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59-493: Notes can distinguish the general pitch class or the specific pitch played by a pitched instrument . Although this article focuses on pitch, notes for unpitched percussion instruments distinguish between different percussion instruments (and/or different manners to sound them) instead of pitch. Note value expresses the relative duration of the note in time . Dynamics for a note indicate how loud to play them. Articulations may further indicate how performers should shape

118-540: A Bes or B ♭ in Northern Europe (notated B [REDACTED] in modern convention) 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, Albanian, Russian, Mongolian, Flemish, Persian, Arabic, Hebrew, Ukrainian, Bulgarian, Turkish and Vietnamese the note names are do–re–mi–fa–sol–la–si rather than C–D–E–F–G–A–B . These names follow

177-566: A difference in this logarithmic scale, however in the regular linear scale of frequency, adding 1 cent corresponds to multiplying a frequency by √ 2  (≅  1.000 578 ). For use with the MIDI (Musical Instrument Digital Interface) standard, a frequency mapping is defined by: where p {\displaystyle p} is the MIDI note number. 69 is the number of semitones between C −1 (MIDI note 0) and A 4 . Conversely,

236-416: A musical scale is the bottom note's second harmonic and has double the bottom note's frequency. Because both notes belong to the same pitch class, they are often called by the same name. That top note may also be referred to as the " octave " of the bottom note, since an octave is the interval between a note and another with double frequency. Two nomenclature systems for differentiating pitches that have

295-472: A pitch class ( p.c. or pc ) is a set of all pitches that are a whole number of octaves apart; for example, the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave position." Important to musical set theory , a pitch class is "all pitches related to each other by octave, enharmonic equivalence , or both." Thus, using scientific pitch notation ,

354-501: A power of 2 multiplied by 440 Hz: The base-2 logarithm of the above frequency–pitch relation conveniently results in a linear relationship with h {\displaystyle h} or v {\displaystyle v} : When dealing specifically with intervals (rather than absolute frequency), the constant log 2 ⁡ ( 440 Hz ) {\displaystyle \log _{2}({\text{440 Hz}})} can be conveniently ignored, because

413-471: A 1 (often written " ⁠ 1 / 1 ⁠ "), which represents a fixed pitch. If a and b are two positive rational numbers, they belong to the same pitch class if and only if for some integer n . Therefore, we can represent pitch classes in this system using ratios ⁠ p / q ⁠ where neither p nor q is divisible by 2, that is, as ratios of odd integers. Alternatively, we can represent just intonation pitch classes by reducing to

472-403: A central reference " concert pitch " of A 4 , currently standardized as 440 Hz. Notes played in tune with the 12 equal temperament system will be an integer number h {\displaystyle h} of half-steps above (positive h {\displaystyle h} ) or below (negative h {\displaystyle h} ) that reference note, and thus have

531-445: A few disadvantages with integer notation. First, theorists have traditionally used the same integers to indicate elements of different tuning systems. Thus, the numbers 0, 1, 2, ... 5, are used to notate pitch classes in 6-tone equal temperament. This means that the meaning of a given integer changes with the underlying tuning system: "1" can refer to C ♯ in 12-tone equal temperament, but D in 6-tone equal temperament. Also,

590-430: A flat (not to be confused with the larger quarter tone ). Although very rarely used, a triple flat ( [REDACTED] ) can sometimes be found. It lowers a note three semitones , or a whole tone and a semitone. The symbol of a quadruple flat ( [REDACTED] [REDACTED] ) , or beyond, could be used but would be extremely rare in ordinary temperament . The Unicode character ♭ (U+266D) can be found in

649-421: A frequency of: Octaves automatically yield powers of two times the original frequency, since h {\displaystyle h} can be expressed as 12 v {\displaystyle 12v} when h {\displaystyle h} is a multiple of 12 (with v {\displaystyle v} being the number of octaves up or down). Thus the above formula reduces to yield

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708-549: A half step. This half step interval is also known as a semitone (which has an equal temperament frequency ratio of √ 2  ≅ 1.0595). The natural symbol ( ♮ ) indicates that any previously applied accidentals should be cancelled. Advanced musicians use the double-sharp symbol ( [REDACTED] ) to raise the pitch by two semitones , the double-flat symbol ( [REDACTED] ) to lower it by two semitones, and even more advanced accidental symbols (e.g. for quarter tones ). Accidental symbols are placed to

767-457: A note's pitch by a semitone results in a note that is enharmonically equivalent to the adjacent named note. In this system, B ♭ and A ♯ are considered to be equivalent. In most tuning systems , however, this is not the case. When used as a temporary accidental sign, the flat symbol is placed to the left of the note head. Temporary accidentals apply to the note on which they are placed, and to all subsequent similar notes in

826-456: A pitch as its "chroma". A chroma is an attribute of pitches (as opposed to tone height ), just like hue is an attribute of color . A pitch class is a set of all pitches that share the same chroma, just like "the set of all white things" is the collection of all white objects. In standard Western equal temperament , distinct spellings can refer to the same sounding object: B ♯ 3 , C 4 , and D [REDACTED] 4 all refer to

885-422: A pitch's fundamental frequency f (measured in hertz ) to a real number p using the equation This creates a linear pitch space in which octaves have size 12, semitones (the distance between adjacent keys on the piano keyboard) have size 1, and middle C (C 4 ) is assigned the number 0 (thus, the pitches on piano are −39 to +48). Indeed, the mapping from pitch to real numbers defined in this manner forms

944-599: Is formed from a sequence in time of consecutive notes (without particular focus on pitch) and rests (the time between notes) of various durations. Music theory in most European countries and others use the solfège naming convention. Fixed do uses the syllables re–mi–fa–sol–la–ti specifically for the C major scale, while movable do labels notes of any major scale with that same order of syllables. Alternatively, particularly in English- and some Dutch-speaking regions, pitch classes are typically represented by

1003-425: Is placed in key signatures to mark lines whose notes are flattened throughout that section of music; it may also be an " accidental " that precedes an individual note and indicates that the note should be lowered temporarily, until the following bar line . The flat symbol, ♭ , is a stylised lowercase b , derived from Italian be molle for "soft B" and German blatt for "planar, dull". It indicates that

1062-482: Is still used in some places. It was the Italian musicologist and humanist Giovanni Battista Doni (1595–1647) who successfully promoted renaming the name of the note from ut to do . For the seventh degree, the name si (from Sancte Iohannes , St. John , to whom the hymn is dedicated), though in some regions the seventh is named ti (again, easier to pronounce while singing). Pitch class In music ,

1121-507: The MIDI standard is clear, the octaves actually played by any one MIDI device don't necessarily match the octaves shown below, especially in older instruments.) Pitch is associated with the frequency of physical oscillations measured in hertz (Hz) representing the number of these oscillations per second. While notes can have any arbitrary frequency, notes in more consonant music tends to have pitches with simpler mathematical ratios to each other. Western music defines pitches around

1180-479: The attack and decay of the note and express fluctuations in a note's timbre and pitch . Notes may even distinguish the use of different extended techniques by using special symbols. The term note can refer to a specific musical event, for instance when saying the song " Happy Birthday to You ", begins with two notes of identical pitch. Or more generally, the term can refer to a class of identically sounding events, for instance when saying "the song begins with

1239-402: The diatonic scale relevant in a tonal context are called diatonic notes . Notes that do not meet that criterion are called chromatic notes or accidentals . Accidental symbols visually communicate a modification of a note's pitch from its tonal context. Most commonly, the sharp symbol ( ♯ ) raises a note by a half step , while the flat symbol ( ♭ ) lowers a note by

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1298-514: The difference between any two frequencies f 1 {\displaystyle f_{1}} and f 2 {\displaystyle f_{2}} in this logarithmic scale simplifies to: Cents are a convenient unit for humans to express finer divisions of this logarithmic scale that are 1 ⁄ 100 of an equally- tempered semitone. Since one semitone equals 100  cents , one octave equals 12 ⋅ 100 cents = 1200 cents. Cents correspond to

1357-585: The duodecimal numeral system, which also uses "t" and "e", or A and B , for "10" and "11"). This allows the most economical presentation of information regarding post-tonal materials. In the integer model of pitch, all pitch classes and intervals between pitch classes are designated using the numbers 0 through 11. It is not used to notate music for performance, but is a common analytical and compositional tool when working with chromatic music, including twelve tone , serial , or otherwise atonal music. Pitch classes can be notated in this way by assigning

1416-421: The note to which it is applied is played one semitone lower, or in modern tuning exactly 100  cents . In traditional and modern microtonal temperaments the size of sharps or flats ( chromatic semitones ) is normally smaller than the size of the diatonic semitones found between E and F or B and C. In those tuning systems, the size of the shift made by the ♭ symbol usually conforms to

1475-417: The (arbitrary) choice of pitch class 0. For example, if one makes a different choice about which pitch class is labeled 0, then the pitch class E will no longer be labeled "4". However, the distance between D and F ♯ will still be assigned the number 4. Both this and the issue in the paragraph directly above may be viewed as disadvantages (though mathematically, an element "4" should not be confused with

1534-456: The English and Dutch names are different, the corresponding symbols are identical. Two pitches that are any number of octaves apart (i.e. their fundamental frequencies are in a ratio equal to a power of two ) are perceived as very similar. Because of that, all notes with these kinds of relations can be grouped under the same pitch class and are often given the same name. The top note of

1593-512: The Gothic ; 𝕭 resembles an H ). Therefore, in current German music notation, H is used instead of B ♮ ( B  natural), and B instead of B ♭ ( B  flat). Occasionally, music written in German for international use will use H for B  natural and B for B  flat (with a modern-script lower-case b, instead of a flat sign, ♭ ). Since

1652-449: The arithmetic used in pitch-class set manipulations. The disadvantage of the scale-based system is that it assigns an infinite number of different names to chords that sound identical. For example, in twelve-tone equal-temperament the C major triad is notated {0, 4, 7}. In twenty-four-tone equal-temperament, this same triad is labeled {0, 8, 14}. Moreover, the scale-based system appears to suggest that different tuning systems use steps of

1711-575: The basis of the MIDI Tuning Standard , which uses the real numbers from 0 to 127 to represent the pitches C −1 to G 9 (thus, middle C is 60). To represent pitch classes , we need to identify or "glue together" all pitches belonging to the same pitch class—i.e. all numbers p and p  + 12. The result is a cyclical quotient group that music theorists call pitch class space and mathematicians call R /12 Z . Points in this space can be labelled using real numbers in

1770-452: 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, cursive " 𝑏  ", and B ♮ ( B  natural) a Gothic script (known as Blackletter ) or "hard-edged" 𝕭 . These evolved into

1829-450: The continuous labeling system described above. First, it eliminates any suggestion that there is something natural about a twelvefold division of the octave. Second, it avoids pitch-class universes with unwieldy decimal expansions when considered relative to 12; for example, in the continuous system, the pitch-classes of 19 equal temperament are labeled 0.63158..., 1.26316..., etc. Labeling these pitch classes {0, 1, 2, 3 ..., 18} simplifies

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1888-414: The continuous system can be more useful. Flat (music) In music , flat means lower in pitch . It may either be used generically, meaning any lowering of pitch, or refer to a particular size: lowering pitch by a chromatic semitone . A flat is the opposite of a sharp ( ♯ ) which raises pitch by the same amount that a flat lowers it. The flat symbol ( ♭ ) is used in two ways: It

1947-453: The first seven letters of the Latin alphabet (A, B, C, D, E, F and G), corresponding to the A minor scale. Several European countries, including Germany, use H instead of B (see § 12-tone chromatic scale for details). Byzantium used the names Pa–Vu–Ga–Di–Ke–Zo–Ni (Πα–Βου–Γα–Δι–Κε–Ζω–Νη). In traditional Indian music , musical notes are called svaras and commonly represented using

2006-420: The formula to determine frequency from a MIDI note p {\displaystyle p} is: 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 (the letter J did not exist until the 16th century), to signify the notes of the two-octave range that

2065-479: The function "+4"). The system described above is flexible enough to describe any pitch class in any tuning system: for example, one can use the numbers {0, 2.4, 4.8, 7.2, 9.6} to refer to the five-tone scale that divides the octave evenly. However, in some contexts, it is convenient to use alternative labeling systems. For example, in just intonation , we may express pitches in terms of positive rational numbers ⁠ p / q ⁠ , expressed by reference to

2124-431: The impracticality of their use, rather than the simpler, equivalent key in 12 TET . This principle applies similarly to the sharp keys. The staff below shows a key signature with three flats ( E ♭ major or its relative minor C minor ), followed by a note with a flat preceding it: The flat symbol placed on the note indicates that it is a D ♭ . In 12 tone equal temperament ( 12 TET ) lowering

2183-442: The lettered pitch class corresponding to each symbol's position. Additional explicitly-noted accidentals can be drawn next to noteheads to override the key signature for all subsequent notes with the same lettered pitch class in that bar . However, this effect does not accumulate for subsequent accidental symbols for the same pitch class. Assuming enharmonicity , accidentals can create pitch equivalences between different notes (e.g.

2242-620: The modern flat ( ♭ ) and natural ( ♮ ) symbols respectively. The sharp symbol arose from a ƀ (barred b), called the "cancelled b". In parts of Europe, including Germany, the Czech Republic, Slovakia, Poland, Hungary, Norway, Denmark, Serbia, Croatia, Slovenia, Finland, and Iceland (and Sweden before the 1990s), the Gothic   𝕭 transformed into the letter H (possibly for hart , German for "harsh", as opposed to blatt , German for "planar", or just because

2301-415: The next (E ♭ ) indicates B ♭ major, and so on, backwards through the circle of fifths . Some keys (such as C ♭ major with seven flats) may be written as an enharmonically equivalent key (B major with five sharps in this case). In rare cases, the flat keys may be extended further: requiring double flats in the key signature. These are called theoretical key signatures , based on

2360-426: The note B ♯ represents the same pitch as the note C). Thus, a 12-note chromatic scale adds 5 pitch classes in addition to the 7 lettered pitch classes. The following chart lists names used in different countries for the 12 pitch classes of a chromatic scale built on C. Their corresponding symbols are in parentheses. Differences between German and English notation are highlighted in bold typeface. Although

2419-529: The number 0 to some note and assigning consecutive integers to consecutive semitones ; so if 0 is C natural, 1 is C ♯ , 2 is D ♮ and so on up to 11, which is B ♮ . The C above this is not 12, but 0 again (12 − 12 = 0). Thus arithmetic modulo 12 is used to represent octave equivalence . One advantage of this system is that it ignores the "spelling" of notes (B ♯ , C ♮ and D [REDACTED] are all 0) according to their diatonic functionality . There are

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2478-438: The octave, 1 ≤  ⁠ p / q ⁠  < 2. It is also very common to label pitch classes with reference to some scale . For example, one can label the pitch classes of n -tone equal temperament using the integers 0 to n  − 1. In much the same way, one could label the pitch classes of the C major scale, C–D–E–F–G–A–B, using the numbers from 0 to 6. This system has two advantages over

2537-424: 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 , whose successive lines began on the appropriate scale degrees. These became the basis of the solfège system. For ease of singing, the name ut was largely replaced by do (most likely from the beginning of Dominus , "Lord"), though ut

2596-400: The pitch class "C" is the set Although there is no formal upper or lower limit to this sequence, only a few of these pitches are audible to humans. Pitch class is important because human pitch-perception is periodic : pitches belonging to the same pitch class are perceived as having a similar quality or color, a property called " octave equivalence ". Psychologists refer to the quality of

2655-580: The range 0 ≤  x  < 12. These numbers provide numerical alternatives to the letter names of elementary music theory: and so on. In this system, pitch classes represented by integers are classes of twelve-tone equal temperament (assuming standard concert A). In music , integer notation is the translation of pitch classes or interval classes into whole numbers . Thus if C = 0, then C ♯  = 1 ... A ♯  = 10, B = 11, with "10" and "11" substituted by "t" and "e" in some sources, A and B in others (like

2714-463: The right of a note's letter when written in text (e.g. F ♯ is F-sharp , B ♭ is B-flat , and C ♮ is C natural ), but are placed to the left of a note's head when drawn on a staff . Systematic alterations to any of the 7 lettered pitch classes are communicated using a key signature . When drawn on a staff, accidental symbols are positioned in a key signature to indicate that those alterations apply to all occurrences of

2773-428: The same measure and octave. In modern notation they do not apply to notes in other octaves, but this was not always the convention. To cancel an accidental signature later in the same measure and octave, another accidental such as a natural (♮) or a sharp (♯) may be used. A double flat ( [REDACTED] ) lowers a note by two semitones, or a whole step. A quarter-tone flat , half flat , or demiflat indicates

2832-405: The same note repeated twice". A note can have a note value that indicates the note's duration relative to the musical meter . In order of halving duration, these values are: Longer note values (e.g. the longa ) and shorter note values (e.g. the two hundred fifty-sixth note ) do exist, but are very rare in modern times. These durations can further be subdivided using tuplets . A rhythm

2891-399: The same numbers are used to represent both pitches and intervals . For example, the number 4 serves both as a label for the pitch class E (if C = 0) and as a label for the distance between the pitch classes D and F ♯ . (In much the same way, the term "10 degrees" can label both a temperature and the distance between two temperatures.) Only one of these labelings is sensitive to

2950-408: The same octave. Because octave-related pitches belong to the same class, when an octave is reached, the numbers begin again at zero. This cyclical system is referred to as modular arithmetic and, in the usual case of chromatic twelve-tone scales, pitch-class numbering is "modulo 12" (customarily abbreviated "mod 12" in the music-theory literature)—that is, every twelfth member is identical. One can map

3009-562: The same pitch class but which fall into different octaves are: For instance, the standard 440 Hz tuning pitch is named A 4 in scientific notation and instead named a′ in Helmholtz notation. Meanwhile, the electronic musical instrument standard called MIDI doesn't specifically designate pitch classes, but instead names pitches by counting from its lowest note: number 0 ( C −1 ≈ 8.1758 Hz) ; up chromatically to its highest: number 127 ( G 9 ≈ 12,544 Hz). (Although

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3068-439: The same pitch, hence share the same chroma, and therefore belong to the same pitch class. This phenomenon is called enharmonic equivalence . To avoid the problem of enharmonic spellings, theorists typically represent pitch classes using numbers beginning from zero, with each successively larger integer representing a pitch class that would be one semitone higher than the preceding one, if they were all realised as actual pitches in

3127-432: The same size ("1") but have octaves of differing size ("12" in 12-tone equal-temperament, "19" in 19-tone equal temperament, and so on), whereas in fact the opposite is true: different tuning systems divide the same octave into different-sized steps. In general, it is often more useful to use the traditional integer system when one is working within a single temperament; when one is comparing chords in different temperaments,

3186-564: The second octave ( a – g ) and double lower-case 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 letter gamma ( Γ ), the lowest note in Medieval music notation. (It is from this gamma that the French word for scale, gamme derives, and the English word gamut , from "gamma-ut".) The remaining five notes of

3245-514: The seven notes, Sa, Re, Ga, Ma, Pa, Dha and Ni. In a score , each note is assigned a specific vertical position on a staff position (a line or 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. 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. Notes that belong to

3304-486: The seven octaves starting from A , B , C , D , E , F , and G ). A modified form of Boethius' notation later appeared in the Dialogus de musica (ca. 1000) by Pseudo-Odo, in a discussion of the division of the monochord . 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

3363-460: The smaller-sized lowering of pitch; however, for some tuning systems it may instead be replaced by a different symbol for raising and lowering pitch, depending on the author's preference and the intricacy of any microtuning involved. The order of flats added onto the key signature is The corresponding order of keys is off by one: Starting with no sharps or flats (C major), adding the first flat (B ♭ ) indicates F major ; adding

3422-410: The use of quarter tones ; it may be marked with various symbols including a flat with a slash ( [REDACTED] ) or a reversed flat sign ( [REDACTED] ). A three-quarter-tone flat , flat and a half or sesquiflat , is represented by a demiflat and a whole flat ( [REDACTED] ). The symbols - , ↓ , [REDACTED] , among others, represent comma flat or eighth-tone flat, or a quarter of

3481-528: Was in use at the time and in modern scientific pitch notation are represented as 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 known to use this nomenclature in the literature, Ptolemy wrote of the two-octave range five centuries before, calling it the perfect system or complete system – as opposed to other, smaller-range note systems that did not contain all possible species of octave (i.e.,

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