WikiMili The Free Encyclopedia

Inverse | unison |
---|---|

Name | |

Other names | - |

Abbreviation | P8 |

Size | |

Semitones | 12 |

Interval class | 0 |

Just interval | 2:1^{ [1] } |

Cents | |

Equal temperament | 1200^{ [1] } |

24 equal temperament | 1200 |

Just intonation | 1200^{ [1] } |

In music, an **octave** (Latin : *octavus*: eighth) or **perfect octave** (sometimes called the **diapason**)^{ [2] } is the interval between one musical pitch and another with double its frequency. 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] } The interval between the first and second harmonics of the harmonic series is an octave.

**Music** is an art form and cultural activity whose medium is sound organized in time. General definitions of music include common elements such as pitch, rhythm, dynamics, and the sonic qualities of timbre and texture. Different styles or types of music may emphasize, de-emphasize or omit some of these elements. Music is performed with a vast range of instruments and vocal techniques ranging from singing to rapping; there are solely instrumental pieces, solely vocal pieces and pieces that combine singing and instruments. The word derives from Greek μουσική . See glossary of musical terminology.

In musical tuning theory, a **Pythagorean interval** is a musical interval with frequency ratio equal to a power of two divided by a power of three, or vice versa. For instance, the perfect fifth with ratio 3/2 (equivalent to 3^{1}/2^{1}) and the perfect fourth with ratio 4/3 (equivalent to 2^{2}/3^{1}) are Pythagorean intervals.

In music theory, an **interval** is the 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.

- Explanation and definition
- Octave equivalence
- Music theory
- Notation
- Octave of a pitch
- Ottava alta and bassa
- Octave bands and fractional octave bands
- See also
- References
- External links

In music notation, notes separated by an octave (or multiple octaves) have the same letter name and are of the same pitch class.

In music, a **pitch class** (**p.c.** or **pc**) is a set of all pitches that are a whole number of octaves apart, e.g., 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, the pitch class "C" is the set

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 *8 ^{a}* or

A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a **perfect fourth** is the fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, because the note F is the fifth semitone above C, and there are four staff positions between C and F. Diminished and augmented fourths span the same number of staff positions, but consist of a different number of semitones.

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.

In music, a **note** is the pitch and duration of a sound, and also its representation in musical notation. A note can also represent a pitch class. Notes are the building blocks of much written music: discretizations of musical phenomena that facilitate performance, comprehension, and analysis.

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 ^{1}⁄_{2} (or ) and 4 (or ) times the frequency, respectively.

The **hertz** (symbol: **Hz**) is the derived unit of frequency in the International System of Units (SI) and is defined as one cycle per second. It is named after Heinrich Rudolf Hertz, the first person to provide conclusive proof of the existence of electromagnetic waves. Hertz are commonly expressed in multiples: kilohertz (10^{3} Hz, kHz), megahertz (10^{6} Hz, MHz), gigahertz (10^{9} Hz, GHz), terahertz (10^{12} Hz, THz), petahertz (10^{15} Hz, PHz), exahertz (10^{18} Hz, EHz), and zettahertz (10^{21} Hz, ZHz).

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

The octave is defined by ANSI ^{ [4] } as the unit of frequency level when the base of the logarithm is two.

In mathematics, the **logarithm** is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the *base* b, must be raised, to produce that number x. In the simplest case, the logarithm counts the number of occurrences of the same factor in repeated multiplication; e.g., since 1000 = 10 × 10 × 10 = 10^{3}, the "logarithm to base 10" of 1000 is 3. The logarithm of x to *base*b is denoted as log_{b} (*x*), or without parentheses, log_{b} *x*, or even without the explicit base, log *x*—if no confusion is possible.

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.^{ [5] }

In music, **unison** is two or more musical parts sounding the same pitch or at an octave interval, usually at the same time.

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".^{ [6] } The conceptualization of pitch as having two dimensions, pitch height (absolute frequency) and pitch class (relative position within the octave), inherently include octave circularity.^{ [6] } Thus all C♯s, or all 1s (if C = 0), in any octave are part of the same pitch class.

Octave equivalence is a part of most "advanced musical cultures", but is far from universal in "primitive" and early music.^{ [7] }^{ [8] } 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.^{ [9] } 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".^{ [10] }

Monkeys experience octave equivalence, and its biological basis apparently is an octave mapping of neurons in the auditory thalamus of the mammalian brain.^{ [11] } Studies have also shown the perception of octave equivalence in rats ( Blackwell & Schlosberg 1943 ), human infants ( Demany & Armand 1984 ),^{ [12] } and musicians ( Allen 1967 ) but not starlings ( Cynx 1993 ), 4–9 year old children ( Sergeant 1983 ), or nonmusicians ( Allen 1967 ).^{ [6] }

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.

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 in more than multiple octaves.

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.

Octaves are identified with various naming systems. Among the most common are the scientific, Helmholtz, organ pipe, MIDI, 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 C_{4}, 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 C_{5}.

**Scientific**C _{−1}C _{0}C _{1}C _{2}C _{3}C _{4}C _{5}C _{6}C _{7}C _{8}C _{9}**Helmholtz**C,,, C,, C, C c c' c'' c''' c'''' c''''' c'''''' **Organ**64 Foot 32 Foot 16 Foot 8 Foot 4 Foot 2 Foot 1 Foot 3 Line 4 Line 5 Line 6 Line **Name**Dbl Contra Sub Contra Contra Great Small 1 Line 2 Line 3 Line 4 Line 5 Line 6 Line **MIDI**-5 -4 -3 -2 -1 0 1 2 3 4 5 **MIDI Note**0 12 24 36 48 60 72 84 96 108 120

The notation *8 ^{a}* or

The abbreviations *col 8*, *coll' 8*, and *c. 8 ^{va}* stand for

An octave band is a frequency band that spans one octave. In this context an octave can be a factor of 2^{ [14] } or a factor of 10^{0.3}.^{ [15] }^{ [16] }

Fractional octave bands such as ^{1}⁄_{3} or ^{1}⁄_{12} of an octave are widely used in engineering acoustics.^{ [17] }

An **equal temperament** is a musical temperament, or a system of tuning, in which the frequency interval between every pair of adjacent notes has the same ratio. In other words, the ratios of the frequencies of any adjacent pair of notes is the same, and, as pitch is perceived roughly as the logarithm of frequency, equal perceived "distance" from every note to its nearest neighbor.

In music, **just intonation** or pure intonation is the tuning of musical intervals as (small) whole number ratios of frequencies. Any interval tuned in this way is called a **just interval**. Just intervals and chords are aggregates of harmonic series partials and may be seen as sharing a (lower) implied fundamental. For example, a tone with a frequency of 300 Hz and another with a frequency of 200 Hz are both multiples of 100 Hz. Their interval is, therefore, an aggregate of the second and third partials of the harmonic series of an implied fundamental frequency 100 Hz.

**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.

**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 can be determined only in sounds that have a frequency that is clear and stable enough to distinguish from noise. Pitch is a major auditory attribute of musical tones, along with duration, loudness, and timbre.

In modern musical notation and tuning, an **enharmonic equivalent** is a note, interval, or key signature that is equivalent to some other note, interval, or key signature but "spelled", or named differently. Thus, the **enharmonic spelling** of a written note, interval, or chord is an alternative way to write that note, interval, or chord. For example, in twelve-tone equal temperament, the notes C♯ and D♭ are *enharmonic* notes. Namely, they are the same key on a keyboard, and thus they are identical in pitch, although they have different names and different roles in harmony and chord progressions. Arbitrary amounts of accidentals can produce further enharmonic equivalents, such as B

In musical tuning, the **Pythagorean comma** (or **ditonic comma**), named after the ancient mathematician and philosopher Pythagoras, is the small interval (or comma) existing in Pythagorean tuning between two enharmonically equivalent notes such as C and B♯ (^{12}/128 = about 1.01364, or about 23.46 cents, roughly a quarter of a semitone (in between 75:74 and 74:73). The comma which musical temperaments often refer to tempering is the Pythagorean comma.

The **cent** is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each. Typically, cents are used to express small intervals, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is too small to be perceived between successive notes.

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. For example, C is adjacent to C♯; the interval between them is a semitone.

**Scientific pitch notation** is a method of specifying musical pitch by combining a musical note name and a number identifying the pitch's octave.

The **twelfth root of two** or is an algebraic irrational number. It is most important in Western music theory, where it represents the frequency ratio of a semitone in twelve-tone equal temperament. This number was proposed for the first time in relationship to musical tuning in the sixteenth and seventeenth centuries. It allows measurement and comparison of different intervals as consisting of different numbers of a single interval, the equal tempered semitone. A semitone itself is divided into 100 cents.

In music, a **fifteenth** or **double octave**, abbreviated * 15^{ma}*, 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

**Music theory** has no axiomatic foundation in modern mathematics, yet the basis of musical sound can be described mathematically and exhibits "a remarkable array of number properties". Elements of music such as its form, rhythm and metre, the pitches of its notes and the tempo of its pulse can be related to the measurement of time and frequency, offering ready analogies in geometry.

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 2^{7/12}. 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.

**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}·3^{1}·5^{1} = 15/8.

- 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. - ↑ William Smith & Samuel Cheetham (1875).
*A Dictionary of Christian Antiquities*. London: John Murray. Archived from the original on 2016-04-30. - ↑ Cooper, Paul (1973).
*Perspectives in Music Theory: An Historical-Analytical Approach*, p. 16. ISBN 0-396-06752-2. - ↑ ANSI/ASA S1.1-2013 Acoustical Terminology
- ↑ "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.

- 1 2 3 Burns, Edward M. (1999). "Intervals, Scales, and Tuning",
*The Psychology of Music*second edition, p. 252. Deutsch, Diana, ed. San Diego: Academic Press. ISBN 0-12-213564-4. - ↑ e.g., Nettl, 1956; Sachs, C. and Kunst, J. (1962). In
*The wellsprings of music*, ed. Kunst, J. The Hague: Marinus Nijhoff. - ↑ e.g., Nettl, 1956; Sachs, C. and Kunst, J. (1962). Cited in Burns, Edward M. (1999), p. 217.
- ↑ Clint Goss (2012). "Flutes of Gilgamesh and Ancient Mesopotamia".
*Flutopedia*. Archived from the original on 2012-06-28. Retrieved 2012-01-08. - ↑ 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. - ↑ "The mechanism of octave circularity in the auditory brain Archived 2010-04-01 at the Wayback Machine ",
*Neuroscience of Music*. - ↑ Demany L, Armand F. The perceptual reality of tone chroma in early infancy. J Acoust Soc Am 1984; 76:57–66.
- ↑ Ebenezer Prout & David Fallows. "All'ottava". In Deane L. Root (ed.).
*Grove Music Online. Oxford Music Online*. Oxford University Press.(subscription required) - ↑ Crocker 1997 Archived 2017-12-05 at the Wayback Machine
- ↑ IEC 61260-1:2014
- ↑ IANSI S1-6-2016
- ↑ "Archived copy". Archived from the original on 2017-05-14. Retrieved 2017-11-23.CS1 maint: Archived copy as title (link)

- Allen, David. 1967. "Octave Discriminability of Musical and Non-Musical Subjects".
*Psychonomic Science*7:421–22. - Blackwell, H. R., & H. Schlosberg. 1943. "Octave Generalization, Pitch Discrimination, and Loudness Thresholds in the White Rat".
*Journal of Experimental Psychology*33:407–19. - Cynx, Jeffrey. 1996. "Neuroethological Studies on How Birds Discriminate Song". In
*Neuroethology of Cognitive and Perceptual Processes*, edited by C. F. Moss and S. J. Shuttleworth, 63. Boulder: Westview Press. - Demany, Laurent, and Françoise Armand. 1984. "The Perceptual Reality of Tone Chroma in Early Infancy".
*Journal of the Acoustical Society of America*76:57–66. - Sergeant, Desmond. 1983. "The Octave: Percept or Concept?"
*Psychology of Music*11, no. 1:3–18.

This page is based on this Wikipedia article

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.