1 (number)

1 (one; /ˈwʌn/ or UK /ˈwɒn/, also called unit, unity, and (multiplicative) identity), is a number, a numeral, and the name of the glyph representing that number. It represents a single entity, the unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1.

As a number

One, sometimes referred to as unity, is the integer before two and after zero. One is the first non-zero number in the natural numbers as well as the first odd number in the natural numbers.

Any number multiplied by one is that number, as one is the identity for multiplication. As a result, one is its own factorial, its own square, its own cube, and so on. One is also the result of the empty product, as any number multiplied by one is itself. It is also the only natural number that is neither composite nor prime with respect to division, but instead considered a unit.

As a digit

The glyph used today in the Western world to represent the number 1, a vertical line, often with a serif at the top and sometimes a short horizontal line at the bottom, traces its roots back to the Indians, who wrote 1 as a horizontal line, much like the Chinese character 一. The Gupta wrote it as a curved line, and the Nagari sometimes added a small circle on the left (rotated a quarter turn to the right, this 9-look-alike became the present day numeral 1 in the Gujarati and Punjabi scripts). The Nepali also rotated it to the right but kept the circle small. This eventually became the top serif in the modern numeral, but the occasional short horizontal line at the bottom probably originates from similarity with the Roman numeral I. In some countries, the little serif at the top is sometimes extended into a long upstroke, sometimes as long as the vertical line, which can lead to confusion with the glyph for seven in other countries. Where the 1 is written with a long upstroke, the number 7 has a horizontal stroke through the vertical line.

Inventions and Sinfonias (Bach)

The Inventions and Sinfonias, BWV 772–801, also known as the Two- and Three-Part Inventions, are a collection of thirty short keyboard compositions by Johann Sebastian Bach (1685–1750): 15 inventions, which are two-part contrapuntal pieces, and 15 sinfonias, which are three-part contrapuntal pieces. They were originally written as musical exercises for his students.

Bach titled the collection:

The two groups of pieces are both arranged in order of ascending key, each group covering eight major and seven minor keys.

The inventions were composed in Köthen; the sinfonias, on the other hand, were probably not finished until the beginning of the Leipzig period.

Media

External links

Bach – Inventions ( 43:26 minutes) at BBC's Discovering Music: Listening Library

Invention

An invention is a unique or novel device, method, composition or process. The invention process is a process within an overall engineering and product development process. It may be an improvement upon a machine or product, or a new process for creating an object or a result. An invention that achieves a completely unique function or result may be a radical breakthrough. Such works are novel and not obvious to others skilled in the same field. An inventor may be taking a big step in success or failure.

Some inventions can be patented. A patent legally protects the intellectual property rights of the inventor and legally recognizes that a claimed invention is actually an invention. The rules and requirements for patenting an invention vary from country to country, and the process of obtaining a patent is often expensive.

Another meaning of invention is cultural invention, which is an innovative set of useful social behaviours adopted by people and passed on to others. The Institute for Social Inventions collected many such ideas in magazines and books. Invention is also an important component of artistic and design creativity. Inventions often extend the boundaries of human knowledge, experience or capability.

Surname

A surname or family name is a name added to a given name. In many cases, a surname is a family name and many dictionaries define "surname" as a synonym of "family name". In the western hemisphere, it is commonly synonymous with last name because it is usually placed at the end of a person's given name.

In most Spanish-speaking and Portuguese-speaking countries, two or more last names (or surnames) may be used. In China, Hungary, Japan, Korea, Madagascar, Taiwan, Vietnam, and parts of India, the family name is placed before a person's given name.

The style of having both a family name (surname) and a given name (forename) is far from universal. In many countries, it is common for ordinary people to have only one name or mononym.

The concept of a "surname" is a relatively recent historical development, evolving from a medieval naming practice called a "byname". Based on an individual's occupation or area of residence, a byname would be used in situations where more than one person had the same name.

Johann Sebastian Bach

Johann Sebastian Bach (31 March [O.S. 21 March] 1685 – 28 July 1750) was a German composer and musician of the Baroque period. He enriched established German styles through his skill in counterpoint, harmonic and motivic organisation, and the adaptation of rhythms, forms, and textures from abroad, particularly from Italy and France. Bach's compositions include the Brandenburg Concertos, the Goldberg Variations, the Mass in B minor, two Passions, and over three hundred cantatas of which around two hundred survive. His music is revered for its technical command, artistic beauty, and intellectual depth.

Bach's abilities as an organist were highly respected during his lifetime, although he was not widely recognised as a great composer until a revival of interest and performances of his music in the first half of the 19th century. He is now generally regarded as one of the greatest composers of all time.

Life

Bach was born in Eisenach, in the duchy of Saxe-Eisenach, into a great musical family. His father, Johann Ambrosius Bach, was the director of the town musicians, and all of his uncles were professional musicians. His father probably taught him to play the violin and harpsichord, and his brother, Johann Christoph Bach, taught him the clavichord and exposed him to much contemporary music. Apparently at his own initiative, Bach attended St. Michael's School in Lüneburg for two years. After graduating, he held several musical posts across Germany: he served as Kapellmeister (director of music) to Leopold, Prince of Anhalt-Köthen, and as Thomaskantor in Leipzig, a position of music director at the main Lutheran churches and educator at the Thomasschule. He received the title of "Royal Court Composer" from Augustus III in 1736. Bach's health and vision declined in 1749, and he died on 28 July 1750.