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The term note has two primary meanings: 1) a sign used in music to represent the relative duration and pitch of a sound; and 2) a pitched sound itself. Notes are the "atoms" of much Western music: discretizations of musical phenomena that facilitate performance, comprehension, and analysis (Nattiez 1990, p.81n9).
   The term "note" can be used in both generic and specific senses: one might say either "the piece Happy Birthday to You begins with two notes having the same pitch," or "the piece begins with two repetitions of the same note." In the former case, one uses "note" to refer to a specific musical event; in the latter, one uses the term to refer to a class of events sharing the same pitch.

Note name

Two notes with fundamental frequencies in a ratio of any power of two (for example half, twice, or four times) will sound very similar. Because of that all notes with these kinds of relations can be grouped under the same pitch class. In traditional music theory pitch classes are represented by the first seven letters of the Latin alphabet (A, B, C, D, E, F and G) (some countries use other names as in the table below). The span of notes between one pitch and another that's twice (or half) its frequency is called an octave. In order to differentiate two notes that have the same pitch class but fall into different octaves, the system of scientific pitch notation combines a letter name with an Arabic numeral designating a specific octave. For example, the now-standard tuning pitch for most Western music, 440 Hz, is named a′ or A4. There are two formal ways to define each note and octave, the Helmholtz system and the Scientific pitch notation.

Accidentals

Letter names are modified by the accidentals sharp (similar to the symbol #) and flat (similar to the letter b). These symbols respectively raise or lower a pitch by a semitone or half-step, which in modern tuning will multiply or divide (respectively) the frequency of the original note by sqrt[12]

For notes in an A440 equal temperament, this formula delivers the standard MIDI note number. Any other frequencies fill the space between the whole numbers evenly. This allows MIDI instruments to be tuned very accurately in any microtuning scale, including non-western traditional tunings.

History of note names

Music notation systems have used letters of the alphabet for centuries. The 6th century philosopher Boethius is known to have used the first fifteen letters of the alphabet to signify the notes of the two-octave range that was in use at the time. Though it isn't known whether this was his devising or common usage at the time, this is nonetheless called Boethian notation.
   Following this, the system of repeating letters A-G in each octave was introduced, these being written as minuscules for the second octave and double minuscules for the third. When the compass of used notes was extended down by one note, to a G, it was given the Greek G (Γ), gamma. (It is from this that the French word for scale, gamme is derived, and the English word gamut, from "Gamma-Ut", the lowest note in Medieval music notation.)
   The remaining five notes of the chromatic scale (the black keys on a piano keyboard) were added gradually; the first being B which was flattened in certain modes to avoid the dissonant tritone interval. This change wasn't always shown in notation, but when written, B (B-flat) was written as a Latin, round "b", and B (B-natural) a Gothic b. These evolved into the modern flat and natural symbols respectively. The sharp symbol arose from a barred b, called the "cancelled b".
   In parts of Europe, including Germany, Poland and Russia, the natural symbol transformed into the letter H: in German music notation, H is B (B-natural) and B is B (B-flat).
   In Italian, Portuguese, Greek, French, Russian, Romanian, Spanish and Hebrew notation the notes of scales are given also in terms of Do - Re - Mi - Fa - Sol - La - Si rather than C - D - E - F - G - A - B. These names follow the original names reputedly given by Guido d'Arezzo, who had taken them from the first syllables of the first six musical phrases of a Gregorian Chant melody Ut queant laxis, which began on the appropriate scale degrees. These became the basis of the solfege system. "Do" later replaced the original "Ut" for ease of singing (most likely from the beginning of Dominus, Lord), though "Ut" is still used in some places. "Si" or "Ti" was added as the seventh degree (from Sancte Johannes, St. John, to which the hymn is dedicated).

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