45-462: [REDACTED] Look up sixth in Wiktionary, the free dictionary. Sixth is the ordinal form of the number six . The Sixth Amendment , to the U.S. Constitution A keg of beer, equal to 5 U.S. gallons or 1 ⁄ 6 barrel The fraction 1 ⁄ 6 Music [ edit ] Sixth interval (music)s : major sixth ,
90-469: A 5:4 ratio is an 8:5 ratio. For intervals identified by an integer number of semitones, the inversion is obtained by subtracting that number from 12. Since an interval class is the lower number selected among the interval integer and its inversion, interval classes cannot be inverted. Intervals can be described, classified, or compared with each other according to various criteria. An interval can be described as In general, The table above depicts
135-512: A Soviet film directed by Samvel Gasparov The Sixth (2024 film) , an American documentary film directed by Andrea Nix Fine and Sean Fine The 6ths , a band created by Stephin Merritt LaSexta (lit. The Sixth), a Spanish television channel Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Sixth . If an internal link led you here, you may wish to change
180-447: A Soviet film directed by Samvel Gasparov The Sixth (2024 film) , an American documentary film directed by Andrea Nix Fine and Sean Fine The 6ths , a band created by Stephin Merritt LaSexta (lit. The Sixth), a Spanish television channel Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Sixth . If an internal link led you here, you may wish to change
225-479: A chromatic semitone. For instance, an augmented sixth such as E ♭ –C ♯ spans ten semitones, exceeding a major sixth (E ♭ —C) by one semitone, while a diminished sixth such as E ♯ –C spans seven semitones, falling short of a minor sixth (E ♯ –C ♯ ) by one semitone. The augmented fourth ( A4 ) and the diminished fifth ( d5 ) are the only augmented and diminished intervals that appear in diatonic scales (see table). Neither
270-612: A different context: frequency ratios or cents. The size of an interval between two notes may be measured by the ratio of their frequencies . When a musical instrument is tuned using a just intonation tuning system, the size of the main intervals can be expressed by small- integer ratios, such as 1:1 ( unison ), 2:1 ( octave ), 5:3 ( major sixth ), 3:2 ( perfect fifth ), 4:3 ( perfect fourth ), 5:4 ( major third ), 6:5 ( minor third ). Intervals with small-integer ratios are often called just intervals , or pure intervals . Most commonly, however, musical instruments are nowadays tuned using
315-402: A different tuning system, called 12-tone equal temperament . As a consequence, the size of most equal-tempered intervals cannot be expressed by small-integer ratios, although it is very close to the size of the corresponding just intervals. For instance, an equal-tempered fifth has a frequency ratio of 2 :1, approximately equal to 1.498:1, or 2.997:2 (very close to 3:2). For a comparison between
360-507: A fourth is augmented ( A4 ) and one fifth is diminished ( d5 ), both spanning six semitones. For instance, in an E-major scale, the A4 is between A and D ♯ , and the d5 is between D ♯ and A. The inversion of a perfect interval is also perfect. Since the inversion does not change the pitch class of the two notes, it hardly affects their level of consonance (matching of their harmonics ). Conversely, other kinds of intervals have
405-430: A frequency ratio of 2:1. This means that successive increments of pitch by the same interval result in an exponential increase of frequency, even though the human ear perceives this as a linear increase in pitch. For this reason, intervals are often measured in cents , a unit derived from the logarithm of the frequency ratio. In Western music theory, the most common naming scheme for intervals describes two properties of
450-422: A melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord . In Western music, intervals are most commonly differences between notes of a diatonic scale . Intervals between successive notes of a scale are also known as scale steps. The smallest of these intervals is a semitone . Intervals smaller than a semitone are called microtones . They can be formed using
495-460: A minor sixth by a chromatic semitone augmented sixth , an interval produced by widening a major sixth by a chromatic semitone Sixth chord , two different kinds of chord Submediant , sixth degree of the diatonic scale Landini sixth , a type of cadence Sixth (interval) See also [ edit ] All pages with titles containing 6th OR sixth All pages with titles beginning with Sixth The Sixth (1981 film) ,
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#1732764818745540-573: A musical interval minor sixth , a musical interval diminished sixth , an interval produced by narrowing a minor sixth by a chromatic semitone augmented sixth , an interval produced by widening a major sixth by a chromatic semitone Sixth chord , two different kinds of chord Submediant , sixth degree of the diatonic scale Landini sixth , a type of cadence Sixth (interval) See also [ edit ] All pages with titles containing 6th OR sixth All pages with titles beginning with Sixth The Sixth (1981 film) ,
585-416: A separate section . Intervals smaller than one semitone (commas or microtones) and larger than one octave (compound intervals) are introduced below. In Western music theory , an interval is named according to its number (also called diatonic number, interval size or generic interval ) and quality . For instance, major third (or M3 ) is an interval name, in which the term major ( M ) describes
630-585: Is a major third , while that from D to G ♭ is a diminished fourth . However, they both span 4 semitones. If the instrument is tuned so that the 12 notes of the chromatic scale are equally spaced (as in equal temperament ), these intervals also have the same width. Namely, all semitones have a width of 100 cents , and all intervals spanning 4 semitones are 400 cents wide. The names listed here cannot be determined by counting semitones alone. The rules to determine them are explained below. Other names, determined with different naming conventions, are listed in
675-410: Is an interval spanning three tones, or six semitones (for example, an augmented fourth). Rarely, the term ditone is also used to indicate an interval spanning two whole tones (for example, a major third ), or more strictly as a synonym of major third. Intervals with different names may span the same number of semitones, and may even have the same width. For instance, the interval from D to F ♯
720-516: Is diatonic, except for the augmented fourth and diminished fifth. The distinction between diatonic and chromatic intervals may be also sensitive to context. The above-mentioned 56 intervals formed by the C-major scale are sometimes called diatonic to C major . All other intervals are called chromatic to C major . For instance, the perfect fifth A ♭ –E ♭ is chromatic to C major, because A ♭ and E ♭ are not contained in
765-584: Is one cent. In twelve-tone equal temperament (12-TET), a tuning system in which all semitones have the same size, the size of one semitone is exactly 100 cents. Hence, in 12-TET the cent can be also defined as one hundredth of a semitone . Mathematically, the size in cents of the interval from frequency f 1 to frequency f 2 is n = 1200 ⋅ log 2 ( f 2 f 1 ) {\displaystyle n=1200\cdot \log _{2}\left({\frac {f_{2}}{f_{1}}}\right)} The table shows
810-408: Is the reason interval numbers are also called diatonic numbers , and this convention is called diatonic numbering . If one adds any accidentals to the notes that form an interval, by definition the notes do not change their staff positions. As a consequence, any interval has the same interval number as the corresponding natural interval, formed by the same notes without accidentals. For instance,
855-417: The harmonic C-minor scale ) is considered diatonic if the harmonic minor scales are considered diatonic as well. Otherwise, it is considered chromatic. For further details, see the main article . By a commonly used definition of diatonic scale (which excludes the harmonic minor and melodic minor scales), all perfect, major and minor intervals are diatonic. Conversely, no augmented or diminished interval
900-453: The 56 diatonic intervals formed by the notes of the C major scale (a diatonic scale). Notice that these intervals, as well as any other diatonic interval, can be also formed by the notes of a chromatic scale. The distinction between diatonic and chromatic intervals is controversial, as it is based on the definition of diatonic scale, which is variable in the literature. For example, the interval B–E ♭ (a diminished fourth , occurring in
945-404: The C above it must be a major sixth. Since compound intervals are larger than an octave, "the inversion of any compound interval is always the same as the inversion of the simple interval from which it is compounded". For intervals identified by their ratio, the inversion is determined by reversing the ratio and multiplying the ratio by 2 until it is greater than 1. For example, the inversion of
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#1732764818745990-405: The C major scale. However, it is diatonic to others, such as the A ♭ major scale. Consonance and dissonance are relative terms that refer to the stability, or state of repose, of particular musical effects. Dissonant intervals are those that cause tension and desire to be resolved to consonant intervals. These terms are relative to the usage of different compositional styles. All of
1035-430: The diatonic intervals with a given interval number always occur in two sizes, which differ by one semitone. For example, six of the fifths span seven semitones. The other one spans six semitones. Four of the thirds span three semitones, the others four. If one of the two versions is a perfect interval, the other is called either diminished (i.e. narrowed by one semitone) or augmented (i.e. widened by one semitone). Otherwise,
1080-457: The diatonic scale), or simply interval . The quality of a compound interval is the quality of the simple interval on which it is based. Some other qualifiers like neutral , subminor , and supermajor are used for non-diatonic intervals . Perfect intervals are so-called because they were traditionally considered perfectly consonant, although in Western classical music the perfect fourth
1125-425: The free dictionary. Sixth is the ordinal form of the number six . The Sixth Amendment , to the U.S. Constitution A keg of beer, equal to 5 U.S. gallons or 1 ⁄ 6 barrel The fraction 1 ⁄ 6 Music [ edit ] Sixth interval (music)s : major sixth , a musical interval minor sixth , a musical interval diminished sixth , an interval produced by narrowing
1170-479: The interval E–E, a perfect unison, is also called a prime (meaning "1"), even though there is no difference between the endpoints. Continuing, the interval E–F ♯ is a second, but F ♯ is only one staff position, or diatonic-scale degree, above E. Similarly, E—G ♯ is a third, but G ♯ is only two staff positions above E, and so on. As a consequence, joining two intervals always yields an interval number one less than their sum. For instance,
1215-437: The interval number. The indications M and P are often omitted. The octave is P8, and a unison is usually referred to simply as "a unison" but can be labeled P1. The tritone , an augmented fourth or diminished fifth is often TT . The interval qualities may be also abbreviated with perf , min , maj , dim , aug . Examples: A simple interval (i.e., an interval smaller than or equal to an octave) may be inverted by raising
1260-630: The interval: the quality (perfect, major, minor, augmented, diminished) and number (unison, second, third, etc.). Examples include the minor third or perfect fifth . These names identify not only the difference in semitones between the upper and lower notes but also how the interval is spelled . The importance of spelling stems from the historical practice of differentiating the frequency ratios of enharmonic intervals such as G–G ♯ and G–A ♭ . The size of an interval (also known as its width or height) can be represented using two alternative and equivalently valid methods, each appropriate to
1305-399: The intervals B–D ♯ (spanning 4 semitones) and B–D ♭ (spanning 2 semitones) are thirds, like the corresponding natural interval B—D (3 semitones). Notice that interval numbers represent an inclusive count of encompassed staff positions or note names, not the difference between the endpoints. In other words, one starts counting the lower pitch as one, not zero. For that reason,
1350-417: The intervals B—D and D—F ♯ are thirds, but joined together they form a fifth (B—F ♯ ), not a sixth. Similarly, a stack of three thirds, such as B—D, D—F ♯ , and F ♯ —A, is a seventh (B-A), not a ninth. This scheme applies to intervals up to an octave (12 semitones). For larger intervals, see § Compound intervals below. The name of any interval is further qualified using
1395-484: The larger version is called major, the smaller one minor. For instance, since a 7-semitone fifth is a perfect interval ( P5 ), the 6-semitone fifth is called "diminished fifth" ( d5 ). Conversely, since neither kind of third is perfect, the larger one is called "major third" ( M3 ), the smaller one "minor third" ( m3 ). Within a diatonic scale, unisons and octaves are always qualified as perfect, fourths as either perfect or augmented, fifths as perfect or diminished, and all
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1440-442: The link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Sixth&oldid=1227013753 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages sixth [REDACTED] Look up sixth in Wiktionary,
1485-588: The link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Sixth&oldid=1227013753 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Interval (music) 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
1530-427: The lower pitch an octave or lowering the upper pitch an octave. For example, the fourth from a lower C to a higher F may be inverted to make a fifth, from a lower F to a higher C. There are two rules to determine the number and quality of the inversion of any simple interval: For example, the interval from C to the E ♭ above it is a minor third. By the two rules just given, the interval from E ♭ to
1575-400: The most widely used conventional names for the intervals between the notes of a chromatic scale . A perfect unison (also known as perfect prime) is an interval formed by two identical notes. Its size is zero cents . A semitone is any interval between two adjacent notes in a chromatic scale, a whole tone is an interval spanning two semitones (for example, a major second ), and a tritone
1620-456: The notes of various kinds of non-diatonic scales. Some of the very smallest ones are called commas , and describe small discrepancies, observed in some tuning systems , between enharmonically equivalent notes such as C ♯ and D ♭ . Intervals can be arbitrarily small, and even imperceptible to the human ear. In physical terms, an interval is the ratio between two sonic frequencies. For example, any two notes an octave apart have
1665-479: The number, nor the quality of an interval can be determined by counting semitones alone. As explained above, the number of staff positions must be taken into account as well. For example, as shown in the table below, there are six semitones between C and F ♯ , C and G ♭ , and C ♭ and E ♯ , but Intervals are often abbreviated with a P for perfect, m for minor , M for major , d for diminished , A for augmented , followed by
1710-449: The opposite quality with respect to their inversion. The inversion of a major interval is a minor interval, the inversion of an augmented interval is a diminished interval. As shown in the table, a diatonic scale defines seven intervals for each interval number, each starting from a different note (seven unisons, seven seconds, etc.). The intervals formed by the notes of a diatonic scale are called diatonic. Except for unisons and octaves,
1755-444: The other intervals (seconds, thirds, sixths, sevenths) as major or minor. Augmented intervals are wider by one semitone than perfect or major intervals, while having the same interval number (i.e., encompassing the same number of staff positions): they are wider by a chromatic semitone . Diminished intervals, on the other hand, are narrower by one semitone than perfect or minor intervals of the same interval number: they are narrower by
1800-459: The positions of B and D. The table and the figure above show intervals with numbers ranging from 1 (e.g., P1 ) to 8 (e.g., d8 ). Intervals with larger numbers are called compound intervals . There is a one-to-one correspondence between staff positions and diatonic-scale degrees (the notes of diatonic scale ). This means that interval numbers can also be determined by counting diatonic scale degrees, rather than staff positions, provided that
1845-437: The quality of the interval, and third ( 3 ) indicates its number. The number of an interval is the number of letter names or staff positions (lines and spaces) it encompasses, including the positions of both notes forming the interval. For instance, the interval B—D is a third (denoted m3 ) because the notes from B to the D above it encompass three letter names (B, C, D) and occupy three consecutive staff positions, including
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1890-436: The size of intervals in different tuning systems, see § Size of intervals used in different tuning systems . The standard system for comparing interval sizes is with cents . The cent is a logarithmic unit of measurement. If frequency is expressed in a logarithmic scale , and along that scale the distance between a given frequency and its double (also called octave ) is divided into 1200 equal parts, each of these parts
1935-477: The terms perfect ( P ), major ( M ), minor ( m ), augmented ( A ), and diminished ( d ). This is called its interval quality (or modifier ). It is possible to have doubly diminished and doubly augmented intervals, but these are quite rare, as they occur only in chromatic contexts. The combination of number (or generic interval) and quality (or modifier) is called the specific interval , diatonic interval (sometimes used only for intervals appearing in
1980-471: The two notes that form the interval are drawn from a diatonic scale. Namely, B—D is a third because in any diatonic scale that contains B and D, the sequence from B to D includes three notes. For instance, in the B- natural minor diatonic scale, the three notes are B–C ♯ –D. This is not true for all kinds of scales. For instance, in a chromatic scale , there are four notes from B to D: B–C–C ♯ –D. This
2025-502: Was sometimes regarded as a less than perfect consonance, when its function was contrapuntal . Conversely, minor, major, augmented, or diminished intervals are typically considered less consonant, and were traditionally classified as mediocre consonances, imperfect consonances, or near-dissonances. Within a diatonic scale all unisons ( P1 ) and octaves ( P8 ) are perfect. Most fourths and fifths are also perfect ( P4 and P5 ), with five and seven semitones respectively. One occurrence of
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