In music theory , an eleventh is a compound interval consisting of an octave plus a fourth .
76-479: A perfect eleventh spans 17 and the augmented eleventh 18 semitones , or 10 steps in a diatonic scale . Since there are only seven degrees in a diatonic scale, the eleventh degree is the same as the subdominant (IV). The eleventh is considered highly dissonant with the major third . An eleventh chord is the stacking of five thirds in the span of an eleventh. In common practice tonality , it usually had subdominant function as minor eleventh chord on
152-411: A 12-tone scale (or half of a whole step ), 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. In a 12-note approximately equally divided scale, any interval can be defined in terms of an appropriate number of semitones (e.g. a whole tone or major second is 2 semitones wide,
228-481: A commonly used version of 5 limit tuning have four different sizes, and can be classified as follows: The most frequently occurring semitones are the just ones ( S 3 , 16:15, and S 1 , 25:24): S 3 occurs at 6 short intervals out of 12, S 1 3 times, S 2 twice, and S 4 at only one interval (if diatonic D ♭ replaces chromatic D ♭ and sharp notes are not used). The smaller chromatic and diatonic semitones differ from
304-456: A diatonic and chromatic semitone in the tuning. Well temperament was constructed so that enharmonic equivalence could be assumed between all of these semitones, and whether they were written as a minor second or augmented unison did not effect a different sound. Instead, in these systems, each key had a slightly different sonic color or character, beyond the limitations of conventional notation. Like meantone temperament, Pythagorean tuning
380-546: A diminished seventh chord , or an augmented sixth chord . Its use is also often the consequence of a melody proceeding in semitones, regardless of harmonic underpinning, e.g. D , D ♯ , E , F , F ♯ . (Restricting the notation to only minor seconds is impractical, as the same example would have a rapidly increasing number of accidentals, written enharmonically as D , E ♭ , F ♭ , G [REDACTED] , A [REDACTED] ). Harmonically , augmented unisons are quite rare in tonal repertoire. In
456-467: A major third 4 semitones, and a perfect fifth 7 semitones). In music theory , a distinction is made between a diatonic semitone , or minor second (an interval encompassing two different staff positions , e.g. from C to D ♭ ) and a chromatic semitone or augmented unison (an interval between two notes at the same staff position, e.g. from C to C ♯ ). These are enharmonically equivalent if and only if twelve-tone equal temperament
532-406: A "tonic" diatonic scale and modulate to the "dominant" scale a fifth above. In the 19th century (to a certain extent), but more in the 20th century, additional types of scales were explored: A large variety of other scales exists, some of the more common being: Scales such as the pentatonic scale may be considered gapped relative to the diatonic scale. An auxiliary scale is a scale other than
608-576: A binary system of twelve zeros or ones to represent each of the twelve notes of a chromatic scale . The most common binary numbering scheme defines lower pitches to have lower numeric value (as opposed to low pitches having a high numeric value). Thus a single pitch class n in the pitch class set is represented by 2^n. This maps the entire power set of all pitch class sets in 12-TET to the numbers 0 to 4095. The binary digits read as ascending pitches from right to left, which some find discombobulating because they are used to low to high reading left to right, as on
684-465: A caustic dissonance, having no resolution. Some composers would even use large collections of harmonic semitones ( tone clusters ) as a source of cacophony in their music (e.g. the early piano works of Henry Cowell ). By now, enharmonic equivalence was a commonplace property of equal temperament , and instrumental use of the semitone was not at all problematic for the performer. The composer was free to write semitones wherever he wished. The exact size of
760-554: A composition, such as in Claude Debussy 's L'Isle Joyeuse . To the right, the first scale is a whole-tone scale, while the second and third scales are diatonic scales. All three are used in the opening pages of Debussy's piece. Scales in traditional Western music generally consist of seven notes and repeat at the octave. Notes in the commonly used scales (see just below) are separated by whole and half step intervals of tones and semitones. The harmonic minor scale includes
836-493: A family of intervals that may vary both in size and name. In Pythagorean tuning , seven semitones out of twelve are diatonic, with ratio 256:243 or 90.2 cents ( Pythagorean limma ), and the other five are chromatic, with ratio 2187:2048 or 113.7 cents ( Pythagorean apotome ); they differ by the Pythagorean comma of ratio 531441:524288 or 23.5 cents. In quarter-comma meantone , seven of them are diatonic, and 117.1 cents wide, while
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#1732844224003912-519: A fundamental part of the musical language, even to the point where the usual accidental accompanying the minor second in a cadence was often omitted from the written score (a practice known as musica ficta ). By the 16th century, the semitone had become a more versatile interval, sometimes even appearing as an augmented unison in very chromatic passages. Semantically , in the 16th century the repeated melodic semitone became associated with weeping, see: passus duriusculus , lament bass , and pianto . By
988-450: A melodic half step, no "tendency was perceived of the lower tone toward the upper, or of the upper toward the lower. The second tone was not taken to be the 'goal' of the first. Instead, the half step was avoided in clausulae because it lacked clarity as an interval." However, beginning in the 13th century cadences begin to require motion in one voice by half step and the other a whole step in contrary motion. These cadences would become
1064-422: A note between G and G ♯ or a note moving between both. In blues, a pentatonic scale is often used. In jazz, many different modes and scales are used, often within the same piece of music. Chromatic scales are common, especially in modern jazz. In Western music, scale notes are often separated by equally tempered tones or semitones, creating 12 intervals per octave. Each interval separates two tones;
1140-449: A piano keyboard. In this scheme, the major scale is 101010110101 = 2741. This binary representation permits easy calculation of interval vectors and common tones, using logical binary operators. It also provides a perfect index for every possible combination of tones, as every scale has its own number. Scales may also be shown as semitones from the tonic. For instance, 0 2 4 5 7 9 11 denotes any major scale such as C–D–E–F–G–A–B, in which
1216-440: A pitch ratio of 16:15 ( play ) or 1.0666... (approximately 111.7 cents ), called the just diatonic semitone . This is a practical just semitone, since it is the interval that occurs twice within the diatonic scale between a: The 16:15 just minor second arises in the C major scale between B & C and E & F, and is, "the sharpest dissonance found in the scale". An "augmented unison" (sharp) in just intonation
1292-477: A semitone depends on the tuning system used. Meantone temperaments have two distinct types of semitones, but in the exceptional case of equal temperament , there is only one. The unevenly distributed well temperaments contain many different semitones. Pythagorean tuning , similar to meantone tuning, has two, but in other systems of just intonation there are many more possibilities. In meantone systems, there are two different semitones. This results because of
1368-400: A semitone. The blue note is an interval that is technically neither major nor minor but "in the middle", giving it a characteristic flavour. A regular piano cannot play blue notes, but with electric guitar , saxophone , trombone and trumpet , performers can "bend" notes a fraction of a tone sharp or flat to create blue notes. For instance, in the key of E, the blue note would be either
1444-410: A single octave, with higher or lower octaves simply repeating the pattern. A musical scale represents a division of the octave space into a certain number of scale steps, a scale step being the recognizable distance (or interval ) between two successive notes of the scale. However, there is no need for scale steps to be equal within any scale and, particularly as demonstrated by microtonal music , there
1520-599: A third (in this case a major third); D and F also create a third (in this case a minor third). A single scale can be manifested at many different pitch levels. For example, a C major scale can be started at C4 (middle C; see scientific pitch notation ) and ascending an octave to C5; or it could be started at C6, ascending an octave to C7. Scales may be described according to the number of different pitch classes they contain: Scales may also be described by their constituent intervals, such as being hemitonic , cohemitonic , or having imperfections. Many music theorists concur that
1596-711: A three-semitone step; the anhemitonic pentatonic includes two of those and no semitones. Western music in the Medieval and Renaissance periods (1100–1600) tends to use the white-note diatonic scale C–D–E–F–G–A–B. Accidentals are rare, and somewhat unsystematically used, often to avoid the tritone . Music of the common practice periods (1600–1900) uses three types of scale: These scales are used in all of their transpositions. The music of this period introduces modulation, which involves systematic changes from one scale to another. Modulation occurs in relatively conventionalized ways. For example, major-mode pieces typically begin in
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#17328442240031672-425: A tritone), and one without tritones is atritonic . A scale or chord that contains semitones is called hemitonic, and without semitones is anhemitonic . Scales can be abstracted from performance or composition . They are also often used precompositionally to guide or limit a composition. Explicit instruction in scales has been part of compositional training for many centuries. One or more scales may be used in
1748-445: Is C–B–A–G–F–E–D–[C], with the bracket indicating an octave lower than the first note in the scale. The distance between two successive notes in a scale is called a scale step . The notes of a scale are numbered by their steps from the first degree of the scale. For example, in a C major scale the first note is C, the second D, the third E and so on. Two notes can also be numbered in relation to each other: C and E create an interval of
1824-477: Is D–E–F ♯ in Chromatic transposition). Since the steps of a scale can have various sizes, this process introduces subtle melodic and harmonic variation into the music. In Western tonal music, the simplest and most common type of modulation (or changing keys) is to shift from one major key to another key built on the first key's fifth (or dominant) scale degree. In the key of C major, this would involve moving to
1900-419: Is a broken circle of fifths . This creates two distinct semitones, but because Pythagorean tuning is also a form of 3-limit just intonation , these semitones are rational. Also, unlike most meantone temperaments, the chromatic semitone is larger than the diatonic. The Pythagorean diatonic semitone has a ratio of 256/243 ( play ), and is often called the Pythagorean limma . It is also sometimes called
1976-401: Is a different, smaller semitone, with frequency ratio 25:24 ( play ) or 1.0416... (approximately 70.7 cents). It is the interval between a major third (5:4) and a minor third (6:5). In fact, it is the spacing between the minor and major thirds, sixths, and sevenths (but not necessarily the major and minor second). Composer Ben Johnston used a sharp ( ♯ ) to indicate a note
2052-455: Is called hemitonia; that of having no semitones is anhemitonia . A musical scale or chord containing semitones is called hemitonic; one without semitones is anhemitonic. The minor second occurs in the major scale , between the third and fourth degree, ( mi (E) and fa (F) in C major), and between the seventh and eighth degree ( ti (B) and do (C) in C major). It is also called the diatonic semitone because it occurs between steps in
2128-522: Is defined by its characteristic interval pattern and by a special note, known as its first degree (or tonic ). The tonic of a scale is the note selected as the beginning of the octave, and therefore as the beginning of the adopted interval pattern. Typically, the name of the scale specifies both its tonic and its interval pattern. For example, C major indicates a major scale with a C tonic. Scales are typically listed from low to high pitch. Most scales are octave -repeating , meaning their pattern of notes
2204-440: Is distinguishable by its "step-pattern", or how its intervals interact with each other. Often, especially in the context of the common practice period , most or all of the melody and harmony of a musical work is built using the notes of a single scale, which can be conveniently represented on a staff with a standard key signature . Due to the principle of octave equivalence, scales are generally considered to span
2280-628: Is no limit to how many notes can be injected within any given musical interval. A measure of the width of each scale step provides a method to classify scales. For instance, in a chromatic scale each scale step represents a semitone interval, while a major scale is defined by the interval pattern W–W–H–W–W–W–H, where W stands for whole step (an interval spanning two semitones, e.g. from C to D), and H stands for half-step (e.g. from C to D ♭ ). Based on their interval patterns, scales are put into categories including pentatonic , diatonic , chromatic , major , minor , and others. A specific scale
2356-449: Is raised 70.7 cents, or a flat ( ♭ ) to indicate a note is lowered 70.7 cents. (This is the standard practice for just intonation, but not for all other microtunings.) Two other kinds of semitones are produced by 5 limit tuning. A chromatic scale defines 12 semitones as the 12 intervals between the 13 adjacent notes, spanning a full octave (e.g. from C 4 to C 5 ). The 12 semitones produced by
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2432-421: Is the diminished octave ( d8 , or dim 8 ). The augmented unison is also the inversion of the augmented octave , because the interval of the diminished unison does not exist. This is because a unison is always made larger when one note of the interval is changed with an accidental. Melodically , an augmented unison very frequently occurs when proceeding to a chromatic chord, such as a secondary dominant ,
2508-429: Is the septimal diatonic semitone of 15:14 ( play ) available in between the 5 limit major seventh (15:8) and the 7 limit minor seventh / harmonic seventh (7:4). There is also a smaller septimal chromatic semitone of 21:20 ( play ) between a septimal minor seventh and a fifth (21:8) and an octave and a major third (5:2). Both are more rarely used than their 5 limit neighbours, although
2584-454: Is the same in every octave (the Bohlen–Pierce scale is one exception). An octave-repeating scale can be represented as a circular arrangement of pitch classes, ordered by increasing (or decreasing) pitch class. For instance, the increasing C major scale is C–D–E–F–G–A–B–[C], with the bracket indicating that the last note is an octave higher than the first note, and the decreasing C major scale
2660-467: Is used; for example, they are not the same thing in meantone temperament , where the diatonic semitone is distinguished from and larger than the chromatic semitone (augmented unison), or in Pythagorean tuning , where the diatonic semitone is smaller instead. See Interval (music) § Number for more details about this terminology. In twelve-tone equal temperament all semitones are equal in size (100 cents). In other tuning systems, "semitone" refers to
2736-531: The Baroque era (1600 to 1750), the tonal harmonic framework was fully formed, and the various musical functions of the semitone were rigorously understood. Later in this period the adoption of well temperaments for instrumental tuning and the more frequent use of enharmonic equivalences increased the ease with which a semitone could be applied. Its function remained similar through the Classical period, and though it
2812-467: The Pythagorean minor semitone . It is about 90.2 cents. It can be thought of as the difference between three octaves and five just fifths , and functions as a diatonic semitone in a Pythagorean tuning . The Pythagorean chromatic semitone has a ratio of 2187/2048 ( play ). It is about 113.7 cents . It may also be called the Pythagorean apotome or the Pythagorean major semitone . ( See Pythagorean interval .) It can be thought of as
2888-419: The diatonic scale . The minor second is abbreviated m2 (or −2 ). Its inversion is the major seventh ( M7 or Ma7 ). Listen to a minor second in equal temperament . Here, middle C is followed by D ♭ , which is a tone 100 cents sharper than C, and then by both tones together. Melodically , this interval is very frequently used, and is of particular importance in cadences . In
2964-482: The functional harmony . It may also appear in inversions of a major seventh chord , and in many added tone chords . In unusual situations, the minor second can add a great deal of character to the music. For instance, Frédéric Chopin 's Étude Op. 25, No. 5 opens with a melody accompanied by a line that plays fleeting minor seconds. These are used to humorous and whimsical effect, which contrasts with its more lyrical middle section. This eccentric dissonance has earned
3040-556: The harmonic overtones series. Many musical scales in the world are based on this system, except most of the musical scales from Indonesia and the Indochina Peninsulae, which are based on inharmonic resonance of the dominant metalophone and xylophone instruments. Some scales use a different number of pitches. A common scale in Eastern music is the pentatonic scale, which consists of five notes that span an octave. For example, in
3116-412: The perfect and deceptive cadences it appears as a resolution of the leading-tone to the tonic . In the plagal cadence , it appears as the falling of the subdominant to the mediant . It also occurs in many forms of the imperfect cadence , wherever the tonic falls to the leading-tone. Harmonically , the interval usually occurs as some form of dissonance or a nonchord tone that is not part of
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3192-615: The Chinese culture, the pentatonic scale is usually used for folk music and consists of C, D, E, G and A, commonly known as gong, shang, jue, chi and yu. Some scales span part of an octave; several such short scales are typically combined to form a scale spanning a full octave or more, and usually called with a third name of its own. The Turkish and Middle Eastern music has around a dozen such basic short scales that are combined to form hundreds of full-octave spanning scales. Among these scales Hejaz scale has one scale step spanning 14 intervals (of
3268-407: The [major] scale ." Play B & C The augmented unison , the interval produced by the augmentation , or widening by one half step, of the perfect unison, does not occur between diatonic scale steps, but instead between a scale step and a chromatic alteration of the same step. It is also called a chromatic semitone . The augmented unison is abbreviated A1 , or aug 1 . Its inversion
3344-532: The break in the circle of fifths that occurs in the tuning system: diatonic semitones derive from a chain of five fifths that does not cross the break, and chromatic semitones come from one that does. The chromatic semitone is usually smaller than the diatonic. In the common quarter-comma meantone , tuned as a cycle of tempered fifths from E ♭ to G ♯ , the chromatic and diatonic semitones are 76.0 and 117.1 cents wide respectively. Extended meantone temperaments with more than 12 notes still retain
3420-409: The constituent intervals of a scale have a large role in the cognitive perception of its sonority, or tonal character. "The number of the notes that make up a scale as well as the quality of the intervals between successive notes of the scale help to give the music of a culture area its peculiar sound quality." "The pitch distances or intervals among the notes of a scale tell us more about the sound of
3496-442: The difference between four perfect octaves and seven just fifths , and functions as a chromatic semitone in a Pythagorean tuning . The Pythagorean limma and Pythagorean apotome are enharmonic equivalents (chromatic semitones) and only a Pythagorean comma apart, in contrast to diatonic and chromatic semitones in meantone temperament and 5-limit just intonation . A minor second in just intonation typically corresponds to
3572-405: The equal-tempered semitone. To cite a few: For more examples, see Pythagorean and Just systems of tuning below. There are many forms of well temperament , but the characteristic they all share is that their semitones are of an uneven size. Every semitone in a well temperament has its own interval (usually close to the equal-tempered version of 100 cents), and there is no clear distinction between
3648-539: The example to the right, Liszt had written an E ♭ against an E ♮ in the bass. Here E ♭ was preferred to a D ♯ to make the tone's function clear as part of an F dominant seventh chord, and the augmented unison is the result of superimposing this harmony upon an E pedal point . In addition to this kind of usage, harmonic augmented unisons are frequently written in modern works involving tone clusters , such as Iannis Xenakis ' Evryali for piano solo. The semitone appeared in
3724-439: The first degree is, obviously, 0 semitones from the tonic (and therefore coincides with it), the second is 2 semitones from the tonic, the third is 4 semitones from the tonic, and so on. Again, this implies that the notes are drawn from a chromatic scale tuned with 12-tone equal temperament. For some fretted string instruments, such as the guitar and the bass guitar , scales can be notated in tabulature , an approach which indicates
3800-407: The former was often implemented by theorist Cowell , while Partch used the latter as part of his 43 tone scale . Under 11 limit tuning, there is a fairly common undecimal neutral second (12:11) ( play ), but it lies on the boundary between the minor and major second (150.6 cents). In just intonation there are infinitely many possibilities for intervals that fall within
3876-438: The fret number and string upon which each scale degree is played. Composers transform musical patterns by moving every note in the pattern by a constant number of scale steps: thus, in the C major scale, the pattern C–D–E might be shifted up, or transposed , a single scale step to become D–E–F. This process is called "scalar transposition" or "shifting to a new key" and can often be found in musical sequences and patterns. (It
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#17328442240033952-449: The higher tone has an oscillation frequency of a fixed ratio (by a factor equal to the twelfth root of two , or approximately 1.059463) higher than the frequency of the lower one. A scale uses a subset consisting typically of 7 of these 12 as scale steps. Many other musical traditions use scales that include other intervals. These scales originate within the derivation of the harmonic series . Musical intervals are complementary values of
4028-454: The irrational [ sic ] remainder between the perfect fourth and the ditone ( 4 3 / ( 9 8 ) 2 = 256 243 ) {\displaystyle \left({\begin{matrix}{\frac {4}{3}}\end{matrix}}/{{\begin{matrix}({\frac {9}{8}})\end{matrix}}^{2}}={\begin{matrix}{\frac {256}{243}}\end{matrix}}\right)} ." In
4104-475: The key of G major (which uses an F ♯ ). Composers also often modulate to other related keys. In some Romantic music era pieces and contemporary music, composers modulate to "remote keys" that are not related to or close to the tonic. An example of a remote modulation would be taking a song that begins in C major and modulating (changing keys) to F ♯ major. Through the introduction of blue notes , jazz and blues employ scale intervals smaller than
4180-407: The larger by the syntonic comma (81:80 or 21.5 cents). The smaller and larger chromatic semitones differ from the respective diatonic semitones by the same 128:125 diesis as the above meantone semitones. Finally, while the inner semitones differ by the diaschisma (2048:2025 or 19.6 cents), the outer differ by the greater diesis (648:625 or 62.6 cents). In 7 limit tuning there
4256-477: The middle eastern type found 53 in an octave) roughly similar to 3 semitones (of the western type found 12 in an octave), while Saba scale , another of these middle eastern scales, has 3 consecutive scale steps within 14 commas, i.e. separated by roughly one western semitone either side of the middle tone. Gamelan music uses a small variety of scales including Pélog and Sléndro , none including equally tempered nor harmonic intervals. Indian classical music uses
4332-438: The minor diatonic semitone is 17:16 or 105.0 cents, and septendecimal limma is 18:17 or 98.95 cents. Though the names diatonic and chromatic are often used for these intervals, their musical function is not the same as the meantone semitones. For instance, 15:14 would usually be written as an augmented unison, functioning as the chromatic counterpart to a diatonic 16:15. These distinctions are highly dependent on
4408-498: The music than does the mere number of tones." Scales may also be described by their symmetry, such as being palindromic , chiral , or having rotational symmetry as in Messiaen's modes of limited transposition . The notes of a scale form intervals with each of the other notes of the chord in combination . A 5-note scale has 10 of these harmonic intervals, a 6-note scale has 15, a 7-note scale has 21, an 8-note scale has 28. Though
4484-405: The music theory of Greek antiquity as part of a diatonic or chromatic tetrachord , and it has always had a place in the diatonic scales of Western music since. The various modal scales of medieval music theory were all based upon this diatonic pattern of tones and semitones. Though it would later become an integral part of the musical cadence , in the early polyphony of the 11th century this
4560-489: The musical context, and just intonation is not particularly well suited to chromatic use (diatonic semitone function is more prevalent). 19-tone equal temperament distinguishes between the chromatic and diatonic semitones; in this tuning, the chromatic semitone is one step of the scale ( play 63.2 cents ), and the diatonic semitone is two ( play 126.3 cents ). 31-tone equal temperament also distinguishes between these two intervals, which become 2 and 3 steps of
4636-486: The notes of a scale, it is customary that each scale degree be assigned its own letter name: for example, the A major scale is written A–B–C ♯ –D–E–F ♯ –G ♯ rather than A–B–D ♭ –D–E–E [REDACTED] –G ♯ . However, it is impossible to do this in scales that contain more than seven notes, at least in the English-language nomenclature system. Scales may also be identified by using
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#17328442240034712-403: The notes of the C major scale using A = 1, B = 2, C = 3, and so on. When we do so, we create a new scale called the A minor scale . See the musical note article for how the notes are customarily named in different countries. The scale degrees of a heptatonic (7-note) scale can also be named using the terms tonic , supertonic , mediant , subdominant , dominant , submediant , subtonic . If
4788-491: The other five are chromatic, and 76.0 cents wide; they differ by the lesser diesis of ratio 128:125 or 41.1 cents. 12-tone scales tuned in just intonation typically define three or four kinds of semitones. For instance, Asymmetric five-limit tuning yields chromatic semitones with ratios 25:24 (70.7 cents) and 135:128 (92.2 cents), and diatonic semitones with ratios 16:15 (111.7 cents) and 27:25 (133.2 cents). For further details, see below . The condition of having semitones
4864-542: The piece its nickname: the "wrong note" étude. This kind of usage of the minor second appears in many other works of the Romantic period, such as Modest Mussorgsky 's Ballet of the Unhatched Chicks . More recently, the music to the movie Jaws exemplifies the minor second. In just intonation a 16:15 minor second arises in the C major scale between B & C and E & F, and is "the sharpest dissonance found in
4940-444: The primary or original scale. See: modulation (music) and Auxiliary diminished scale . In many musical circumstances, a specific note of the scale is chosen as the tonic —the central and most stable note of the scale. In Western tonal music, simple songs or pieces typically start and end on the tonic note. Relative to a choice of a certain tonic, the notes of a scale are often labeled with numbers recording how many scale steps above
5016-467: The range of the semitone (e.g. the Pythagorean semitones mentioned above), but most of them are impractical. In 13 limit tuning, there is a tridecimal 2 / 3 tone (13:12 or 138.57 cents) and tridecimal 1 / 3 tone (27:26 or 65.34 cents). In 17 limit just intonation, the major diatonic semitone is 15:14 or 119.4 cents ( Play ), and
5092-412: The same two semitone sizes, but there is more flexibility for the musician about whether to use an augmented unison or minor second. 31-tone equal temperament is the most flexible of these, which makes an unbroken circle of 31 fifths, allowing the choice of semitone to be made for any pitch. 12-tone equal temperament is a form of meantone tuning in which the diatonic and chromatic semitones are exactly
5168-472: The same, because its circle of fifths has no break. Each semitone is equal to one twelfth of an octave. This is a ratio of 2 (approximately 1.05946), or 100 cents, and is 11.7 cents narrower than the 16:15 ratio (its most common form in just intonation , discussed below ). All diatonic intervals can be expressed as an equivalent number of semitones. For instance a major sixth equals nine semitones. There are many approximations, rational or otherwise, to
5244-483: The scale is not a chord , and might never be heard more than one note at a time, still the absence, presence, and placement of certain key intervals plays a large part in the sound of the scale, the natural movement of melody within the scale, and the selection of chords taken naturally from the scale. A musical scale that contains tritones is called tritonic (though the expression is also used for any scale with just three notes per octave, whether or not it includes
5320-512: The scale, respectively. 53-ET has an even closer match to the two semitones with 3 and 5 steps of its scale while 72-ET uses 4 ( play 66.7 cents ) and 7 ( play 116.7 cents ) steps of its scale. In general, because the smaller semitone can be viewed as the difference between a minor third and a major third, and the larger as the difference between a major third and a perfect fourth, tuning systems that closely match those just intervals (6/5, 5/4, and 4/3) will also distinguish between
5396-491: The second degree ( supertonic ) of the major scale . This music theory article is a stub . You can help Misplaced Pages by expanding it . Semitone A semitone , also called a minor second , 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
5472-405: The subtonic is a semitone away from the tonic, then it is usually called the leading-tone (or leading-note); otherwise the leading-tone refers to the raised subtonic. Also commonly used is the (movable do) solfège naming convention in which each scale degree is denoted by a syllable. In the major scale, the solfège syllables are: do, re, mi, fa, so (or sol), la, ti (or si), do (or ut). In naming
5548-425: The tonic they are. For example, the notes of the C major scale (C, D, E, F, G, A, B) can be labeled {1, 2, 3, 4, 5, 6, 7}, reflecting the choice of C as tonic. The expression scale degree refers to these numerical labels. Such labeling requires the choice of a "first" note; hence scale-degree labels are not intrinsic to the scale itself, but rather to its modes. For example, if we choose A as tonic, then we can label
5624-457: The two types of semitones and closely match their just intervals (25/24 and 16/15). Scale (music) In music theory , a scale is "any consecutive series of notes that form a progression between one note and its octave ", typically by order of pitch or fundamental frequency . The word "scale" originates from the Latin scala , which literally means " ladder ". Therefore, any scale
5700-401: Was not the case. Guido of Arezzo suggested instead in his Micrologus other alternatives: either proceeding by whole tone from a major second to a unison, or an occursus having two notes at a major third move by contrary motion toward a unison, each having moved a whole tone. "As late as the 13th century the half step was experienced as a problematic interval not easily understood, as
5776-401: Was used more frequently as the language of tonality became more chromatic in the Romantic period, the musical function of the semitone did not change. In the 20th century, however, composers such as Arnold Schoenberg , Béla Bartók , and Igor Stravinsky sought alternatives or extensions of tonal harmony, and found other uses for the semitone. Often the semitone was exploited harmonically as
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