Note

In music, the term note has two primary meanings: Notes are the "atoms" of much Western music: discretizations of musical phenomena that facilitate performance, comprehension, and analysis.
 * 1) A sign used in musical notation to represent the relative duration and pitch of a sound;
 * 2) A pitched sound itself.

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 equal to any power of two (e.g. half, twice, or four times) are perceived as very similar. Because of that, all notes with these kinds of relations can be grouped under the same pitch class. In traditional music theory within the English-speaking and Dutch-speaking world, pitch classes are typically represented by the first seven letters of the Latin alphabet (A, B, C, D, E, F and G). A few European countries, including Germany, adopt an almost identical notation, in which H is substituted for B (see below for details). However, most other countries in the world use the naming convention Do-Re-Mi-Fa-Sol-La-Si, including for instance Italy, Spain, France, most Latin American countries, Greece, Turkey, Russia, and all the Arabic-speaking or Persian-speaking countries.

The eighth note, or octave is given the same name as the first, but has double its frequency. The name octave is also used to indicate the span between a note and another with double frequency. 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 systems to define each note and octave, the Helmholtz pitch notation and the Scientific pitch notation.

Accidentals
Letter names are modified by the accidentals. A sharp ♯ raises a note by a semitone or half-step, and a flat ♭ lowers it by the same amount. In modern tuning a half step has a frequency ratio of $$\sqrt[12]{2}$$, approximately 1.059. The accidentals are written after the note name: so, for example, F♯ represents F-sharp, B♭ is B-flat.

Additional accidentals are the double-sharp 𝄪, raising the frequency by two semitones, and double-flat 𝄫, lowering it by that amount.

In musical notation, accidentals are placed before the note symbols. Systematic alterations to the seven lettered pitches in the scale can be indicated by placing the symbols in the key signature, which then apply implicitly to all occurrences of corresponding notes. Explicitly noted accidentals can be used to override this effect for the remainder of a bar. A special accidental, the natural symbol ♮, is used to indicate an unmodified pitch. Effects of key signature and local accidentals do not cumulate. If the key signature indicates G-sharp, a local flat before a G makes it G-flat (not G natural), though often this type of rare accidental is expressed as a natural, followed by a flat (♮♭) to make this clear. Likewise (and more commonly), a double sharp 𝄪 sign on a key signature with a single sharp ♯ indicates only a double sharp, not a triple sharp.

Assuming enharmonicity, many accidentals will create equivalences between pitches that are written differently. For instance, raising the note B to B♯ is equal to the note C. Assuming all such equivalences, the complete chromatic scale adds five additional pitch classes to the original seven lettered notes for a total of 12 (the 13th note completing the octave), each separated by a half-step.

Notes that belong to the diatonic scale relevant in the context are sometimes called diatonic notes; notes that do not meet that criterion are then sometimes called chromatic notes.

Another style of notation, rarely used in English, uses the suffix "is" to indicate a sharp and "es" (only "s" after A and E) for a flat, e.g. Fis for F♯, Ges for G♭, Es for E♭. This system first arose in Germany and is used in almost all European countries whose main language is not English, Greek, or a Romance language.

In most countries using these suffixes, the letter H is used to represent what is B natural in English, the letter B is used instead of B♭, and Heses (i.e., H𝄫) is used instead of B𝄫 (not Bes, which would also have fit into the system). Dutch-speakers in Belgium and the Netherlands use the same suffixes, but applied throughout to the notes A to G, so that B, B♭ and B𝄫 have the same meaning as in English, although they are called B, Bes, and Beses instead of B, B flat and B double flat. Denmark also uses H, but uses Bes instead of Heses for B𝄫.

12-tone chromatic scale
The following chart lists the names used in different countries for the 12 notes of a chromatic scale built on C. The corresponding symbols are shown within parenthesis. Differences between German and English notation are highlighted in bold typeface. Although the English and Dutch names are different, the corresponding symbols are identical.

Note designation in accordance with octave name
The table of each octave and the frequencies for every note of pitch class A is shown below. The traditional (Helmholtz) system centers on the great octave (with capital letters) and small octave (with lower case letters). Lower octaves are named "contra" (with primes before), higher ones "lined" (with primes after). Another system (scientific) suffixes a number (starting with 0, or sometimes -1). In this system A4 is nowadays standardised to 440 Hz, lying in the octave containing notes from C4 (middle C) to B4. The lowest note on most pianos is A0, the highest C8. The MIDI system for electronic musical instruments and computers uses a straight count starting with note 0 for C-1 at 8.1758 Hz up to note 127 for G9 at 12,544 Hz.

Written notes
A written note can also have a note value, a code that determines the note's relative duration. In order of halving duration, we have: double note (breve); whole note (semibreve); half note (minim); quarter note (crotchet); eighth note (quaver); sixteenth note (semiquaver). Smaller still are the thirty-second note (demisemiquaver), sixty-fourth note (hemidemisemiquaver), and hundred twenty-eighth note (semihemidemisemiquaver).

When notes are written out in a score, each note is assigned a specific vertical position on a staff position (a line or a space) on the staff, as determined by the clef. Each line or space is assigned a note name. These names are memorized by musicians and allow them to know at a glance the proper pitch to play on their instruments for each note-head marked on the page.

The staff above shows the notes C, D, E, F, G, A, B, C and then in reverse order, with no key signature or accidentals.

Note frequency (hertz)
In all technicality, music can be composed of notes at any arbitrary physical frequency. Since the physical causes of music are vibrations of mechanical systems, they are often measured in hertz (Hz), with 1 Hz = no. of vibrations per second. For historical and other reasons, especially in Western music, only twelve notes of fixed frequencies are used. These fixed frequencies are mathematically related to each other, and are defined around the central note, A4. The current "standard pitch" or modern "concert pitch" for this note is 440 Hz, although this varies in actual practice (see History of pitch standards).

The note-naming convention specifies a letter, any accidentals, and an octave number. Any note is an integer of half-steps away from middle A (A4). Let this distance be denoted n. If the note is above A4, then n is positive; if it is below A4, then n is negative. The frequency of the note (f) (assuming equal temperament) is then:
 * $$f = 2^{n/12} \times 440 \,\text{Hz}\,$$

For example, one can find the frequency of C5, the first C above A4. There are 3 half-steps between A4 and C5 (A4 → A♯4 → B4 → C5), and the note is above A4, so n = +3. The note's frequency is:


 * $$f = 2^{3/12} \times 440 \,\text{Hz} \approx 523.2 \,\text{Hz}$$

To find the frequency of a note below A4, the value of n is negative. For example, the F below A4 is F4. There are 4 half-steps (A4 → A♭4 → G4 → G♭4 → F4), and the note is below A4, so n = −4. The note's frequency is:


 * $$f = 2^{-4/12} \times 440 \,\text{Hz} \approx 349.2 \,\text{Hz}$$

Finally, it can be seen from this formula that octaves automatically yield powers of two times the original frequency, since n is therefore a multiple of 12 (12k, where k is the number of octaves up or down), and so the formula reduces to:


 * $$f = 2^{12k/12} \times 440 \,\text{Hz} = 2^k \times 440 \,\text{Hz}$$

yielding a factor of 2. In fact, this is the means by which this formula is derived, combined with the notion of equally-spaced intervals.

The distance of an equally tempered semitone is divided into 100 cents. So 1200 cents are equal to one octave — a frequency ratio of 2:1. This means that a cent is precisely equal to the 1200th root of 2, which is approximately 1.000578.

For use with the MIDI (Musical Instrument Digital Interface) standard, a frequency mapping is defined by:


 * $$p = 69 + 12 \times \log_2{f \over 440 \,\text{Hz}}$$

Where p is the MIDI note number. And in the opposite direction, to obtain the frequency from a MIDI note p, the formula is defined as:


 * $$f=2^{(p-69)/12} \times 440\,\text{Hz}$$

For notes in an A440 equal temperament, this formula delivers the standard MIDI note number (p). 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 fourteen letters of the classical Latin alphabet,
 * A-B-C-D-E-F-G-H-I-K-L-M-N-O

to signify the notes of the two-octave range that was in use at the time, and which in modern scientific pitch notation is represented as
 * A2-B2-C3-D3-E3-F3-G3-A3-B3-C4-D4-E4-F4-G4.

Though it is not known whether this was his devising or common usage at the time, this is nonetheless called Boethian notation. Although Boethius is the first author which is known to have used this nomenclature in the literature, the above mentioned two-octave range was already known five centuries before by Ptolemy, who called it the "perfect system" or "complete system", as opposed to other systems of notes of smaller range, which did not contain all the possible species of octave (i.e., the seven octaves starting from A, B, C, D, E, F, and G).

Following this, the range (or compass) of used notes was extended to three octaves, and the system of repeating letters A-G in each octave was introduced, these being written as lower case for the second octave (a-g) and double lowercase letters for the third (aa-gg). When the range was extended down by one note, to a G, that note was denoted using 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♭, since B was flattened in certain modes to avoid the dissonant tritone interval. This change was not always shown in notation, but when written, B♭ (B-flat) was written as a Latin, round "b", and B♮ (B-natural) a Gothic or "hard-edged" 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, the Czech Republic, Poland, Hungary, Norway and Finland, the Gothic b transformed into the letter H (possibly for hart, German for hard, or just because the Gothic b resembled an H). Therefore, in German music notation, H is used in lieu of B♮ (B-natural), and B in lieu of B♭ (B-flat). Occasionally, music written in German for international use will use H for B-natural and Bb for B-flat (with a modern-script lowercase b instead of a flat sign). Since a Bes or B♭ in Northern Europe (i.e. a B𝄫 elsewhere) is both rare and unorthodox (more likely to be expressed as Heses), it is generally clear what this notation means.

In Italian, Portuguese, Spanish, French, Romanian, Greek, Russian, Mongolian, Flemish, Persian, Arabic, Hebrew, Bulgarian and Turkish notation the notes of scales are given 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 whom the hymn is dedicated). The use of 'Si' versus 'Ti' varies regionally.

The two notation systems most commonly used nowadays are the Helmholtz pitch notation system and the Scientific pitch notation system. As shown in the table above, they both include several octaves, each starting from C rather than A. The reason is that the most commonly used scale in Western music is the major scale, and the sequence C-D-E-F-G-A-B (the C-major scale) is the simplest example of a major scale. Indeed, it is the only major scale which can be obtained using natural notes (the white keys on the piano keyboard), and typically the first musical scale taught in music schools.

In a newly developed system, primarily in use in the United States, notes of scales become independent to the music notation. In this system the natural symbols C-D-E-F-G-A-B refer to the absolute notes, while the names Do-Re-Mi-Fa-So-La-Ti are relativized and show only the relationship between pitches, where Do is the name of the base pitch of the scale, Re is the name of the second pitch, etc. The idea of so-called movable-do, originally suggested by John Curwen in the 19th century, was fully developed and involved into a whole educational system by Zoltán Kodály in the middle of the 20th century, which system is known as the Kodály Method or Kodály Concept.