Pre-U Edexcel Music: Formula & Theorem Quick Reference | Edexcel 大学预科音乐：公式定理速查手册

📚 Pre-U Edexcel Music: Formula & Theorem Quick Reference | Edexcel 大学预科音乐：公式定理速查手册

This quick-reference handbook collates the essential formulas, rules, and theoretical axioms required for the Edexcel Pre-U Music examination. From interval calculation to serialism, each entry is presented as a concise formula in English followed by its Chinese counterpart, enabling efficient revision and bilingual comprehension.

本速查手册汇总了 Edexcel 大学预科音乐考试所必需的核心公式、规则与理论公理。从音程计算到序列主义，每个条目以英文与中文配对呈现，便于高效复习和双语理解。

---

1. Interval Formulas | 音程公式

An interval is measured by counting letter names inclusively for its number, and counting semitones for its quality. The basic semitone counts for simple intervals within an octave are fixed formulas.

音程的度数通过包含首尾音名在内计数得出，其性质由所含半音数量决定。八度以内基本音程的半音数是固定的公式。

Minor 2nd: 1 semitone. Major 2nd: 2 semitones. Minor 3rd: 3 semitones. Major 3rd: 4 semitones. Perfect 4th: 5 semitones. Tritone (augmented 4th / diminished 5th): 6 semitones. Perfect 5th: 7 semitones. Minor 6th: 8 semitones. Major 6th: 9 semitones. Minor 7th: 10 semitones. Major 7th: 11 semitones. Octave: 12 semitones.

小二度：1 个半音。大二度：2 个半音。小三度：3 个半音。大三度：4 个半音。纯四度：5 个半音。三全音（增四度 / 减五度）：6 个半音。纯五度：7 个半音。小六度：8 个半音。大六度：9 个半音。小七度：10 个半音。大七度：11 个半音。纯八度：12 个半音。

Compound intervals are found by adding 7 to the simple interval number (e.g. major 9th = octave + major 2nd). Semitone count: add 12.

复音程的度数等于单音程度数加 7（如大九度 = 八度 + 大二度）。半音数增加 12。

Inversions follow the formula: inversion semitone sum = 12. Minor becomes Major, Perfect stays Perfect, Diminished becomes Augmented, and vice versa.

音程转位遵循公式：转位半音数总和 = 12。小变大，大变小；纯不变；减变增，增变减。

---

2. Scale Formulas | 音阶公式

Scales are constructed using fixed sequences of tones (T) and semitones (S). The major scale formula is the foundation: T-T-S-T-T-T-S.

音阶通过全音（T）与半音（S）的固定序列构建。大调音阶公式是基础：全-全-半-全-全-全-半。

Natural minor scale formula: T-S-T-T-S-T-T. Harmonic minor: T-S-T-T-S-3S-S (augmented 2nd between 6th and 7th). Melodic minor ascending: T-S-T-T-T-T-S; descending: natural minor.

自然小调音阶公式：全-半-全-全-半-全-全。和声小调：全-半-全-全-半-增二度-半（第六级与第七级间为增二度）。旋律小调上行：全-半-全-全-全-全-半；下行同自然小调。

Modes are rotations of the major scale. Ionian: T-T-S-T-T-T-S (major). Dorian: T-S-T-T-T-S-T. Phrygian: S-T-T-T-S-T-T. Lydian: T-T-T-S-T-T-S. Mixolydian: T-T-S-T-T-S-T. Aeolian: T-S-T-T-S-T-T (natural minor). Locrian: S-T-T-S-T-T-T.

调式是大调音阶的轮转。伊奥尼亚：全-全-半-全-全-全-半（大调）。多利亚：全-半-全-全-全-半-全。弗里几亚：半-全-全-全-半-全-全。利底亚：全-全-全-半-全-全-半。混合利底亚：全-全-半-全-全-半-全。爱奥利亚：全-半-全-全-半-全-全（自然小调）。洛克里亚：半-全-全-半-全-全-全。

Pentatonic major formula: degrees 1, 2, 3, 5, 6 of the major scale (omit 4 and 7). Pentatonic minor: 1, b3, 4, 5, b7. Whole-tone scale: T-T-T-T-T-T. Chromatic scale: all semitones.

五声大调公式：取大调音阶第 1, 2, 3, 5, 6 级（省略 4 和 7）。五声小调：1, 降3, 4, 5, 降7。全音音阶：全-全-全-全-全-全。半音音阶：全部半音。

---

3. Chord Construction Formulas | 和弦构建公式

Triads are built by stacking intervals of a third above a root. The quality is determined by the semitone spacings between successive notes.

三和弦由根音上方叠置两个三度构成。其性质由相邻音之间的半音间距决定。

Major triad formula: root + 4 semitones + 3 semitones. Minor triad: root + 3 + 4. Diminished triad: root + 3 + 3. Augmented triad: root + 4 + 4.

大三和弦公式：根音 + 4 半音 + 3 半音。小三和弦：根音 + 3 + 4。减三和弦：根音 + 3 + 3。增三和弦：根音 + 4 + 4。

Seventh chords extend the triad by a third. Major 7th: major triad + major 3rd (4+3+4). Dominant 7th: major triad + minor 3rd (4+3+3). Minor 7th: minor triad + minor 3rd (3+4+3). Half-diminished 7th: dim triad + major 3rd (3+3+4). Diminished 7th: dim triad + minor 3rd (3+3+3).

七和弦在三和弦上再叠置一个三度。大七和弦：大三和弦 + 大三度 (4+3+4)。属七和弦：大三和弦 + 小三度 (4+3+3)。小七和弦：小三和弦 + 小三度 (3+4+3)。半减七和弦：减三和弦 + 大三度 (3+3+4)。减七和弦：减三和弦 + 小三度 (3+3+3)。

Chord inversions are labelled with figured bass. Root position: 5/3. First inversion: 6/3 (or 6). Second inversion: 6/4. Seventh chord inversions: 6/5, 4/3, 4/2.

和弦转位用数字低音标记。原位：5/3。第一转位：6/3（或简记 6）。第二转位：6/4。七和弦转位：6/5, 4/3, 4/2。

---

4. Cadence Formulas | 终止式公式

Cadences are two-chord progressions that close a phrase. They are defined by the scale degrees of the roots and the voice-leading conventions.

终止式是收束乐句的两个和弦的进行。其类型由根音级数及声部进行惯例决定。

Perfect cadence: V → I (or V⁷ → I). Both chords in root position, with the tonic in the soprano of the I chord for a perfect authentic cadence.

正格终止：V → I（或 V⁷ → I）。两和弦均用原位，且 I 和弦上方声部为主音时构成完满正格终止。

Plagal cadence: IV → I. Often used for ‘Amen’. Root movement up a perfect 4th or down a perfect 5th.

变格终止：IV → I。常用于“阿们”。根音上行纯四度或下行纯五度。

Imperfect cadence: any chord → V. Most commonly I, ii, or IV moving to V. Phrase ends on the dominant.

半终止：任何和弦 → V。最常用 I, ii 或 IV 进行到 V。乐句停在属和弦上。

Interrupted cadence: V → vi (or sometimes V → IV⁶, or V → ♭VI in minor). Surprise resolution avoiding the tonic.

阻碍终止：V → vi（有时 V → IV⁶，或小调中 V → ♭VI）。意外进行，避免解决到主和弦。

---

5. Harmonic Progression Rules | 和声进行规则

Common-practice harmony follows functional patterns. The circle of fifths progression is foundational: roots move down a 5th (or up a 4th).

传统功能和声遵循功能性进行。五度圈进行是基础：根音下行五度（或上行四度）。

Diatonic chord function formula: I (tonic) can go to any chord. ii (supertonic) → V or vii°. iii (mediant) → vi or IV. IV (subdominant) → V, I, or ii. V (dominant) → I or vi. vi (submediant) → ii or IV. vii° (leading-tone) → I.

调内和弦功能公式：I (主) 可进行到任何和弦。ii (上主) → V 或 vii°。iii (中音) → vi 或 IV。IV (下属) → V, I, 或 ii。V (属) → I 或 vi。vi (下中音) → ii 或 IV。vii° (导) → I。

The leading note must rise when resolving from V or vii° to I. In minor keys, the raised 7th (leading note) creates augmented 2nd intervals; these must be handled carefully in voice-leading.

导音在 V 或 vii° 解决到 I 时必须上行。小调中，升高第 7 级音构成增二度，声部进行需谨慎处理。

Modulation formula: establish new key by a pivot chord (common to both keys) followed by a cadence in the new key. Closely related keys are those no more than one accidental away on the circle of fifths.

转调公式：通过共同和弦（两调共有）确立新调，随后在新调上作终止。近关系调是在五度圈上相差不超过一个调号的调。

---

6. Rhythm and Meter Formulas | 节奏与节拍公式

Time signatures define the meter. Simple time: each beat divides into two equal parts. Compound time: each beat divides into three equal parts.

拍号定义节拍类型。单拍子：每拍划分为两个均等部分。复拍子：每拍划分为三个均等部分。

Simple duple beat formula: 2/4, 2/2. Simple triple: 3/4, 3/2. Simple quadruple: 4/4. Compound duple: 6/8 (two dotted-crotchet beats). Compound triple: 9/8 (three beats). Compound quadruple: 12/8 (four beats).

单二拍：2/4, 2/2。单三拍：3/4, 3/2。单四拍：4/4。复二拍：6/8（两拍附点四分音符）。复三拍：9/8（三拍）。复四拍：12/8（四拍）。

Syncopation shifts stress away from the strong beats. Hemiola formula: three groups of two beats in a triple meter, or two groups of three beats in a duple meter, creating cross-rhythm.

切分音将重音从强拍移开。赫米奥拉比例公式：在三拍子中出现三组二拍，或在二拍子中出现两组三拍，产生交错节奏。

Dotted rhythm: a dot adds half the value of the note. Double dot adds three-quarters. Triplet: three notes in the time of two. Duplet: two notes in the time of three.

附点节奏：附点增加原音符时值的一半。双附点增加四分之三。三连音：三音代替二音。二连音：二音代替三音。

---

7. Melody Writing Axioms | 旋律写作公理

A well-formed melody balances stepwise motion and leaps. Leaps larger than a 4th should be approached and left in the opposite direction where possible.

一条精良的旋律平衡级进与跳进。大于四度的跳进应尽量从反方向进入并反向离开。

Climax placement formula: usually located in the latter half of the phrase, often on a high, long note. Avoid multiple high points.

高潮点位置公式：通常位于乐句后半部分，常在一个高音长音上。避免多个高点。

Sequence formula: a melodic pattern repeated at a higher or lower pitch. Real sequence keeps exact intervals; tonal sequence adjusts to stay diatonic.

模进公式：一个旋律型在更高或更低的音高上重复。完全模进保持精确音程；调性模进调整以保持调内。

Question and answer phrasing: antecedent ends on V, consequent ends on I. Period structure: 4 + 4 bars. Sentence structure: presentation (2+2) + continuation (4).

问答式乐句：前句终止于 V，后句终止于 I。乐段结构：4 + 4 小节。乐句群结构：呈示 (2+2) + 延续 (4)。

Passing and auxiliary notes are non-chord tones. A passing note moves by step between two chord tones. An auxiliary note decorates a single chord tone by step above and below.

经过音与助音是和弦外音。经过音在两个和弦音之间级进。助音在同一个和弦音以级进上方或下方进行装饰。

---

8. 12-Tone Serialism Formulas | 十二音序列公式

A 12-tone row arranges all twelve chromatic pitches in a fixed order. The row can be manipulated using four basic forms: Prime, Retrograde, Inversion, Retrograde Inversion.

十二音序列将全部十二个半音排列成固定顺序。可通过四种基本形式操作：原型、逆行、倒影、逆行倒影。

Transformation formulas: Inversion reverses the direction of each interval. Retrograde plays the row backwards. Any form can be transposed to start on any of the 12 pitches (yielding 48 forms total).

变换公式：倒影反转每个音程的方向。逆行倒序演奏序列。任何形式均可移调至十二个音中的任意起始音（共得 48 种形式）。

Matrix construction: write P0 as a row. The inversion I0 uses the same starting pitch with inverted intervals. Subsequent transpositions fill the grid by maintaining interval content.

矩阵构建：将 P0 写为一行。倒影 I0 使用相同的起始音，音程倒影。随后的移调通过保持音程内容填充网格。

Hexachordal combinatoriality: a row’s first six notes (hexachord) can map onto the second hexachord of another form without pitch duplication under transposition or inversion.

六音组组合性：一个序列的前六个音（六音组）可在移调或倒影下映射到另一形式的第二个六音组，而无音高重复。

---

9. Acoustics and Tuning Formulas | 声学与调律公式

The frequency ratio of an octave is 2:1. Other just intonation intervals: perfect 5th = 3:2, perfect 4th = 4:3, major 3rd = 5:4, minor 3rd = 6:5.

八度的频率比为 2:1。纯律中其他音程比：纯五度 = 3:2，纯四度 = 4:3，大三度 = 5:4，小三度 = 6:5。

Equal temperament formula divides the octave into 12 equal semitones. The frequency ratio of a semitone is the 12th root of 2:

平均律公式将八度均分为 12 个半音。半音的频率比为 2 的 12 次方根：

semitone ratio = ¹²√2 ≈ 1.05946

Cent formula to compare two frequencies:

分音公式用于比较两个频率：

cents = 1200 × log₂(f₂ / f₁)

One semitone = 100 cents. A just noticeable difference is about 5-6 cents. The harmonic series formula: the nth harmonic frequency is n × fundamental frequency.

一个半音 = 100 音分。可察觉的最小差异约为 5-6 音分。泛音列公式：第 n 泛音频率 = n × 基频。

Standing wave on a string: fundamental wavelength = 2L (L = string length). Frequency f = v/(2L). Nodes at ends and antinode in centre for fundamental.

弦上驻波：基波波长 = 2L（L 为弦长）。频率 f = v/(2L)。基波两端为波节，中央为波腹。

---

10. Dynamic and Articulation Formulae | 力度与演奏法公式

Dynamics indicate relative loudness. Standard gradual change formulas: crescendo (cresc.) — gradually louder, diminuendo (dim.) or decrescendo — gradually softer.

力度标记相对响度。标准渐变公式：渐强 (cresc.)、渐弱 (dim. 或 decresc.)。

Static dynamic levels: pp (pianissimo, very soft), p (piano, soft), mp (mezzo-piano, moderately soft), mf (mezzo-forte, moderately loud), f (forte, loud), ff (fortissimo, very loud). Extreme: ppp, fff.

静态力度级别：pp (非常弱), p (弱), mp (中弱), mf (中强), f (强), ff (非常强)。极端标记：ppp, fff。

Articulation formulas: legato (smooth, notes tied together in one bow), staccato (short, detached, indicated by a dot), tenuto (held, slight stress, indicated by a line), accent (strong attack), marcato (marked, stronger accent).

演奏法公式：连奏（平滑，音符连成一体），断奏（短促断开，用圆点表示），保持音（持续，稍有强调，用横线表示），重音（强力起奏），加强重音（更有力的重音）。

Bowings for strings: down-bow (drawn from frog to tip), up-bow (tip to frog). Tremolo: rapid repetition of a single note or alternation between two notes.

弦乐弓法：下弓（从弓根拉向弓尖），上弓（从弓尖拉向弓根）。震音：单音快速重复或两音快速交替。

---

11. Form and Structure Axioms | 曲式与结构公理

Binary form: AB, each section usually repeated. Rounded binary: A (modulates) BA’ (returns to tonic). This form follows the formula ||: A :||: B A’ :||

二段体：AB，每段通常反复。有再现的二段体：A（转调）BA’（回到主调）。结构公式：||: A :||: B A’ :||

Ternary form: ABA, with a contrasting B section and a return to A (often ornamented). Minuet and Trio is a compound ternary form: Minuet (A) – Trio (B) – Minuet (A).

三段体：ABA，对比的 B 段后 A 段再现（常加装饰）。小步舞曲与中段是复三段体：小步舞曲 (A) – 中段 (B) – 小步舞曲 (A)。

Sonata form exposition formula: First subject (tonic) – transition (modulates) – Second subject (dominant or relative major) – codetta. Development: themes treated freely, modulating through distant keys.

Published by TutorHao | Pre-U 音乐 Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）