricist Neil Peart referenced The Music of the Spheres on the song “The Analog Kid” which appeared on the Signals album in 1982.

Josef Strauss (20 August 1827 – 22 July 1870) was an Austrian composer.

He was born in Mariahilf (now Vienna), the son of Johann Strauss I and Maria Anna Streim, and brother of Johann Strauss II and Eduard Strauss. His father wanted him to choose a career in the Austrian Habsburg military. He studied music with Franz Dolleschal and learned to play the violin with Franz Anton Ries.

He received training as an engineer, and worked for the city of Vienna as an engineer and designer. He designed a horse-drawn revolving brush street-sweeping vehicle and published two textbooks on mathematical subjects. Strauss had talents as an artist, painter, poet, dramatist, singer, composer and inventor.

Josef Strauss wrote 283 opus numbers. He wrote many waltzes, including: Sphären-Klänge (Music of the Spheres), Delirien (Deliriums), Transaktionen (Transactions), Mein Lebenslauf ist Lieb’ und Lust (My Character is Love and Joy), and Dorfschwalben aus Österreich (Village Swallows from Austria), polkas, most famously the Pizzicato Polka with his brother Johann, quadrilles, and other dance music, and also some marches. The waltz The Mysterious Powers of Magnetism (Dynamiden) with the use of minor keys showed a quality that distinguished his waltzes from those of his more popular elder brother. The polka-mazurka shows influence by Strauss, where he wrote many examples like Die Emancipierte and Die Libelle (per Wikipedia).

Allmusic.com per Robert Cummings writes: The Sphärenklänge Waltzes are considered one of the finest efforts of the melancholic Josef Strauss, a composer who might have developed a deeper musical language had his Strauss family heritage not constrained him to do otherwise. Still, he could turn out waltzes and other dances with nearly the craftsmanship, if not the facility, of his older brother Johann II. Josef used more inventive harmonies and understood melodic subtleties with a keenness not possessed by his older brother. The Sphärenklänge Waltzes here divulge his many strengths, from his mastery of form to his colorful orchestral scoring.

In the dreamy opening, Josef divulges a vague Wagnerian sense in his subtle, suggestive harmonies. The main theme is not immediately catchy, but wears on the listener on repeated hearings, exhibiting a sort of serene grace in its first subject and a playful joy in its second subject. In the middle section, Strauss imaginatively develops his thematic material, deftly retaining the air of festivity and playfulness, the dance step never missing a beat or a sense of continuity in the celebration. One can safely assess that this is one of the most sophisticated waltz works ever composed by a Strauss. Lasting about 12 minutes, it will appeal to a wide audience in and out of classical realms.

Here is Andre Rieu and his Johann Strauss Orchestra performing Josef Strauss’ Sphären-Klänge (Music of the Spheres). I hope you enjoy this! 

(https://www.youtube.com/watch?v=B5nDpPbTyuI)

Thought for the Day:

“As material fortune is associated with the properties of the body, so honor belongs to those of the soul.” –  Ptolemy

Have a great day!

Dave & Colleen

© 2021 David J. Bilinsky and Colleen E. Bilinsky

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