📚 A-Level Eduqas Music: Quick Reference Formulas and Theorems | A-Level Eduqas 音乐：公式定理速查手册
This quick reference handbook distils essential musical formulas, rules and structural theorems that underpin the A-Level Eduqas Music specification. From interval calculation and chord construction to modulatory patterns and formal analysis, each entry is presented as a concise, formula-like statement followed by its practical application. Use these pages for rapid revision, dictation preparation, and score annotation tasks.
本速查手册提炼了 A-Level Eduqas 音乐课程中的核心音乐公式、规则与结构定理。从音程计算、和弦建构到转调模式与曲式分析，每一条目均以简明公式形式呈现，并附实际应用说明。可用于快速复习、听写准备及乐谱批注练习。
1. Interval Semitone Count and Inversion Rule | 音程半音数与转位法则
An interval is defined by its number (unison, second, third, etc.) and its quality (perfect, major, minor, augmented, diminished). The number of semitones for the basic qualities in a diatonic context can be memorised as fixed quantities. For perfect intervals: P1 = 0 semitones, P4 = 5 semitones, P5 = 7 semitones, P8 = 12 semitones. For major intervals: M2 = 2, M3 = 4, M6 = 9, M7 = 11. A minor interval is always one semitone smaller than its major counterpart; an augmented interval is one semitone larger than perfect or major; a diminished interval is one semitone smaller than perfect or minor.
音程由其度数（同度、二度、三度等）和性质（纯、大、小、增、减）定义。在自然调式语境中，基础性质对应的半音数可固记。纯音程：纯一度 = 0 半音，纯四度 = 5，纯五度 = 7，纯八度 = 12。大音程：大二度 = 2，大三度 = 4，大六度 = 9，大七度 = 11。小音程比同度数大音程少一半音；增音程比纯或大音程多一半音；减音程比纯或小音程少一半音。
Interval inversion theorem: the sum of the interval numbers of an interval and its inversion always equals 9, and the quality transforms: major ↔ minor, perfect ↔ perfect, augmented ↔ diminished.
音程转位定理：原音程与转位音程的度数之和恒为 9，性质互换：大↔小，纯↔纯，增↔减。
| Original | Inversion |
|---|---|
| M3 (4 semitones) | m6 (8 semitones) |
| P5 (7 semitones) | P4 (5 semitones) |
| aug4 (6 semitones) | dim5 (6 semitones) |
2. Key Signature Formula and the Circle of Fifths | 调号公式与五度圈
The order of sharps in key signatures follows the sequence F–C–G–D–A–E–B, which can be remembered as ‘Father Charles Goes Down And Ends Battle’. The order of flats is the reverse: B–E–A–D–G–C–F (‘Battle Ends And Down Goes Charles’ Father’). In major keys, the last sharp in the signature is the leading note (semitone below the tonic); the second-to-last flat is the tonic.
升号调的顺序为 F–C–G–D–A–E–B，可记为 ‘Father Charles Goes Down And Ends Battle’。降号调顺序为其逆行：B–E–A–D–G–C–F。大调中，最后一个升号是导音（主音下方半音）；倒数第二个降号即为主音。
Relative minor theorem: the tonic of the relative minor is always a minor third (three semitones) below the tonic of its relative major. Thus, G major (one sharp) relates to E minor; F major (one flat) relates to D minor.
关系大小调定理：关系小调的主音总是比关系大调主音低小三度（三个半音）。故 G 大调（1 个升号）关系小调为 e 小调；F 大调（1 个降号）关系小调为 d 小调。
- C major – no sharps/flats – relative A minor
- G major – 1 sharp (F♯) – relative E minor
- D major – 2 sharps (F♯, C♯) – relative B minor
- A major – 3 sharps (F♯, C♯, G♯) – relative F♯ minor
- F major – 1 flat (B♭) – relative D minor
- B♭ major – 2 flats (B♭, E♭) – relative G minor
升号大调：G (1升) → D (2升) → A (3升) → E (4升) → B (5升) → F♯ (6升) → C♯ (7升)。降号大调：F (1降) → B♭ (2降) → E♭ (3降) → A♭ (4降) → D♭ (5降) → G♭ (6降) → C♭ (7降)。每个大调均可直接对照其关系小调。
3. Chord Construction and Roman Numeral Analysis | 和弦构建与数字低音分析
A triad is built by stacking two thirds above a root. The formula for a major triad (I, IV, V in a major key) is: root + major third (4 semitones) + perfect fifth (7 semitones). Minor triad (ii, iii, vi in major) is: root + minor third (3 semitones) + perfect fifth (7 semitones). Diminished triad (vii°) is: root + minor third (3 semitones) + diminished fifth (6 semitones). Augmented triad (III+ in minor only in common-practice) is: root + major third (4 semitones) + augmented fifth (8 semitones).
三和弦由根音上方叠加两个三度构成。大调中的正三和弦（I, IV, V）公式：根音 + 大三度（4 半音）+ 纯五度（7 半音）。小三和弦（ii, iii, vi）公式：根音 + 小三度（3 半音）+ 纯五度（7 半音）。减三和弦（vii°）公式：根音 + 小三度 + 减五度（6 半音）。增三和弦（常见于和声小调 III+）公式：根音 + 大三度 + 增五度（8 半音）。
Seventh chords add a further third. Diatonic seventh chords in a major key follow this pattern: Imaj7, ii7, iii7, IVmaj7, V7 (dominant seventh), vi7, viiø7 (half-diminished). Formula for dominant seventh: major triad + minor seventh (10 semitones above root). For diminished seventh (vii°7 in harmonic minor): diminished triad + diminished seventh (9 semitones above root).
七和弦再叠加一个三度。大调音阶上的七和弦模式为：Imaj7, ii7, iii7, IVmaj7, V7（属七）, vi7, viiø7（半减七）。属七和弦公式：大三和弦 + 小七度（根音上方 10 半音）。减七和弦（和声小调 vii°7）公式：减三和弦 + 减七度（根音上方 9 半音）。
Roman numeral analysis in a major key assigns uppercase for major and augmented chords, lowercase for minor and diminished. In C major: I = C, ii = Dm, iii = Em, IV = F, V = G, vi = Am, vii° = Bdim.
大调数字低音标记：大写表示大三与增三和弦，小写表示小三与减三和弦。以 C 大调为例：I = C, ii = dm, iii = em, IV = F, V = G, vi = am, vii° = bdim。
4. Cadence Identification and Common Chord Progression Patterns | 终止式辨别与常见和弦进行模式
The four core cadences are defined by the chords that conclude a phrase. Perfect cadence: V → I (authentic). Plagal cadence: IV → I. Imperfect cadence: any chord → V (often I, ii, or IV → V). Interrupted/deceptive cadence: V → vi (or V → VI in minor).
四种基础终止式由结束乐句的和弦决定。正格终止：V → I。变格终止：IV → I。不完全终止：任何和弦至 V（常为 I, ii 或 IV → V）。阻碍终止：V → vi（小调中 V → VI）。
Common functional chord progressions in Western tonality follow the cycle of descending fifths: iii → vi → ii → V → I. The cadential 6/4 (I⁶₄) is a second-inversion tonic used as an embellishment of the dominant: Ic – V – I. The progression I – IV – V – I forms the basis of tonal closure, while the blues progression I – IV – I – V – IV – I (12-bar blues) is essential for 20th-century popular styles.
西方调性音乐常见功能性进行遵循下行五度循环：iii → vi → ii → V → I。终止四六和弦 (I⁶₄) 是主和弦第二转位，作为属和弦的装饰：Ic – V – I。I – IV – V – I 是调性收束的基础，而布鲁斯进行 I – IV – I – V – IV – I（12 小节布鲁斯）对 20 世纪流行风格至关重要。
5. Modes and Scale Construction Formulae | 调式与音阶构建公式
Each mode can be derived by rotating the major scale pattern of tones (T) and semitones (S): T–T–S–T–T–T–S. The seven modes (Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, Locrian) are obtained by starting on successive degrees. Their interval structures can be expressed as alterations of the major or natural minor scale.
每种调式可通过轮转大调音阶全全半全全全半的模式得出。七种调式（伊奥尼亚、多利亚、弗里吉亚、利底亚、混合利底亚、爱奥利亚、洛克里亚）由依次以不同音级起始获得。其音程结构可表述为对自然大调或自然小调的变动。
| Mode | Formula relative to major | Semitone pattern from tonic |
|---|---|---|
| Ionian (major) | 1 2 3 4 5 6 7 | T-T-S-T-T-T-S |
| Dorian | 1 2 b3 4 5 6 b7 | T-S-T-T-T-S-T |
| Phrygian | 1 b2 b3 4 5 b6 b7 | S-T-T-T-S-T-T |
| Lydian | 1 2 3 #4 5 6 7 | T-T-T-S-T-T-S |
| Mixolydian | 1 2 3 4 5 6 b7 | T-T-S-T-T-S-T |
| Aeolian (natural minor) | 1 2 b3 4 5 b6 b7 | T-S-T-T-S-T-T |
| Locrian | 1 b2 b3 4 b5 b6 b7 | S-T-T-S-T-T-T |
Harmonic minor scale: 1 2 b3 4 5 b6 7 (augmented second between b6 and 7). Melodic minor (ascending): 1 2 b3 4 5 6 7 (descending reverts to natural minor). Pentatonic major: 1 2 3 5 6; pentatonic minor: 1 b3 4 5 b7.
和声小调：1 2 b3 4 5 b6 7（b6 与 7 之间为增二度）。旋律小调（上行）：1 2 b3 4 5 6 7（下行回到自然小调）。五声大调：1 2 3 5 6；五声小调：1 b3 4 5 b7。
6. Rhythmic Division Rules and Time Signature Theory | 节奏划分规则与拍号理论
Time signatures are classified as simple or compound based on the subdivision of the beat. In simple time (e.g., 2/4, 3/4, 4/4), each beat divides into two equal parts. In compound time (e.g., 6/8, 9/8, 12/8), each beat divides into three equal parts; the lower number represents the note value of the division (eighth note). To find the number of beats per bar in compound time, divide the upper number by 3. Thus, 6/8 = 2 dotted-crotchet beats; 9/8 = 3 beats; 12/8 = 4 beats.
拍号根据拍子的细分方式分为单拍子与复拍子。单拍子（如 2/4, 3/4, 4/4）每拍均分为两部分。复拍子（如 6/8, 9/8, 12/8）每拍均分为三部分；下方数字代表细分音符的时值（八分音符）。复拍子每小节拍数 = 上方数字 ÷ 3。故 6/8 = 两个附点四分音符拍；9/8 = 三拍；12/8 = 四拍。
Dotted rhythms and double-dotted formulas: a dot adds half the preceding note’s value; a second dot adds half the first dot’s value. Triplets fit three notes into the time of two; duplets fit two notes into the time of three (in compound time). Syncopation is created by shifting accents to weak beats or between beats; hemiola is a specific ratio effect where two groups of three beats are juxtaposed with three groups of two beats (e.g., 3/2 against 6/4).
附点节奏公式：附点增加前一音符时值的一半；双附点再加第一个附点时值的一半。三连音在两者时值内演奏三个音；二连音（复拍子中）在三者时值内演奏两个音。切分音通过将重音转移至弱拍或拍点之间产生；交错节奏（赫米奥拉）特指两组三拍与三组两拍的并置效果（如 3/2 对 6/4）。
7. Texture and Sonority Shorthand | 织体与音响速记
Textures can be categorised using a few recurring models. Monophonic: a single unaccompanied melodic line. Homophonic: melody plus chordal accompaniment, with all parts moving in similar rhythm (melody-dominated homophony) or in block chords. Polyphonic/contrapuntal: two or more independent melodic lines woven together; imitative polyphony uses entries of the same melodic material at different times, non-imitative uses contrasting material. Heterophony: simultaneous variation of a single melody, common in folk and non-Western traditions.
织体可用几类常见模式归类。单声部：单一无伴奏旋律线。主调织体：旋律加和弦伴奏，所有声部节奏相似（旋律主导的主调织体）或块状和弦。复调/对位织体：两条或以上独立旋律线交织；模仿复调在不同时间进入相同旋律素材，非模仿复调使用对比素材。支声复调：同一条旋律在不同声部同时变奏，常见于民间音乐和非西方传统。
Key sonority terms for the Eduqas specification: arco/pizzicato, con sordino/senza sordino, divisi, flutter-tonguing, tremolo, sul ponticello/sul tasto. Vocal techniques include falsetto, vibrato, portamento, and Sprechstimme. Instrumental ranges and transpositions must be memorised: Bb clarinet sounds a tone lower than written; French horn in F sounds a perfect fifth lower; trumpet in Bb sounds a major second lower; double bass sounds an octave lower than written.
Eduqas 考试涉及的音响术语：拉奏/拨奏、加弱音器/去弱音器、分奏、花舌、震音、近码奏/近指板奏。声乐技巧包括假声、颤音、滑音、说唱。乐器音域及移调须牢记：降 B 调单簧管实音比记谱低大二度；F 调圆号低纯五度；降 B 调小号低大二度；低音提琴低八度。
8. Melodic Formulas and Ornamentation Rules | 旋律公式与装饰音规则
Common ornaments in Baroque and Classical traditions have specific rhythmic executions. A trill starts on the upper auxiliary note and alternates rapidly with the principal note; in later styles it may begin on the principal note. A mordent (upper or lower) is a single rapid alternation. A turn is a four-note figure: upper note – principal – lower note – principal. An appoggiatura takes half the value of the main note and is on the beat; an acciaccatura is a crushed grace note before the beat.
巴洛克与古典时期常见装饰音有其特定节奏执行方式。颤音从上助音开始，与主要音快速交替；后期风格可从主要音开始。波音（上波音或下波音）为单次快速交替。回音为四音音型：上助音–主要音–下助音–主要音。长倚音占主干音一半时值，位于拍点上；短倚音为拍前的挤入式装饰音。
Melodic sequence is a repetition of a pattern at a higher or lower pitch. Real sequence transposes the exact intervals; tonal sequence adjusts intervals to stay within the key. Conjunct motion moves by step; disjunct motion moves by leap. Periodic phrase structure (4+4 bar antecedent-consequent) typifies Classical melody. Sequences are often labelled by their intervallic step: a descending fifth sequence, ascending third sequence, etc.
旋律模进是将某一音型以更高或更低音高重复。严格模进精确移调所有音程；调性模进调整音程以保持在该调内。级进为音阶式进行；跳进为跳越进行。周期性乐句结构（4+4 小节的呼-应）是古典主义旋律的典型。模进常依据音程步距命名：下行五度模进、上行三度模进等。
9. Structural Formulae: Sonata, Fugue, Binary, Ternary | 曲式公式：奏鸣曲式、赋格、二部曲式、三部曲式
In Eduqas set works and analysis, familiarity with standard formal outlines is essential. Sonata form comprises three main sections: Exposition (two contrasting themes in tonic and a related key, often dominant or relative major), Development (thematic fragmentation, modulation), and Recapitulation (both themes now in the tonic). An optional Coda may follow. A bridge/transition modulates between first and second subjects.
在 Eduqas 指定曲目与分析中，掌握标准曲式框架至关重要。奏鸣曲式包含三大部分：呈示部（两个对比主题，分别在主调和关系调如属调或关系大调）、展开部（主题碎片化、转调）和再现部（两个主题均回到主调）。可选尾声附后。连接部/过渡段在第一与第二主题之间转调。
Fugue is a contrapuntal procedure rather than a fixed form. Its basic formula is: Exposition (subject, answer, countersubject entries in all voices), Episodes (modulatory passages using fragments of subject/countersubject), and further entries in related keys, culminating in a tonic entry, often with stretto (overlapping entries). A subject’s answer is usually real (exact transposition) or tonal (adjusted to preserve key).
赋格是一种对位程序而非固定曲式。基本公式：呈示部（主题、答题、对题在所有声部依次进入）→ 插句（运用主题/对题片段的转调段落）→ 关系调上的再次进入，最终回到主调进入，常伴随密接和应（声部重叠进入）。答题通常为完全答题（精确移调）或调性答题（调整以保持调性）。
Binary form (AB) consists of two related sections, each usually repeated. Balanced binary: A ends in V (major) or III (minor); B begins in that key and returns to I. Rounded binary: B ends with a return of A material. Ternary form (ABA) has a contrasting middle section and a return of A (often abbreviated or ornamented).
二部曲式（AB）由两个相互关联的部分组成，各部分通常反复。均衡二部曲式：A 段结束于属调（大调）或关系大调（小调）；B 段从该调开始并回到 I。圆滑二部曲式：B 段末尾再现 A 段素材。三部曲式（ABA）包含对比性中段与 A 段的再现（常为缩减或装饰化）。
10. Dynamics, Articulation and Expressive Markings | 力度、运音法与表情记号
Dynamic markings often appear as abbreviations that follow a standard expanding or diminishing scale: pp (pianissimo, very soft), p (piano, soft), mp (mezzo-piano, moderately soft), mf (mezzo-forte, moderately loud), f (forte, loud), ff (fortissimo, very loud). Gradual changes: cresc. (crescendo, getting louder), dim. or decresc. (diminuendo, getting softer). Sforzando (sfz, sf, fz) indicates a sudden strong accent on a single note or chord.
力度标记常以缩写形式出现，遵循标准渐变序列：pp（极弱）、p（弱）、mp（中弱）、mf（中强）、f（强）、ff（极强）。渐强：cresc.；渐弱：dim. 或 decresc.。特强（sfz, sf, fz）表示对单一音符或和弦的突然性重音。
Articulation symbols alter the attack and length of notes. Staccato (dot) shortens the note, usually by half its written length. Staccatissimo (wedge) is even shorter. Tenuto (line) indicates full value and slight pressure. Accent (>) stresses the beginning of the note. Marcato (^) is a strong, separated attack. Slurs indicate legato, smooth connection.
运音法符号改变音符的触键与长度。断奏（圆点）缩短音符时值，通常至记谱长度的一半。短断奏（楔形）更短。保持音（横线）表示奏满时值并略带压力。重音（>）强调音符开始处。强调（^）为强烈、分离的触键。连线表示连奏，平滑连接。
11. Chromatic Harmony and Modulation Devices | 半音和声与转调手法
Pivot chord modulation uses a chord common to two keys to pivot smoothly between them. Typically, a diatonic chord in the old key takes on a new function in the new key (e.g., the IV of C major becomes the bVI of E minor). Direct/phrase modulation shifts abruptly without pivot. Enharmonic modulation exploits a single pitch written differently to change key, often using the German augmented sixth or diminished seventh chord.
共同和弦转调使用两调共有的和弦作为枢纽平稳过渡。通常原调中的自然音和弦在新调中获得新功能（如 C 大调的 IV 成为 e 小调的 bVI）。直接/乐句转调无共同和弦突然转换。等音转调利用同一音高记谱不同来转调，常运用德国增六和弦或减七和弦。
Augmented sixth chords (Italian⁶₃, French⁴₃, German⁶₅) are pre-dominant chords that resolve to V. Neapolitan sixth (bII⁶) is a major chord built on the flattened supertonic, usually in first inversion, functioning as a chromatic predominant. These chords follow specific voice-leading formulas: the augmented sixth interval expands to an octave on the dominant; the bII moves down by step to the leading note.
增六和弦（意大利增六⁶₃、法兰西增六⁴₃、德意志增六⁶₅）是解决到属和弦的下属功能变和弦。拿波里六和弦（bII⁶）是建立在降上主音上的大三和弦，通常为第一转位，作为半音化下属性功能。这些和弦遵循特定声部进行公式：增六度音程扩张至属音上的八度；bII 级音级进下行至导音。
Extended chromaticism includes secondary dominants (V/V, V/ii, etc.), borrowed chords from the parallel minor or major, and tritone substitution in jazz and popular music. The formula for a secondary dominant: treat the target chord as a temporary tonic and build its dominant. V/ii in C major is A major (A–C♯–E), leading to D minor.
扩展半音化包括副属和弦（V/V, V/ii 等），从平行小调或大调借用的和弦，以及爵士与流行音乐中的三全音替代。副属和弦公式：将目标和弦视为临时主音，构建其属和弦。C 大调的 V/ii 为 A 大三和弦（A–C♯–E），导向 d 小调。
12. Score Reading, Abbreviations and Analytical Shorthand | 总谱读法、缩略语与分析速记
When annotating scores, a standard set of abbreviations accelerates analysis. ‘M’ = melody, ‘H’ = homophonic texture, ‘P’ = polyphonic, ‘SQ’ = sequence, ‘IM’ = imitation, ‘PED’ = pedal point, ‘CAD’ = cadence, ‘DOM’ = dominant preparation, ‘MOD’ = modulation. Phrases may be bracketed and labelled as antecedent (A) and consequent (C). Letter names are used for keys, with uppercase for major, lowercase for minor (G maj, e min).
乐谱批注时一套标准缩略语可加速分析。“M” = 旋律，“H” = 主调织体，“P” = 复调，“SQ” = 模进，“IM” = 模仿，“PED” = 持续音，“CAD” = 中止式，“DOM” = 属准备，“MOD” = 转调。乐句可用连线划分并标为呼 (A) 与应 (C)。调性用字母标记，大写表大调，小写表小调（G 大，e 小）。
Transposing instruments are read by applying the transposition formula: for Bb instruments, read up a major second to obtain sounding pitch; for F instruments, read up a perfect fifth. When writing for transposing instruments, the part must be written higher than sounding pitch by the same interval. Orchestral score order: woodwind, brass, percussion, strings. String quartet score: Violin I, Violin II, Viola, Cello.
移调乐器读谱需应用移调公式：降 B 调乐器将记谱上移大二度得到实际音高；F 调乐器上移纯五度。为移调乐器创作时，分谱需比实际音高记高相应音程。管弦乐总谱排列：木管、铜管、打击乐、弦乐。弦乐四重奏：小提琴 I、小提琴 II、中提琴、大提琴。
A structural overview of the piece can be summarised using a timeline chart: mark bar numbers, themes, keys, and textural changes. Roman numerals for harmony should be placed below the bass staff. Cadences are marked with brackets and the cadence type. Such systematic annotation prepares you for the written commentary and aural analysis in the Eduqas examination.
作品的结构概览可使用时间线图表概括：标注小节数、主题、调性与织体变化。和声数字低音记于低音谱表下方。终止式用括号注明类型。这种系统化批注帮助你应对 Eduqas 考试中的书面评论与听觉分析题。
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