Go to: Chamber, Classical, Complete, Concert, Disciple, Harmonic, Literacy, Mathematics, Tuning systems

Chamber music: type of music designed for ensembles that can perform in a small room. For example, duets, trios or quartets are respectively for two, three of four instruments (See Britannica).

Classical, adjective (per Merriam-Webster)

1. STANDARD, CLASSIC
2. • of or relating to the ancient Greek and Roman world and especially to its literature, art, architecture, or ideals (classical civilization)
   • versed in the classics (a classical scholar)
3. • of or relating to music of the late 18th and early 19th centuries characterized by an emphasis on balance, clarity, and moderation
   • of, relating to, or being music in the educated European tradition that includes such forms as art song, chamber music, opera, and symphony as distinguished from folk or popular music or jazz
4. • AUTHORITATIVE, TRADITIONAL
     • of or relating to a form or system considered of first significance in earlier times classical Mendelian genetics
     • not involving relativity, wave mechanics, or quantum theory classical physics
   • conforming to a pattern of usage sanctioned by a body of literature rather than by everyday speech
5. concerned with or giving instruction in the humanities, the fine arts, and the broad aspects of science a classical curriculum

Complete: used here in echo to Gödel’s theorems of incompleteness. For a long period extending from antiquity to the 19th century, music, arithmetic, geometry and astronomy constituted what the medievals called the quadrivium of classical education. Tuning systems show how mathematics and music are linked. During the 19th century, mathematicians like Hilbert became confident they would soon prove their discipline’s completeness. They thought all truths would be proven by mathematics. However, in 1931, Gödel proved the reverse: mathematics must accept some truths that will forever stay outside their reach.

Concert: social institution for the public performance of music outside of a religious or dramatic context. Concerts developed in their present form from the informal music-making of the 17th century. The social influences affecting the development of the concert also affected the music conceived for it, and the evolution in music from Mozart to Beethoven has a counterpart in the patronage of the concert (see Britannica).

Disciple etymology: Old English discipulus, discipul, from Latin discipulus ‘learner’, from discere ‘learn’; reinforced by Old French deciple . (see also Mathematics)

Form (Sonata Form, Cyclic form,…)

Harmonic, noun (per Merriam-Webster)

1. • OVERTONE, especially : one whose vibration frequency is an integral multiple of that of the fundamental
   • a flutelike tone produced on a stringed instrument by touching a vibrating string at a nodal point
2. a component frequency of a complex wave (as of electromagnetic energy) that is an integral multiple of the fundamental frequency

Literacy: the ability to read and write. Music literacy is thus the ability to read and write printed music.

Mathematics etymology: mid 16th century: plural of obsolete mathematic ‘mathematics’, from Old French mathematique, from Latin (ars) mathematica ‘mathematical (art)’, from Greek mathēmatikē (epistēmē), from the base of manthanein ‘learn’. (see also disciple)

Tuning systems, the various systems of pitches used to tune an instrument, and their theoretical bases. Four tuning systems are worth mentioning here. Violins and cellos are tuned per the Just or Pythagorean tuning. The tuning of pianos is equal tempered.

• Just intonation. In just intonation, the frequencies of the scale notes are related to one another by simple numeric ratios, a common example of this being 1:1, 9:8, 5:4, 4:3, 3:2, 5:3, 15:8, 2:1 to define the ratios for the seven notes in a C major scale.
• Pythagorean tuning. Pythagorean tuning is technically a type of just intonation, in which the frequency ratios of the notes are all derived from the number ratio 3:2. Using this approach for example, the 12 notes of the Western chromatic scale would be tuned to the following ratios: 1:1, 256:243, 9:8, 32:27, 81:64, 4:3, 729:512, 3:2, 128:81, 27:16, 16:9, 243:128, 2:1.
• Meantone temperament. A system of tuning that averages out pairs of ratios used for the same interval (such as 9:8 and 10:9).
• Equal temperament. The twelve-tone equal temperament was invented in the 17th century and is a special case of meantone temperament, in which the twelve notes are separated by logarithmically equal distances (100 cents).