Musical Note

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In music, the term note has two primary meanings:

 a sign used in musical notation to represent the relative duration and pitch of a sound;

a pitched sound itself.

 Notes are the "atoms" of much Western music: discretizations of musical phenomena that facilitate performance, comprehension, and analysis.

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 (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 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 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 of notes having a frequency ratio of two. 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


Frequency vs Position on Treble Clef. Each note shown has a frequency of the previous note multiplied by 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 , 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 if 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, 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 or a Romance language.

In most countries using this system, the letter H is used to represent what is B natural in English, the letter B represents the B♭, and Heses represents the B♭♭ (not Bes, which would also have fit into the system). Belgium and the Netherlands use the same suffixes, but applied throughout to the notes A to G, so that B♭ is Bes. Denmark also uses H, but uses bes instead of heses for B♭♭



This is a complete chart of a chromatic scale built on the note C4, or "middle C":


Style Type prime second third fourth fifth sixth seventh

 English name Natural C D E F G A B



Sharp C sharp D sharp F sharp G sharp A sharp


Flat D flat E flat G flat A flat B flat


Symbol Sharp C♯ D♯ F♯ G♯ A♯


Flat D♭ E♭ G♭ A♭ B♭



Northern European name Natural C D E F G A H

 Sharp Cis Dis Fis Gis Ais



Flat Des Es Ges As B


Dutch name (sometimes used in Scandinavia after 1990s) Natural C D E F G A B



Sharp Cis Dis Fis Gis Ais



Flat Des Es Ges As Bes

 Byzantine Natural Ni Pa Vu Ga Di Ke Zo


Sharp Ni diesi (or diez) Pa diesi Ga diesi Di diesi Ke diesi


Flat Pa iphes Vu iphes Di iphes Ke iphes Zo iphes



Southern & Eastern European Natural Do Re Mi Fa Sol La Si



Sharp Do diesis Re diesis Fa diesis Sol diesis La diesis


Flat Re bemolle Mi bemolle Sol bemolle La bemolle Si bemolle

 Variant names Ut - - - So - Ti

 Indian style Sa Re Komal Re Ga Komal Ga Ma Ma Teevra Pa Dha Komal Dha Ni Komal Ni


Korean style Da La Ma Ba Sa Ga Na

Approx. Frequency [Hz] 262 277 294 311 330 349 370 392 415 440 466 494
MIDI note number 60 61 62 63 64 65 66 67 68 69 70 71

 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.


Octave naming systems frequency

 of A (Hz)


traditional shorthand numbered MIDI nr

 subsubcontra Cˌˌˌ – Bˌˌˌ C-1 – B-1 0 – 11 13.75

 sub-contra Cˌˌ – Bˌˌ C0 – B0 12 – 23 27.5



contra Cˌ – Bˌ C1 – B1 24 – 35 55



great C – B C2 – B2 36 – 47 110

 small c – b C3 – B3 48 – 59 220

 one-lined c′ – b′ C4 – B4 60 – 71 440

 two-lined c′′ – b′′ C5 – B5 72 – 83 880

 three-lined c′′′ – b′′′ C6 – B6 84 – 95 1760



four-lined c′′′′ – b′′′′ C7 – B7 96 – 107 3520


five-lined c′′′′′ – b′′′′′ C8 – B8 108 – 119 7040

 six-lined c′′′′′′ – b′′′′′′ C9 – B9 120 – 127


up to G9 14080


Written notes



A written note can also have a note value, a code which determines the note's relative duration. These note values include quarter notes (crotchets), eighth notes (quavers), and so on.

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.

Note frequency (hertz)

 In all technicality, music can be composed of notes at any arbitrary frequency. Since the physical causes of music are vibrations of mechanical systems, they are often measured in hertz (Hz), with 1 Hz = 1 complete vibration 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 (sharps/flats), 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 = 2n/12 × 440 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 = 23/12 × 440 Hz ≈ 523.2511 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 × 440 Hz ≈ 349.2290 Hz.



Finally, it can be seen from this formula that octaves automatically yield factors 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 = 212k/12 × 440 Hz = 2k × 440 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 1.0005777895.

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

 p = 69 + 12 × log2 (f / (440 Hz))



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 is not 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 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 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, Flemish, Romanian, Spanish, 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 which the hymn is dedicated). The uses of 'Si' in place of 'Ti' or vice versa do depend on region- for example, in England, the scale is read as Do-Re/Ray-Mi-Fa/Fah-So-La-Ti-Do but in parts of America it is read as Do-Re-Mi-Fa-Sol-La-Si-Do

In music notation, a note value indicates the relative duration of a note, using the color or shape of the note head, the presence or absence of a stem, and the presence or absence of flags/beams.

A rest indicates a silence of an equivalent duration.

Note Rest American name British name


longa longa


breve (or double whole note) breve


whole note semibreve


half note minim


quarter note crotchet


eighth note quaver


sixteenth note semiquaver


thirty-second note demisemiquaver


sixty-fourth note hemidemisemiquaver


hundred twenty-eighth note Quasihemidemisemiquaver / Semihemidemisemiquaver

Variations

Variants of the breveThe breve appears in several different versions, as shown at right.

Sometimes the longa is used to indicate a very long note of indefinite duration, as at the end of a piece.

When a stem is present, it can go either up (from the right side of the note head) or down (from the left side, except in the case of the longa). In most cases, the stem goes down if the notehead is on the center line or above, and up otherwise. Any flags always go to the right of the stem.

Beamed notesWhen two or more notes which would normally have flags (eighth notes or shorter) appear successively, the flags may be replaced by beams, as shown at right. Notes are typically beamed only if they appear in the same beat within the bar. Beams also imply that the notes should be slightly more connected than non-beamed notes.

Modifiers

A note value may be augmented by adding a dot after it. This dot adds the next lower note value, making it one and a half times its original duration. Two dots add two lower note values, making a total of one and three quarters times its original duration. The rare three dots make it one and seven eights the duration, and so on.

To divide a note value into three equal parts, or some other value than two, tuplets may be used. However, see swung note and notes inégales.

 History


 Gregorian chant


Although note heads of various shapes, and notes with and without stems appear in early Gregorian chant manuscripts, most scholars agree that these symbols do not indicate different durations, although the dot is used for augmentation. See neume.

In the 13th century, chant was sometimes performed according to rhythmic modes, roughly equivalent to meters; however, the note shapes still did not indicate duration in the same way as modern note values

Mensural notation


Around 1250, Franco of Cologne invented different symbols for different durations, although the relation between different note values could vary; three was the most common ratio. Philippe de Vitry's treatise Ars nova (1320) described a system in which the ratios of different note values could be 2:1 or 3:1, with a system of mensural time signatures to distinguish between them.

This black mensural notation gave way to white mensural notation around 1450, in which all note values were written with white (outline) noteheads. In white notation the use of triplets was indicated by coloration, i.e. filling in the noteheads to make them black (or sometimes red). Both black and white notation periodically made use of ligatures, a holdover from the clivis and porrectus neumes used in chant.

Around 1600 the modern notational system was generally adopted, along with barlines and the practice of writing multipart music in scores rather than only individual parts. In the 17th century, however, old usages came up occasionally.

Origins of the names



The British names go back at least to English renaissance music, and the terms of Latin origin had international currency at that time. Obviously, longa means 'long', and the rest mostly indicate relative shortness. Breve is from Latin brevis, 'short', minim is from minimus, 'very small', and quaver refers to the quivering effect of very fast notes. The elements semi-, demi- and hemi- mean 'half' in Latin, French and Greek respectively, while quasi- means 'almost'. The chain semantic shift whereby notes which were originally perceived as short came progressively to be long notes is interesting both linguistically and musically. However, the crotchet is named after the shape of the note, from the Old French for a 'little hook', and it is possible to argue that the same is true of the minim, since the word is also used in palaeography to mean a vertical stroke in mediaeval handwriting.

The American names are loan translations of the German terms: when American orchestras were first established in the 19th century they were populated to a significant degree by German emigrants.


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