Quotes about harmonize (116 quotes, page 2)

“Z-relation, or rather, "that certain pitch-class collections share the same 'interval vector' even though they are neither transpositionally nor inversionally equivalent was first pointed out by Howard Hanson in Harmonic Materials of Modern Music (New York: Appleton-Century-Crofts, 1960), p. 22, and by David Lewin in "Re: The Intervallic Content of a Collection of Notes," Journal of Music Theory 4:1 (1960). For a general criticism of Forte's concepts of pitch-class set equivalence see Perle, "Pitch-Class Set Analysis: An Evaluation," Journal of Musicology 8:2”

George Perle (1915–2009) American composer

1990
Page 67, note 8
See: Musical set theory
The Listening Composer

Music

“I met with an accident about five weeks ago in London, which has prevented my walking ever since, and I think I broke one of the metatarsal bones; this has been a favourable circumstance, for it has increased my literary application in a considerable degree. I have been studying, not the theory of the winds, but of the air, and I have made observations on harmonics which I believe are new. Several circumstances unknown to the English mathematicians which I thought I had first discovered, I since find to have been discovered and demonstrated by the foreign mathematicians; in fact, Britain is very much behind its neighbours in many branches of the mathematics: were I to apply deeply to them, I would become a disciple of the French and German school; but the field is too wide and too barren for me.”

Thomas Young (scientist) (1773–1829) English polymath

Letter to Dr. Bostock (June, 1798) as quoted by George Peacock, Life of Thomas Young (1855)

School , Mathematics , Thinking , Study

“Everything harmonizes with me, which is harmonious to thee, O Universe. Nothing for me is too early or too late, which is in due time for thee.”

Marcus Aurelius book Meditations

XII, 30
Meditations (c. 121–180 AD), Book XII
Context: Everything harmonizes with me, which is harmonious to thee, O Universe. Nothing for me is too early or too late, which is in due time for thee. There is one light of the sun, though it is interrupted by walls, mountains and infinite other things. There is one common substance, though it is distributed among countless bodies which have their several qualities. There is one soul, though it is distributed among several natures and individual limitations. There is one intelligent soul, though it seems to be divided.

Universe , Time

“A will whose maxims necessarily harmonize with the laws of autonomy is a holy, absolutely good will.”

Immanuel Kant (1724–1804) German philosopher

Groundwork of the Metaphysics of Morals (1785)
Context: Morality is thus the relation of actions to the autonomy of the will, that is, to a possible giving of universal law through its maxims. An action that can coexist with the autonomy of the will is permitted; one that does not accord with it is forbidden. A will whose maxims necessarily harmonize with the laws of autonomy is a holy, absolutely good will. The dependence upon the principle of autonomy of a will that is not absolutely good (moral necessitation) is obligation. This, accordingly, cannot be attributed to a holy being. The objective of an action from obligation is called duty.

Law

“It is necessary that every thing which is harmonized, should be generated from that which is void of harmony, and that which is void of harmony from that which is harmonized. …But there is no difference, whether this is asserted of harmony, or of order, or composition… the same reason will apply to all of these.”

Aristotle book Physics

Book I, Ch. VI, p. 57.
Physics

“Of the cosmic Gods some make the world be, others animate it, others harmonize it, consisting as it does of different elements; the fourth class keep it when harmonized.”

Sallustius Roman philosopher and writer

VI. On Gods Cosmic and Hypercosmic.
On the Gods and the Cosmos

God , World , Animals

“A solid stores energy in the vibrations of the atoms about their equilibrium positions. In the simplest approximation, which Einstein considered, each atom vibrates with the same frequency, ν, in each of three dimensions, so a solid containing N atoms can be thought of as 3N one-dimensional simple harmonic oscillators.”

Jim Peebles (1935) Canadian-American astronomer

[Quantum Mechanics, 1992, Princeton University Press, 11, https://books.google.com/books?id=hTaw4Ht4Vi8C&pg=PA11]

“The bases of music are rhythm and harmony. Rhythm is ordered recurrence in time… As the planets move around the sun, they repeat their orbits periodically; thus there is already a primitive kind of rhythm in their motion. …Harmony …can be considered a special kind of rhythm. …pure musical tones are produced when the vibrations are… periodic or… repeat themselves regularly in time. Two tones harmonize if their intervals of repetition are in rhythm—or, in mathematical language, if their periods are in proportion.”

Frank Wilczek (1951) physicist

Kepler... in the third book of Harmonice mundi... attempted to make other... related, connections between musical harmony and mathematical proportion.
Longing for the Harmonies: Themes and Variations from Modern Physics (1987)

Music , Sun , Time , Mathematics

“I firmly believe that the provisional agreement between the Vatican and (mainland) China on the appointment of bishops will help harmonize the Universal Church and the Catholic Church in (mainland) China.”

Chen Chien-jen (1951) Vice President of the Republic of China, Taiwanese epidemiologist and academic

Chen Chien-jen (2019) cited in " Holy See values relations with Taiwan: Vice President Chen http://focustaiwan.tw/news/aipl/201910120004.aspx" on Focus Taiwan, 12 October 2019.

Universe , Help

“It was Pythagoras who discovered that the 5th and the octave of a note could be produced on the same string by stopping at 2⁄3 and ½ of its length respectively. Harmony therefore depends on a numerical proportion. It was this discovery, according to Hankel, which led Pythagoras to his philosophy of number. It is probable at least that the name harmonical proportion was due to it, since1:½ :: (1-½):(2⁄3-½).Iamblichus says that this proportion was called ύπ eναντία originally and that Archytas and Hippasus first called it harmonic.”

James Gow (scholar) (1854–1923) scholar

Nicomachus gives another reason for the name, viz. that a cube being of 3 equal dimensions, was the pattern άρμονία: and having 12 edges, 8 corners, 6 faces, it gave its name to harmonic proportion, since:<center>12:6 :: 12-8:8-6</center>
Footnote, citing Vide Cantor, Vorles [Vorlesüngen über Geschichte der Mathematik ?] p 152. Nesselmann p. 214 n. Hankel. p. 105 sqq.
A Short History of Greek Mathematics (1884)

Dependency

“It is a matter of harmonizing these movements, thus arriving at a new possibility for beauty.”

Alexander Calder (1898–1976) American artist

1930s, It Shall Move - On Mobile Sculptures (1932)

Beauty

“Harmonize your day by putting music and words in time with your heart.”

Prevale (1983) Italian DJ and producer

Original: (it) Armonizza la tua giornata mettendo musica e parole a tempo con il cuore.
Source: prevale.net

Music , Time , Heart

“I have an ambition to push at the level of the African Union, that we should have a harmonized legislation in the petroleum and also the mining sector so as to avoid ruinous competition with the aim of attracting investors.”

Macky Sall (1961) current President and former Prime Minister of Senegal

Source: Macky Sall (2021) cited in: " Senegal's President Calls on Africa to Harmonize Oil Legislation https://www.oedigital.com/news/492909-senegal-s-president-calls-on-africa-to-harmonize-oil-legislation" in Offshore Engineer, 16 December 2021.