Octave

Last updated
Octave
A perfect octave between two Cs
Perfect octave
Inverse unison
Name
Other names-
AbbreviationP8
Size
Semitones 12
Interval class 0
Just interval 2:1 [1]
Cents
12-Tone equal temperament 1200 [1]
Just intonation 1200 [1]

In music, an octave (Latin : octavus: eighth) or perfect octave (sometimes called the diapason) [2] is a series of eight notes occupying the interval between (and including) two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems". [3] [4] The interval between the first and second harmonics of the harmonic series is an octave. In Western music notation, notes separated by an octave (or multiple octaves) have the same name and are of the same pitch class.

Contents

To emphasize that it is one of the perfect intervals (including unison, perfect fourth, and perfect fifth), the octave is designated P8. Other interval qualities are also possible, though rare. The octave above or below an indicated note is sometimes abbreviated 8a or 8va (Italian : all'ottava), 8va bassa (Italian : all'ottava bassa, sometimes also 8vb), or simply 8 for the octave in the direction indicated by placing this mark above or below the staff.

Explanation and definition

An octave is the interval between one musical pitch and another with double or half its frequency. For example, if one note has a frequency of 440  Hz, the note one octave above is at 880 Hz, and the note one octave below is at 220 Hz. The ratio of frequencies of two notes an octave apart is therefore 2:1. Further octaves of a note occur at times the frequency of that note (where n is an integer), such as 2, 4, 8, 16, etc. and the reciprocal of that series. For example, 55 Hz and 440 Hz are one and two octaves away from 110 Hz because they are +12 (or ) and 4 (or ) times the frequency, respectively.

The number of octaves between two frequencies is given by the formula:

Music theory

Most musical scales are written so that they begin and end on notes that are an octave apart. For example, the C major scale is typically written C D E F G A B C (shown below), the initial and final C's being an octave apart.

Octave

Because of octave equivalence, notes in a chord that are one or more octaves apart are said to be doubled (even if there are more than two notes in different octaves) in the chord. The word is also used to describe melodies played in parallel one or more octaves apart (see example under Equivalence, below).

While octaves commonly refer to the perfect octave (P8), the interval of an octave in music theory encompasses chromatic alterations within the pitch class, meaning that G to G (13 semitones higher) is an Augmented octave (A8), and G to G (11 semitones higher) is a diminished octave (d8). The use of such intervals is rare, as there is frequently a preferable enharmonically-equivalent notation available (minor ninth and major seventh respectively), but these categories of octaves must be acknowledged in any full understanding of the role and meaning of octaves more generally in music.

Notation

Octave of a pitch

Octaves are identified with various naming systems. Among the most common are the scientific, Helmholtz, organ pipe, and MIDI note systems. In scientific pitch notation, a specific octave is indicated by a numerical subscript number after note name. In this notation, middle C is C4, because of the note's position as the fourth C key on a standard 88-key piano keyboard, while the C an octave higher is C5.

An 88-key piano, with the octaves numbered and Middle C (turquoise) and A440 (yellow) highlighted Piano Frequencies.svg
An 88-key piano, with the octaves numbered and Middle C (turquoise) and A440 (yellow) highlighted
Octave
ScientificC−1C0C1C2C3C4C5C6C7C8C9
HelmholtzC,,,C,,C,Ccc'c''c'''c''''c'''''c''''''
Organ64 Foot32 Foot16 Foot8 Foot4 Foot2 Foot1 Foot3 Line4 Line5 Line6 Line
NameDbl ContraSub ContraContraGreatSmall1 Line2 Line3 Line4 Line5 Line6 Line
MIDI Note01224364860728496108120

Ottava alta and bassa

Octave
Example of the same three notes expressed in three ways: (1) regularly, (2) in an 8va bracket, and (3) in a 15ma bracket
Octave
Similar example with 8vb and 15mb

The notation 8a or 8va is sometimes seen in sheet music, meaning "play this an octave higher than written" (all' ottava: "at the octave" or all' 8va). 8a or 8va stands for ottava, the Italian word for octave (or "eighth"); the octave above may be specified as ottava alta or ottava sopra). Sometimes 8va is used to tell the musician to play a passage an octave lower (when placed under rather than over the staff), though the similar notation 8vb (ottava bassa or ottava sotto) is also used. Similarly, 15ma (quindicesima) means "play two octaves higher than written" and 15mb (quindicesima bassa) means "play two octaves lower than written."

The abbreviations col 8, coll' 8, and c. 8va stand for coll'ottava, meaning "with the octave", i.e. to play the notes in the passage together with the notes in the notated octaves. Any of these directions can be cancelled with the word loco, but often a dashed line or bracket indicates the extent of the music affected. [5]

Equivalence

Octave
Octave
Octave
Demonstration of octave equivalence. The melody to "Twinkle, Twinkle, Little Star" with parallel harmony. The melody is paralleled in three ways: (1) in octaves (consonant and equivalent); (2) in fifths (fairly consonant but not equivalent); and (3) in seconds (neither consonant nor equivalent).

After the unison, the octave is the simplest interval in music. The human ear tends to hear both notes as being essentially "the same", due to closely related harmonics. Notes separated by an octave "ring" together, adding a pleasing sound to music. The interval is so natural to humans that when men and women are asked to sing in unison, they typically sing in octave. [6]

For this reason, notes an octave apart are given the same note name in the Western system of music notation—the name of a note an octave above A is also A. This is called octave equivalence, the assumption that pitches one or more octaves apart are musically equivalent in many ways, leading to the convention "that scales are uniquely defined by specifying the intervals within an octave". [7] The conceptualization of pitch as having two dimensions, pitch height (absolute frequency) and pitch class (relative position within the octave), inherently include octave circularity. [7] Thus all Cs (or all 1s, if C = 0), any number of octaves apart, are part of the same pitch class.

Octave equivalence is a part of most advanced [ clarification needed ] musical cultures, but is far from universal in "primitive" and early music. [8] [ failed verification ] [9] [ clarification needed ] The languages in which the oldest extant written documents on tuning are written, Sumerian and Akkadian, have no known word for "octave". However, it is believed that a set of cuneiform tablets that collectively describe the tuning of a nine-stringed instrument, believed to be a Babylonian lyre, describe tunings for seven of the strings, with indications to tune the remaining two strings an octave from two of the seven tuned strings. [10] Leon Crickmore recently proposed that "The octave may not have been thought of as a unit in its own right, but rather by analogy like the first day of a new seven-day week". [11]

Monkeys experience octave equivalence, and its biological basis apparently is an octave mapping of neurons in the auditory thalamus of the mammalian brain. [12] Studies have also shown the perception of octave equivalence in rats, [13] human infants, [14] and musicians [15] but not starlings, [16] 4–9-year-old children, [17] or non-musicians. [15] [7] [ clarification needed ]

See also

Related Research Articles

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In music, just intonation or pure intonation is the tuning of musical intervals as whole number ratios of frequencies. An interval tuned in this way is said to be pure, and is called a just interval. Just intervals consist of tones from a single harmonic series of an implied fundamental. For example, in the diagram, if the notes G3 and C4 are tuned as members of the harmonic series of the lowest C, their frequencies will be 3 and 4 times the fundamental frequency. The interval ratio between C4 and G3 is therefore 4:3, a just fourth.

In music, notes are distinct and isolatable sounds that act as the most basic building blocks for nearly all of music. This discretization facilitates performance, comprehension, and analysis. Notes may be visually communicated by writing them in musical notation.

<span class="mw-page-title-main">Pythagorean tuning</span> Method of tuning a musical instrument

Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2. This ratio, also known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3. As Novalis put it, "The musical proportions seem to me to be particularly correct natural proportions." Alternatively, it can be described as the tuning of the syntonic temperament in which the generator is the ratio 3:2, which is ≈ 702 cents wide.

In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.

<span class="mw-page-title-main">Pitch (music)</span> Perceptual property in music ordering sounds from low to high

Pitch is a perceptual property of sounds that allows their ordering on a frequency-related scale, or more commonly, pitch is the quality that makes it possible to judge sounds as "higher" and "lower" in the sense associated with musical melodies. Pitch is a major auditory attribute of musical tones, along with duration, loudness, and timbre.

In music, two written notes have enharmonic equivalence if they produce the same pitch but are notated differently. Similarly, written intervals, chords, or key signatures are considered enharmonic if they represent identical pitches that are notated differently. The term derives from Latin enharmonicus, in turn from Late Latin enarmonius, from Ancient Greek ἐναρμόνιος, from ἐν ('in') and ἁρμονία ('harmony').

<span class="mw-page-title-main">Perfect fifth</span> Musical interval

In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.

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<span class="mw-page-title-main">Semitone</span> Musical interval

A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent notes in a 12-tone scale, visually seen on a keyboard as the distance between two keys that are adjacent to each other. For example, C is adjacent to C; the interval between them is a semitone.

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<span class="mw-page-title-main">Comma (music)</span> Very small interval arising from discrepancies in tuning

In music theory, a comma is a very small interval, the difference resulting from tuning one note two different ways. Strictly speaking, there are only two kinds of comma, the syntonic comma, "the difference between a just major 3rd and four just perfect 5ths less two octaves", and the Pythagorean comma, "the difference between twelve 5ths and seven octaves". The word comma used without qualification refers to the syntonic comma, which can be defined, for instance, as the difference between an F tuned using the D-based Pythagorean tuning system, and another F tuned using the D-based quarter-comma meantone tuning system. Intervals separated by the ratio 81:80 are considered the same note because the 12-note Western chromatic scale does not distinguish Pythagorean intervals from 5-limit intervals in its notation. Other intervals are considered commas because of the enharmonic equivalences of a tuning system. For example, in 53TET, B and A are both approximated by the same interval although they are a septimal kleisma apart.

Quarter-comma meantone, or  1 / 4 -comma meantone, was the most common meantone temperament in the sixteenth and seventeenth centuries, and was sometimes used later. In this system the perfect fifth is flattened by one quarter of a syntonic comma ( 81 : 80 ), with respect to its just intonation used in Pythagorean tuning ; the result is  3 / 2 × [ 80 / 81 ] 1 / 4 = 45 ≈ 1.49535, or a fifth of 696.578 cents. This fifth is then iterated to generate the diatonic scale and other notes of the temperament. The purpose is to obtain justly intoned major thirds. It was described by Pietro Aron in his Toscanello de la Musica of 1523, by saying the major thirds should be tuned to be "sonorous and just, as united as possible." Later theorists Gioseffo Zarlino and Francisco de Salinas described the tuning with mathematical exactitude.

<span class="mw-page-title-main">Fifteenth</span> Musical interval

In music, a fifteenth or double octave, abbreviated 15ma, is the interval between one musical note and another with one-quarter the wavelength or quadruple the frequency. It has also been referred to as the bisdiapason. The fourth harmonic, it is two octaves. It is referred to as a fifteenth because, in the diatonic scale, there are 15 notes between them if one counts both ends. Two octaves do not make a sixteenth, but a fifteenth. In other contexts, the term two octaves is likely to be used.

<span class="mw-page-title-main">Music and mathematics</span> Relationships between music and mathematics

Music theory analyzes the pitch, timing, and structure of music. It uses mathematics to study elements of music such as tempo, chord progression, form, and meter. The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of set theory, abstract algebra and number theory.

<span class="mw-page-title-main">Musical temperament</span> Musical tuning system

In musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Most modern Western musical instruments are tuned in the equal temperament system. Tempering is the process of altering the size of an interval by making it narrower or wider than pure. "Any plan that describes the adjustments to the sizes of some or all of the twelve fifth intervals in the circle of fifths so that they accommodate pure octaves and produce certain sizes of major thirds is called a temperament." Temperament is especially important for keyboard instruments, which typically allow a player to play only the pitches assigned to the various keys, and lack any way to alter pitch of a note in performance. Historically, the use of just intonation, Pythagorean tuning and meantone temperament meant that such instruments could sound "in tune" in one key, or some keys, but would then have more dissonance in other keys.

<span class="mw-page-title-main">Interval ratio</span> In music, ratio of pitch frequencies

In music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval. For example, a just perfect fifth is 3:2, 1.5, and may be approximated by an equal tempered perfect fifth which is 27/12. If the A above middle C is 440 Hz, the perfect fifth above it would be E, at (440*1.5=) 660 Hz, while the equal tempered E5 is 659.255 Hz.

<span class="mw-page-title-main">Five-limit tuning</span>

Five-limit tuning, 5-limit tuning, or 5-prime-limit tuning (not to be confused with 5-odd-limit tuning), is any system for tuning a musical instrument that obtains the frequency of each note by multiplying the frequency of a given reference note (the base note) by products of integer powers of 2, 3, or 5 (prime numbers limited to 5 or lower), such as 2−3·31·51 = 15/8.

<span class="mw-page-title-main">833 cents scale</span> Musical tuning scale

The 833 cents scale is a musical tuning and scale proposed by Heinz Bohlen based on combination tones, an interval of 833.09 cents, and, coincidentally, the Fibonacci sequence. The golden ratio is , which as a musical interval is 833.09 cents. In the 833 cents scale this interval is taken as an alternative to the octave as the interval of repetition, however the golden ratio is not regarded as an equivalent interval. Other music theorists such as Walter O'Connell, in his 1993 "The Tonality of the Golden Section", and Loren Temes appear to have also created this scale prior to Bohlen's discovery of it.

Abbreviations in music are of two kinds, namely, abbreviations of terms related to musical expression, and the true musical abbreviations by the help of which certain passages, chords, etc., may be notated in a shortened form, to the greater convenience of both composer and performer. Abbreviations of the first kind are like most abbreviations in language; they consist for the most part of the initial letter or first syllable of the word employed—as for instance, p or f for the dynamic markings piano and forte, cresc. for crescendo, Ob. for oboe, Fag. for bassoon. This article is about abbreviations used in music notation.

References

  1. 1 2 3 Duffin, Ross W. (2008). How equal temperament ruined harmony : (and why you should care) (First published as a Norton paperback. ed.). New York: W. W. Norton. p. 163. ISBN   978-0-393-33420-3. Archived from the original on 5 December 2017. Retrieved 28 June 2017.
  2. William Smith & Samuel Cheetham (1875). A Dictionary of Christian Antiquities. London: John Murray. ISBN   9780790582290. Archived from the original on 2016-04-30.
  3. Cooper, Paul (1973). Perspectives in Music Theory: An Historical-Analytical Approach, p. 16. ISBN   0-396-06752-2.
  4. "Dictionary.com | Meanings & Definitions of English Words". Dictionary.com. Retrieved 2024-01-24.
  5. Prout, Ebenezer & Fallows, David (2001). "All'ottava". In Sadie, Stanley & Tyrrell, John (eds.). The New Grove Dictionary of Music and Musicians (2nd ed.). London: Macmillan Publishers. ISBN   978-1-56159-239-5.
  6. "Music". Vox Explained. Event occurs at 12:50. Retrieved 2018-11-01. When you ask men and women to sing in unison, what typically happens is they actually sing an octave apart.
  7. 1 2 3 Burns, Edward M. (1999). "Intervals, Scales, and Tuning". In Diana Deutsch (ed.). The Psychology of Music (2nd ed.). San Diego: Academic Press. p. 252. ISBN   0-12-213564-4.
  8. e.g., Nettl,[ clarification needed ] 1956;[ incomplete short citation ] Sachs, C[urt]. and Kunst, J[aap]. (1962). In The Wellsprings of Music, ed. Kunst, J. The Hague: Marinus Nijhoff.[ incomplete short citation ]
  9. e.g., Nettl, 1956;[ incomplete short citation ] Sachs, C. and Kunst, J. (1962).[ incomplete short citation ] Cited in Burns 1999 , p. 217.
  10. Clint Goss (2012). "Flutes of Gilgamesh and Ancient Mesopotamia". Flutopedia. Archived from the original on 2012-06-28. Retrieved 2012-01-08.
  11. Leon Crickmore (2008). "New Light on the Babylonian Tonal System". ICONEA 2008: Proceedings of the International Conference of Near Eastern Archaeomusicology, Held at the British Museum, December 4–6, 2008. 24: 11–22.
  12. "The mechanism of octave circularity in the auditory brain Archived 2010-04-01 at the Wayback Machine ", Neuroscience of Music.
  13. Blackwell & Schlosberg 1943.
  14. Demany & Armand 1984.
  15. 1 2 Allen 1967.
  16. Cynx 1993.
  17. Sergeant 1983.

Sources