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Augmented second
Augmented second
Augmented second
View on Wikipedia
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Augmented second
Inversediminished seventh
Name
Other names-
AbbreviationA2[1]
Size
Semitones3
Interval class3
Just interval75:64,[2] 81:68, 125:108, 7:6, 19683:16384
Cents
12-Tone equal temperament300
Just intonation275, 253, 267, 318

In Western classical music, an augmented second is an interval created by widening a major second by a chromatic semitone, spanning three semitones and enharmonically equivalent to a minor third in 12-tone equal temperament.[1][3] For instance, the interval from C to D is a major second, two semitones wide, and the interval from C to D♯ is an augmented second, spanning three semitones.

{ \override Score.TimeSignature #'stencil = ##f \relative c' { \time 4/4 \set Score.tempoHideNote = ##t \tempo 1 = 20 <c dis>1 } }

Usage

[edit]

Augmented seconds occur in many scales, including the various modes of the harmonic minor and double harmonic scales. In harmonic minor, the augmented second occurs between the sixth and seventh scale degrees. For example, in the scale of A harmonic minor, the notes F and G♯ form the interval of an augmented second. This distinguishing feature of harmonic minor scales occurs as a consequence of the seventh scale degree having been chromatically raised in order to allow chords in a minor key to follow the same rules of cadence observed in major keys, where the V chord is "dominant" (that is, contains a major triad plus a minor seventh). An augmented second also appears in the diminished seventh chord (in 1st, 2nd, and 3rd inversion) between the diminished seventh and the root, and in the German sixth chord between the ♭scale degree 3 and ♯scale degree 4 degrees.

Tuning

[edit]

An augmented second is enharmonically equivalent to a minor third in 12-tone equal temperament (Playⓘ), but is distinguished in other tunings. In tunings near quarter-comma meantone it approximates the septimal minor third of ratio 7:6 (Playⓘ). In pythagorean tuning and schismatic temperament, however, it closely approximates the classical minor third of ratio 6:5 (Playⓘ). In superpyth temperament, the fifth is sharpened so that the augmented second reaches the classical major third of ratio 5:4 (Playⓘ).

The 75:64 just augmented second (Playⓘ) arises in the justly tuned C harmonic minor scale between A♭ (tuned to 8:5) and B (tuned to 15:8).[4] It is very close to the 7:6 septimal minor third, differing by a septimal kleisma.

References

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Augmented second

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from Grokipedia
In music theory, an is a dissonant interval spanning three s (half steps), which is one semitone larger than a major second of two semitones. It is formed by raising the upper note of a major second by a semitone, such as from C to D♯, and is enharmonically equivalent in pitch to a (e.g., C to E♭) under , though the two are notated and perceived differently due to their interval quality. Unlike the , the augmented second produces a tense, unstable sound that evokes emotional intensity and is rarely used in consonant harmonies but frequently in melodic contexts for dramatic effect. The augmented second plays a key role in the harmonic minor scale, where it occurs between the sixth and seventh scale degrees—for instance, from F to G♯ in A harmonic minor—strengthening the leading tone and facilitating resolution to the tonic. This interval's prominence in the harmonic minor mode, which alters the seventh degree upward from the natural minor, enhances the scale's utility for building dominant chords and creating a sense of pull toward resolution in tonal music. Historically, its harsh dissonance led to melodic avoidance in some Western traditions, contributing to the evolution of the melodic minor scale, which raises both the sixth and seventh degrees in ascent to replace the augmented second with stepwise motion. Beyond classical contexts, it appears in jazz, popular music, and non-Western traditions to add color and tension, underscoring its versatility despite its challenging sonority.

Definition and Properties

Interval Measurement

The augmented second spans three s or half steps. In twelve-tone , this equates to 300 cents. This interval is obtained by augmenting a major second, which spans two semitones or 200 cents, through the addition of one further semitone. The augmented second often exhibits a tense or exotic sound due to its dissonant quality in melodic contexts, despite being enharmonically equivalent to the consonant .

Notation and Enharmonic Equivalents

The augmented second is notated as second with an accidental raising the upper note by one , typically represented using the interval symbol A2 or +2 preceding the numeral 2. For instance, the interval from C to D♯ or from E to F♯ exemplifies this notation, where the sharp accidental on the second degree creates the augmentation. This spans three s, as established in interval measurement contexts. Enharmonically, the augmented second is equivalent to a minor third, producing the same pitch class despite differing spellings; for example, C to D♯ sounds identical to C to E♭ in equal temperament, with the distinction arising from harmonic function and theoretical context rather than auditory perception. This equivalence highlights the flexibility of notation in Western music, where the choice between "augmented second" and "minor third" depends on the surrounding chord or scale structure. The inversion of an is a , which covers nine semitones; augmented intervals invert to their diminished counterparts, maintaining the complementary relationship in the . For compound forms, the augmented ninth extends the simple by an , resulting in a fifteen-semitone interval, though discussions here remain focused on the simple variant.

Construction and Occurrence

In Diatonic and Chromatic Contexts

The originates from the within the , which spans two semitones between adjacent scale degrees, such as from C to D in the scale. This diatonic foundation provides the structural base for the interval, representing a whole tone step inherent to the natural major or minor scales without chromatic alteration. Chromatic augmentation transforms this major second into an augmented second by raising the upper note by a or lowering the lower note by a , resulting in a three- span. For instance, raising D to D♯ in the C-to-D yields C to D♯, while lowering D to D♭ in the D-to-E produces D♭ to E. These alterations introduce non-diatonic pitches, expanding the interval beyond standard scalar steps. In chromatic harmony, the augmented second serves to generate tension, often functioning through leading tones that propel resolution or within altered chords that deviate from diatonic norms. The raised upper note, such as D♯ resolving to E, acts as a sharpened leading tone, heightening dissonance and directing harmonic motion. Although rare in purely diatonic music, where intervals adhere strictly to scale degrees, the augmented second emerges prominently through , enriching harmonic complexity in tonal compositions.

In Specific Scales and Modes

The augmented second prominently features in the , occurring between the sixth and seventh scale degrees due to the raised seventh degree relative to the natural minor. In A harmonic minor, for instance, the notes F to G♯ form this interval, spanning three semitones and creating a distinctive tension that facilitates the leading tone function. This placement arises from chromatic alteration of the natural minor's , enhancing harmonic resolution in minor keys. In the double harmonic scale and its variants, such as the Hungarian minor, the augmented second appears twice, contributing to the scale's exotic and symmetrical character. The , for example, includes augmented seconds between the ♭2 and 3 (e.g., D♭ to E in C double harmonic major: C, D♭, E, F, G, A♭, B) and between the ♭6 and ♮7 (A♭ to B). The Hungarian minor variant (double harmonic minor) positions augmented seconds between the ♭3 and ♯4 (E♭ to F♯) and ♭6 and 7 (A♭ to B) in C: C, D, E♭, F♯, G, A♭, B. These intervals result from stacking two harmonic tetrachords separated by a whole step, amplifying the scale's intense, Middle Eastern-inspired flavor. The augmented second also occurs in several modal contexts derived from or akin to the harmonic . In the Phrygian dominant mode (fifth mode of harmonic ), it lies between the second and third degrees; for E Phrygian dominant (E, F, G♯, A, B, C, D), the jump from F to G♯ exemplifies this, producing a bright yet tense profile often used for dominant functions. Gypsy scales, typically referring to the double harmonic , incorporate the augmented second in positions mirroring the Hungarian , as in G gypsy: G, A♭, B♭, C♯, D, E♭, F♯. Byzantine modes, equivalent to the double harmonic major, feature the interval similarly, with augmented seconds at ♭2–3 and ♭6–7, as in D Byzantine: D, E♭, F♯, G, A, B♭, C♯. Similar intervals appear in non-Western traditions, such as maqams, where the augmented second (or approximations thereof) defines modes like Hijaz, with the interval between the second and third degrees (e.g., D to F in D Hijaz: D, E♭, F, G, A♭, B♭, C). While maqam Bayati emphasizes a neutral second rather than a full augmented second, the broader system parallels Western usages through chromatic tetrachords incorporating three-semitone jumps.

Historical and Theoretical Context

Development in Western Music Theory

The augmented second first emerged as a recognizable interval during the , amid chromatic experiments in 16th-century , where composers like Cipriano de Rore and incorporated altered pitches to heighten emotional expression within modal frameworks. These alterations often arose from the flexible application of in vocal , allowing for brief dissonant leaps that deviated from strict diatonicism, though such intervals were not yet systematically classified. Theorists such as , in his Le Istitutioni harmoniche (1558), addressed chromatic alterations indirectly through discussions of mutation between hexachords, where an augmented second could occur as a consequence of shifting syllables, but it was generally treated with restraint to maintain modal coherence. By the period, the augmented second gained more formal theoretical recognition as an altered dissonant interval, particularly in the harmonically oriented treatises of the early . This codification reflected the era's shift toward tonal , where the interval served to intensify resolutions toward consonances. In the , the augmented second expanded in theoretical and compositional significance amid Romantic 's embrace of , appearing prominently in the to facilitate the leading tone's strong pull toward the tonic. However, its ascending melodic use was deliberately avoided in the , which raised both the sixth and seventh degrees, precisely to circumvent the interval's "forbidden" leap—a holdover from earlier traditions that deemed it disruptively wide and dissonant in vocal lines. Theorists like Simon Sechter and later figures in conservatory debated its dissonant character, often classifying it as a harsh interval requiring preparation and resolution, with rules from Classical (e.g., no parallel augmented seconds or unadorned leaps) persisting to limit its melodic prominence until the modernist era relaxed such constraints for expressive effect. This evolution underscored a tension between the interval's harmonic utility and its melodic awkwardness, shaping its cautious integration into Western tonal practice. The augmented second and minor third are enharmonically equivalent in equal temperament, each encompassing three semitones (approximately 300 cents), yet they remain theoretically and contextually distinct in Western music theory. The augmented second is constructed by raising a major second by a chromatic semitone, emphasizing an alteration from a basic diatonic step and often implying heightened tension in melodic lines. In contrast, the minor third derives from lowering a major third, positioning it as a stable, consonant component in triadic harmony. This distinction influences voice leading: the augmented second, such as from C to D♯, tends to resolve with more urgency due to its augmented character, while the minor third, like C to E♭, integrates more smoothly into chordal progressions. Compared to the , the augmented second introduces additional dissonance through its chromatic sharpening, transforming the whole tone—fundamental to diatonic scales and perceived as stable and agreeable—into an interval of color and instability. The (two s, or 200 cents) facilitates smooth stepwise motion, whereas the augmented second's extra semitone creates a harsher, more restless quality, often used intentionally to heighten expressive tension before resolving to consonance. This perceptual shift underscores the augmented second's role in evoking unease rather than the 's neutral progression. In historical tunings like Pythagorean intonation, the and align closely at about 294 cents (32/27 ratio), but the —a discrepancy of roughly 23.46 cents arising from twelve pure fifths exceeding seven octaves—can lead to subtle pitch variations in recognition and execution across scalar contexts. This affects how these intervals are perceived in chains of fifths, potentially causing the augmented second to sound slightly wider or narrower relative to the minor third depending on the tuning chain. A practical for naming prioritizes the interval based on the simplest letter-name span: adjacent letters (e.g., C to D♯ as a second) take precedence over skipping one (C to E♭ as a third), ensuring contextual clarity in notation and .

Usage in Musical Practice

In Classical and Romantic Eras

In the Classical , the augmented second was employed sparingly by composers such as and Haydn, primarily to enhance chromatic passages and facilitate modulations. These instances reflect the era's restrained approach to , where the augmented second served to heighten expressivity without disrupting diatonic norms. During the Romantic period, the augmented second gained prominence, particularly in works by Chopin and Liszt, where it evoked an exotic flavor drawn from folk influences. Liszt incorporated the augmented second extensively in his to mimic Gypsy scales and national motifs. This usage marked a shift toward greater chromatic freedom, allowing the interval to symbolize cultural otherness in . Harmonically, the augmented second often functioned within dominant chords or Neapolitan progressions, providing tension leading to resolution. In dominant contexts, it appeared as part of altered harmonies, such as the raised fourth scale degree enharmonically spelling an augmented second against the root, as seen in transitional passages in Beethoven's late quartets, which influenced Romantic practices. In Neapolitan sixth chords, the interval between the chord's and augmented sixth created a characteristic dissonance, resolving to the dominant in works like Chopin's Op. 7, No. 1, where it supports the subdominant's expressive pull. Melodically, the augmented second was largely avoided in strict due to its awkward leap, which disrupted smooth ; ascending uses were particularly rare until Wagner's chromatic innovations. In species treatises influencing Classical composers, the interval was prohibited in outer voices to prevent parallel motion issues, as its three-semitone span clashed with the era's emphasis on stepwise motion. Wagner, however, embraced ascending augmented seconds in operas like , where they propel leitmotifs forward, as in the prelude's chromatic ascent from G-sharp to B, enharmonically an augmented second that heightens the work's psychological intensity. This evolution underscored the Romantic departure from Classical restraint.

In Folk, Ethnic, and Modern Genres

In Eastern European folk traditions, particularly Romani (often referred to as "gypsy") , the augmented second plays a central role in characteristic scales and melodies, contributing to the genre's distinctive emotive intensity. The "," typically structured as a harmonic minor with a raised fourth (e.g., C-D-E♭-F♯-G-A♭-B-C), features an augmented second between the third and fourth degrees (e.g., E♭ to F♯), creating a tense, wandering quality that evokes longing and passion. This interval is prominent in dances and tunes from Hungarian and Romanian Romani repertoires, where it underscores improvisational and lines. Similarly, in Jewish from the same , the "freygish" mode—equivalent to the Phrygian dominant—relies on the augmented second to convey a mix of sorrow and exuberance, as heard in tunes and horas collected in early 20th-century ethnomusicological recordings. Middle Eastern ethnic music, especially in and Turkish maqam systems, frequently employs the augmented second as a defining structural element, imparting a sense of yearning or exotic allure to modal improvisations. In the Hijaz maqam, for instance, the interval appears between the second and third scale degrees (e.g., D-E♭-F♯ in D Hijaz), forming a that is foundational to vocal and instrumental taqsims in classical traditions. This usage extends to Ottoman and Persian repertoires, where the augmented second facilitates modulations and heightens emotional peaks in pieces for or . In , a Spanish genre with deep Moorish and Romani roots, the (e.g., E-F-G♯-A-B-C-D-E) integrates the augmented second between the second and third degrees, driving the passionate strumming and singing that define palos like soleá and . In jazz and blues, the augmented second appears more sporadically, often as part of altered tensions rather than a scalar staple, adding dissonance to dominant harmonies or evoking raw emotional bends. Jazz improvisers over altered dominant chords (e.g., G7alt) may emphasize the #9 (an augmented second from the root, like A to B in G), drawing from the to create outside tension resolving to the tonic, as in bebop heads by . In blues, the interval manifests in "blue notes," where the flattened third (enharmonically an augmented second spanning three semitones from the root) clashes against major triads, producing the genre's signature wail, particularly in vocal slides or guitar bends in traditions. Modern and popular genres incorporate the augmented second through world music fusions and cinematic evocations, often to convey cultural "otherness" or suspense. , influenced by Eastern European folk collecting, wove the interval into his compositions, blending ethnic authenticity with modernist edge. In film scores, augmented seconds appear in exoticized cues using Phrygian dominant inflections to suggest amid orchestral swells. This extends to video game soundtracks with influences, like those in series, where the interval heightens tension in modal themes for and percussion ensembles. In as of 2025, the augmented second continues in fusions like electronic and hip-hop samples drawing from modal traditions. Culturally, the augmented second often symbolizes the "exotic" or fraught in global contexts, serving as an Orientalist motif that bridges Western perceptions of Eastern tension with authentic modal practices.

Tuning and Performance Considerations

In Equal Temperament

In twelve-tone (12-TET), the augmented second spans exactly three semitones, measuring 300 cents, which renders it enharmonically identical to the and eliminates any beat frequency discrepancies between the two notations. This equivalence arises because 12-TET divides the into twelve equal parts of 100 cents each, ensuring uniform interval sizes regardless of key. On keyboard instruments like , the augmented second is realized straightforwardly by skipping one white key to reach a black key, such as from C to D♯, leveraging the fixed layout of half steps. This direct mapping facilitates quick performance without adjustments, aligning with the system's design for consistent pitch relationships across the instrument. A key advantage of performing the augmented second in 12-TET is its simplification of transposition and modulation in orchestral and ensemble settings, as the interval remains identical in every key without requiring retuning. This uniformity supports complex harmonic progressions and key changes, enabling composers to explore distant tonalities seamlessly. However, 12-TET's equal division introduces limitations by forgoing the variable intonations of historical tunings, which diminishes the interval's potential for expressive tension through subtle pitch adjustments. As a result, the augmented second in this lacks the nuanced and emotional depth achievable in systems that prioritize consonant ratios for specific contexts.

In Just Intonation and Microtonal Systems

In , the augmented second is commonly realized as the 5-limit ratio 75/64, measuring approximately 275 cents. This interval differs from the of 6/5 (approximately 316 cents), resulting in distinct pitches for enharmonic notes (e.g., D♯ vs. E♭) and potential beats in chords involving both, emphasizing its tense quality. During the , meantone tunings—prevalent from the late 15th to early 18th centuries—rendered the augmented second as a approximating the just ratio 6/5 (about 316 cents), providing a more alternative to the narrower Pythagorean of 32/27 (294 cents) and facilitating chromatic expressivity in polyphonic music. In these systems, such as quarter-comma meantone, the interval is approximately 310 cents, enhancing harmonic purity for thirds while narrowing fifths elsewhere. In microtonal systems like or traditions, the augmented second is approximated variably, often around 350 cents in maqams such as Hijaz, where it forms a characteristic large step between the second and third degrees, blending neutral seconds (about 150 cents each) for an exotic, undulating quality distinct from Western . This approximation supports modal improvisation in 24 divisions per , diverging from just ratios to emphasize cultural idiomatic intonation. Performers in ethnic traditions, such as those employing approximations in Middle Eastern or Indian music, adjust the augmented second dynamically: singers tune by ear to minimize beating against accompanying drones or harmonies, while string players subtly bend notes to achieve consonance, reflecting adaptive practices rooted in historical vocal and extended techniques. The interval's notation as augmented second versus influences perceptual quality, with performers using to convey tension or resolution.

References

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  40. http://www.jameslouder.com/id20.html
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