D-sharp minor
D-sharp minor is a minor scale and key in music theory based on the note D♯, consisting of the pitches D♯, E♯, F♯, G♯, A♯, B, and C♯ for its natural form.[1] Its key signature features six sharps: F♯, C♯, G♯, D♯, A♯, and E♯.[2] The relative major of D♯ minor is F♯ major, which shares the same key signature, while its parallel major is D♯ major.[3] D♯ minor is enharmonically equivalent to E♭ minor, which uses six flats instead, making the latter more common due to the awkward double sharps (such as E♯) in D♯ minor notation that complicate reading and performance.[4] This key requires five black keys and two white keys per octave on the piano, contributing to its relative rarity in compositions.[5] In classical music, D♯ minor is infrequently used as a principal key, often evoking deep distress or anxiety according to historical characterizations.[6] Notable works include Johann Sebastian Bach's Prelude and Fugue No. 8 in D♯ minor, BWV 877, from The Well-Tempered Clavier, Book II (c. 1742), featuring imitative counterpoint in the prelude and a four-voice fugue with melancholic tension.[6] Another example is Alexander Scriabin's Étude Op. 8, No. 12 in D♯ minor (1894), a virtuosic Romantic piece noted for its feverish passion and technical demands like wide leaps.[6] The key's diatonic chords include D♯ minor, E♯ diminished, F♯ major, G♯ minor, A♯ minor, B augmented, and C♯ major, providing a framework for harmonic progressions in such pieces.[2]Key signature and notation
Notation and key signature
The key signature of D-sharp minor features six sharps: F♯, C♯, G♯, D♯, A♯, and E♯. These accidentals are arranged in the conventional order of sharps, which follows the cycle of fifths.[7][8] This key signature renders D-sharp minor notationally challenging, as the prevalence of sharps—particularly the E♯, which is an augmented unison from E—leads to frequent double-sharps (such as C𝄪 in the harmonic minor variant) and a cluttered appearance on the page, especially in polyphonic writing or for instruments like the piano. As a result, D-sharp minor is infrequently notated directly in compositions, with musicians and composers typically opting for its enharmonic equivalent, E-flat minor, which employs six flats and simplifies readability while producing identical pitches on equal-tempered instruments. The theoretical recognition of D-sharp minor dates to 18th-century music treatises, where it was discussed as part of explorations into remote keys enabled by emerging tuning systems like well temperament. One early example appears in Friedrich Wilhelm Marpurg's Abhandlung von der Fuge (1753–1754), a seminal work on counterpoint that references D-sharp minor in analyses of fugal subjects and modulations, reflecting the era's growing interest in chromatic and sharply keyed structures.Enharmonic relationships
D-sharp minor is enharmonically equivalent to E-flat minor, sharing the same set of pitches but differing in notational spelling, where notes like D♯ correspond to E♭, E♯ to F, F♯ to G♭, G♯ to A♭, A♯ to B♭, B to C♭, and C♯ to D♭.[9][10] This equivalence arises from the twelve-tone equal temperament system, where the pitch classes form an identical collection despite the sharp-based (D♯, E♯, F♯, G♯, A♯, B, C♯ for the natural minor scale) versus flat-based (E♭, F, G♭, A♭, B♭, C♭, D♭) nomenclature.[4][10] In practice, composers typically favor E-flat minor notation over D-sharp minor due to its key signature of six flats (B♭, E♭, A♭, D♭, G♭, C♭), which aligns better with flat-oriented harmonic contexts and reduces the complexity of accidentals, as opposed to D-sharp minor's six sharps (F♯, C♯, G♯, D♯, A♯, E♯) that introduce unusual symbols like E♯ and necessitate double sharps (such as C𝄪) in the harmonic minor variant.[4][10] An illustrative case of enharmonic transposition occurs in Johann Sebastian Bach's The Well-Tempered Clavier, Book I, where the prelude (BWV 853) is composed in E-flat minor, but the accompanying fugue employs D-sharp minor notation to better accommodate the fugal subject's intervallic structure and voice leading.[11][12]Scale construction
Natural minor scale
The natural minor scale in D♯, also known as the Aeolian mode, follows the standard intervallic pattern for minor scales: whole step, half step, whole step, whole step, half step, whole step, whole step (W-H-W-W-H-W-W).[13] This pattern yields the sequence of notes D♯, E♯, F♯, G♯, A♯, B, C♯, D♯ for both ascending and descending forms, spanning one octave from the tonic.[14][8] On the piano keyboard, a typical one-octave rendition starts on D♯3 (the black key just below middle C) and ascends to D♯4, utilizing black keys for D♯, F♯, G♯, A♯, and C♯, while E♯ (enharmonically equivalent to F natural) and B fall on white keys.[8] The relative major of D♯ minor is F♯ major, which shares the same key signature of six sharps (F♯, C♯, G♯, D♯, A♯, E♯).[4]Harmonic and melodic minor variants
The harmonic minor scale in D-sharp minor modifies the natural minor by raising the seventh degree from C♯ to C♯♯, creating a leading tone that strengthens resolution in harmonic progressions. This results in the scale degrees D♯, E♯, F♯, G♯, A♯, B, C♯♯, D♯.[15][16] The primary purpose of this alteration is to form a major triad on the dominant (A♯ major), facilitating the V-i cadence essential for tonal closure in minor keys.[17] This raised seventh introduces an augmented second interval between the sixth degree (B) and the seventh (C♯♯), spanning three semitones, which can produce a distinctive, tense melodic contour in harmonic contexts.[15] The melodic minor scale addresses this intervallic awkwardness for ascending lines by raising both the sixth and seventh degrees relative to the natural minor, yielding D♯, E♯, F♯, G♯, A♯, B♯, C♯♯, D♯.[18] In descent, it reverts to the natural minor scale to maintain smoother stepwise motion. This variant creates a more fluid ascent with consistent whole and half steps akin to the major scale's upper tetrachord, avoiding the augmented second while preserving the leading tone.[19]Harmonic structure
Diatonic triads
In the natural D-sharp minor scale, diatonic triads are constructed by stacking thirds on each scale degree, using only notes from the scale: D♯, E♯, F♯, G♯, A♯, B, and C♯.[20] These triads form the foundational harmony in the key and follow the standard pattern for natural minor keys.[21] The diatonic triads, labeled with Roman numerals, are as follows:| Degree | Roman Numeral | Chord Name | Notes |
|---|---|---|---|
| 1 | i | D♯ minor | D♯–F♯–A♯ |
| 2 | ii° | E♯ diminished | E♯–G♯–B |
| 3 | III | F♯ major | F♯–A♯–C♯ |
| 4 | iv | G♯ minor | G♯–B–D♯ |
| 5 | v | A♯ minor | A♯–C♯–E♯ |
| 6 | VI | B major | B–D♯–F♯ |
| 7 | VII | C♯ major | C♯–E♯–G♯ |
Seventh chords and extensions
In D-sharp minor, seventh chords are formed by stacking an additional third atop the diatonic triads of the natural minor scale, resulting in a set of four-note harmonies that enrich the key's harmonic palette. These chords follow the standard pattern for natural minor keys: minor seventh (i7, iv7, v7), half-diminished seventh (iiø7), major seventh (III7, VI7), and dominant seventh (VII7). The notes are derived directly from the scale degrees (D♯, E♯, F♯, G♯, A♯, B, C♯).[23] The diatonic seventh chords in D-sharp minor are as follows:| Roman Numeral | Chord Name | Notes |
|---|---|---|
| i7 | D♯m7 | D♯–F♯–A♯–C♯ |
| iiø7 | E♯ø7 | E♯–G♯–B–D♯ |
| III7 | F♯maj7 | F♯–A♯–C♯–E♯ |
| iv7 | G♯m7 | G♯–B–D♯–F♯ |
| v7 | A♯m7 | A♯–C♯–E♯–G♯ |
| VI7 | Bmaj7 | B–D♯–F♯–A♯ |
| VII7 | C♯7 | C♯–E♯–G♯–B |