staff. scale on a staff.
Distinguishing pitches of a scale 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, and certainly in all of
Germany, pitch classes are typically represented by 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 and
Czechia, use H instead of B (see for details).
Byzantium used the names
Pa–Vu–Ga–Di–Ke–Zo–Ni (Πα–Βου–Γα–Δι–Κε–Ζω–Νη). A single note is sometimes called a monad. In traditional
Indian music, musical notes are called
svaras and commonly represented using the seven notes, Sa, Re, Ga, Ma, Pa, Dha and Ni.
Writing notes on a staff 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. \relative c' { c1 d1 e1 f1 g1 a1 b1 c1 b1 a1 g1 f1 e1 d1 c1 } \layout { \context { \Staff \remove Time_signature_engraver \remove Bar_engraver } } \midi { \tempo 1 = 120 } 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.
Accidentals Notes that belong to 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 a half step. This half step
interval is also known as a
semitone (which has an
equal temperament frequency ratio of Twelfth root of two| ≅ 1.0595). The
natural symbol () indicates that any previously applied accidentals should be cancelled. Advanced musicians use the
double-sharp symbol () to raise the pitch by two
semitones, the
double-flat symbol () to lower it by two semitones, and even more advanced accidental symbols (e.g. for
quarter tones). Accidental symbols are placed to
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 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.
12-tone chromatic scale Assuming
enharmonicity, accidentals can create pitch equivalences between different notes (e.g. 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 the English and Dutch names are different, the corresponding symbols are identical.
Distinguishing pitches of different octaves 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 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.
Middle C Middle
C is often used as a common reference point when discussing octaves. This is the
C between the typical treble and bass staves; either one
ledger line below the treble staff, or one ledger line above the bass. In standard tuning it has a pitch of 261.626 Hz. Middle
C is a convenient reference, as it can be played on most common instruments. It can be sung by both male and female singers. It also falls near the middle of a standard 88-key piano. The most common tuning, the
A440 pitch standard, defines the
A above middle
C to be exactly 440 Hz.
Scientific versus Helmholtz pitch notation Several nomenclature systems for differentiating pitches that have the same pitch class but which fall into different octaves. •
Scientific pitch notation, where a pitch class letter (
C,
D,
E,
F,
G,
A,
B) is followed by a subscript
Arabic numeral designating a specific octave. • Middle
C is named
C4 and is the start of the 4th octave. • Higher octaves use successively higher number and lower octaves use successively lower numbers (including negative numbers) • The lowest note on most pianos is
A0, the highest is
C8. •
Helmholtz pitch notation, which distinguishes octaves using
prime symbols and
letter case of the pitch class letter. • The scale is based on the
C one octave below middle
C (
C3 in scientific pitch notation), sometimes called *tenor
C*. • The octave starting at tenor
C are written as
lower case letters, so tenor
C itself is written
c in Helmholtz notation. • Higher octaves are notated by appending additional prime symbols above the letter. Thus, middle C is written
c′, the next octave
c′′, etc. • Octaves below tenor
C are written with
upper case letters, with sub-prime symbols prepended for each additional octave. Thus the octaves below tenor
C are written
C,
͵C,
͵͵C, etc. • A number of typographic
variants exist for Helmholtz notation. For instance, primes and sub-primes may be replaced with apostrophe and comma characters, sub-primes can be placed either before or after the note letter, or letters can be repeated (
͵͵C =
C͵͵ =
C,, =
CCC). • Octaves are also named (see table below). • The
MIDI standard for
electronic musical instruments doesn't specifically designate pitch classes, but instead names pitches sequentially. • The supported lowest note, , is numbered 0. • Subsequent notes are numbered chromatically to the highest, number 127 • Although 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. For instance, the standard
440 Hz tuning pitch is named
A4 in scientific notation,
a′ in Helmholtz notation, and number 69 in MIDI. :
Pitch frequency in hertz 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 tend to have pitches with simpler mathematical ratios to each other. Western music defines pitches around a central reference "
concert pitch" of A4,
currently standardized as 440 Hz. Notes played
in tune with the
12 equal temperament system will be an
integer number h of half-steps above (positive h) or below (negative h) that reference note, and thus have a frequency of: :f = 2^\frac{h}{12} \times 440 \text{ Hz}.\, Octaves automatically yield
powers of two times the original frequency, since h can be expressed as 12v when h is a multiple of 12 (with v being the number of octaves up or down). Thus the above formula reduces to yield a
power of 2 multiplied by 440 Hz: :\begin{align} f &= 2^\frac{12v}{12} \times \text{440 Hz}\\ &= 2^v \times \text{440 Hz} \,. \end{align}
Logarithmic scale of frequency in
hertz versus pitch of a
chromatic scale starting on
middle C. Each subsequent note has a pitch equal to the frequency of the prior note's pitch multiplied by .|thumb|228x228pxThe
base-2 logarithm of the above frequency–pitch relation conveniently results in a linear relationship with h or v: :\begin{align} \log_{2}(f) &= \tfrac{h}{12} + \log_{2}(\text{440 Hz})\\ &= v + \log_{2}(\text{440 Hz}). \end{align} When dealing specifically with intervals (rather than absolute frequency), the constant \log_{2}(\text{440 Hz}) can be conveniently ignored, because the
difference between any two frequencies f_1 and f_2 in this logarithmic scale simplifies to: :\begin{align} \log_{2}(f_1) - \log_{2}(f_2) &= \tfrac{h_1}{12} - \tfrac{h_2}{12}\\ &= v_1 - v_2 \,. \end{align}
Cents are a convenient unit for humans to express finer divisions of this logarithmic scale that are of an equally-
tempered semitone. Since one semitone equals 100
cents, one octave equals 12 ⋅ 100 cents = 1200 cents. Cents correspond to a
difference in this logarithmic scale, however in the regular linear scale of frequency, adding 1 cent corresponds to
multiplying a frequency by (≅ ).
MIDI For use with the
MIDI (Musical Instrument Digital Interface) standard, a frequency mapping is defined by: :p = 69 + 12 \times \log_2\frac{f}{440 \text{ Hz}} \, , where p is the MIDI note number. 69 is the number of semitones between C−1 (MIDI note 0) and A4. Conversely, the formula to determine frequency from a MIDI note p is: :f=2^\frac{p-69}{12} \times 440 \text{ Hz} \, .
Pitch names and their history 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), :
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 in modern
scientific pitch notation are represented as :
A B C D E F G A B C D E F G 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., 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 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 (), the lowest note in Medieval music notation. (It is from this gamma that the French word for scale, derives, and the English word
gamut, from "gamma-ut".) 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, cursive "", and
B (
B natural) a Gothic script (known as
Blackletter) or "hard-edged" . These evolved into the modern flat () and natural () symbols respectively. The sharp symbol arose from a (barred b), called the "cancelled b".
B♭, B and H In parts of Europe, including Germany, Czechia, Slovakia, Poland, Hungary, Norway, Denmark, Serbia, Croatia, Slovenia, Finland, and Iceland (as well as Sweden before the 1990s), the
Gothic transformed into the letter
h (possibly for
hart, German for "harsh", as opposed to
blatt, German for "planar", or just because the Gothic and resemble each other). 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 a or
B in Northern Europe (notated
B in modern convention) is both rare and unorthodox (more likely to be expressed as Heses), it is generally clear what this notation means.
System "do–re–mi–fa–sol–la–si" 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 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 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). == See also ==