📚 OCR Year 11 Music Formula & Theorem Quick Reference Handbook | OCR 十一年级音乐公式定理速查手册
Welcome to your OCR Year 11 Music 'Formula & Theorem' Quick Reference Handbook. In music, formulas are not about algebra but about the precise rules that govern pitch, rhythm, harmony, and form. This handbook distils the essential building blocks of Western notation and theory into clear, repeatable patterns – your go-to revision companion for the listening, appraising, and performing components.
欢迎使用 OCR 十一年级音乐“公式定理速查手册”。音乐中的“公式”并非代数，而是支配音高、节奏、和声与曲式的精确规则。这本手册将西式记谱和理论的基本构件浓缩为清晰、可重复的模式——是您备考听力、鉴赏和演奏的理想伴侣。
1. Note and Rest Duration Formulas | 音符与休止符时值公式
Every rhythm is built on mathematical relationships between note values. In simple time, the semibreve (whole note) is the longest commonly used duration, and each shorter note is an exact binary subdivision. The corresponding rests follow exactly the same proportional logic.
每个节奏都建立在音符时值之间的数学关系上。在单拍子中，全音符是最长常用的时值，每一种更短的音符都是精确的二分细分。相应的休止符遵循完全相同的比例逻辑。
1 Semibreve = 2 Minims = 4 Crotchets = 8 Quavers = 16 Semiquavers
1 全音符 = 2 二分音符 = 4 四分音符 = 8 八分音符 = 16 十六分音符
Dotted notes increase the value by one half: a dotted crotchet equals three quavers, a dotted minim equals three crotchets. Double dots add another half of the added value, making a double-dotted crotchet equivalent to seven semiquavers. Ties merge durations across bar lines, creating notes that last longer than a single beat unit.
附点音符将时值增加一半：附点四分音符等于三个八分音符，附点二分音符等于三个四分音符。复附点再增加所加时值的一半，使复附点四分音符等于七个十六分音符。延音线跨小节线合并时值，创造出长于单个节拍单位的音符。
Dotted-note rule: note × 1.5; Double-dotted: note × 1.75
附点规则：原时值 × 1.5；复附点：原时值 × 1.75
2. Time Signatures & Beat Grouping | 拍号与节拍分组公式
A time signature is not a fraction but a formula: the upper number tells how many beats per bar, the lower number tells which note value counts as one beat. Simple time signatures have a beat that divides into two equal quavers; compound time signatures have a dotted beat that divides into three quavers.
拍号不是分数而是一个公式：上方数字指明每小节有几拍，下方数字指明以哪种音符为一拍。单拍子的每一拍可以均分为两个八分音符；复拍子的每一拍是附点拍，可均分为三个八分音符。
Simple duple: 2/4, 2/2 | Compound duple: 6/8 (beat = dotted crotchet)
单二拍：2/4, 2/2 | 复二拍：6/8（一拍 = 附点四分音符）
condary stress on beat 4 (counted as 1-2-3, 4-5-6). Irregular time signatures such as 5/4 or 7/8 break the mould and must be memorised as unique groupings (e.g. 5/4 = 3+2 or 2+3).
4/4 拍的强弱规律是强-弱-次强-弱。3/4 拍是强-弱-弱。复拍子 6/8 的主重音在第 1 拍，次重音在第 4 拍（数作 1-2-3, 4-5-6）。不规则拍号如 5/4 或 7/8 打破常规，需按特殊分组记忆（如 5/4 = 3+2 或 2+3）。
3. Interval Calculation Formulae | 音程计算公式
Intervals are the DNA of melody and harmony. They are measured in two ways: the number of letter names (ordinal count) and the precise number of semitones. The combination of these two determines whether an interval is perfect, major, minor, augmented, or diminished.
音程是旋律与和声的 DNA。音程的衡量有两种方式：字母名数目（序数数）以及准确的半音数量。两者结合决定了音程是纯音程、大音程、小音程、增音程还是减音程。
Perfect Unison (0 st), minor 2nd (1 st), Major 2nd (2 st), minor 3rd (3 st), Major 3rd (4 st), Perfect 4th (5 st), Tritone (6 st), Perfect 5th (7 st), minor 6th (8 st), Major 6th (9 st), minor 7th (10 st), Major 7th (11 st), Perfect Octave (12 st)
纯一度（0 半音），小二度（1 半音），大二度（2 半音），小三度（3 半音），大三度（4 半音），纯四度（5 半音），三全音（6 半音），纯五度（7 半音），小六度（8 半音），大六度（9 半音），小七度（10 半音），大七度（11 半音），纯八度（12 半音）
To identify any interval, count the letter names from the lower note to the higher note (inclusive), then check the semitone count against the reference table. For example, C to Eb spans three letters (C-D-E), so it is a third; it contains 3 semitones, so it is a minor third. C to Ab spans six letters and 8 semitones – a minor sixth. Always observe the key signature and any accidentals.
识别任何音程时，先从低音数到高音的字母名（包含首尾），再与半音参照表比对。例如 C 到 E♭ 跨三个字母（C-D-E），因此是三度；它包含 3 个半音，所以是小三度。C 到 A♭ 跨六个字母，8 个半音——小六度。务必考虑调号和临时记号。
4. Major Scale Construction | 大调音阶构建公式
Every major scale follows the same interval formula: Tone, Tone, Semitone, Tone, Tone, Tone, Semitone. This pattern can be applied starting from any tonic note, shaping the scale's distinctive bright and stable character.
每个大调音阶都遵循相同的音程公式：全音-全音-半音-全音-全音-全音-半音。将此模式应用于任何主音，就能塑造出大调音阶明亮、稳定的特性。
Major Scale Formula: T – T – s – T – T – T – s (T = tone, s = semitone)
大调音阶公式：全 – 全 – 半 – 全 – 全 – 全 – 半
When constructing a major scale, use every letter name once and adjust accidentals to fit the formula. For G major, you need F♯ to preserve the semitone between the 7th and 8th degrees. For F major, B♭ is required to keep the semitone between the 3rd and 4th degrees. The degrees of the scale are named: Tonic, Supertonic, Mediant, Subdominant, Dominant, Submediant, Leading Note, Tonic.
构建大调音阶时，每个字母名使用一次，并用临时记号调整以符合公式。G 大调需要升 F 以保持第 7 级到第 8 级之间的半音。F 大调需要降 B 以保持第 3 级与第 4 级之间的半音。音阶级数命名为：主音、上主音、中音、下属音、属音、下中音、导音、主音。
5. Minor Scale Variants | 小调音阶变体公式
OCR students must be fluent in three minor scale forms: natural, harmonic, and melodic. Each alters the basic minor pattern in a specific way, creating distinct melodic and harmonic flavours that are essential for recognising keys and composing.
OCR 学生必须熟练掌握三种小调音阶形式：自然小调、和声小调与旋律小调。每种形式以特定方式改变基本小调模式，创造出独特的旋律与和声色彩，这对判断调性和作曲至关重要。
Natural minor: T – s – T – T – s – T – T (Aeolian mode)
自然小调：全 – 半 – 全 – 全 – 半 – 全 – 全（爱奥尼亚调式）
Harmonic minor: T – s – T – T – s – T+1/2 (augmented 2nd) – s
和声小调：全 – 半 – 全 – 全 – 半 – 增二度（3半音） – 半
Melodic minor (ascending): T – s – T – T – T – T – s
旋律小调（上行）：全 – 半 – 全 – 全 – 全 – 全 – 半
The harmonic minor raises the 7th degree to create a leading note, making the dominant chord major and strengthening the pull to the tonic. The melodic minor raises both 6th and 7th degrees ascending to avoid the awkward augmented 2nd; descending, it reverts to the natural minor. In exam extracts, the presence of a sharpened 7th in a minor key often signals the harmonic form, while a sharpened 6th ascending points to melodic minor.
和声小调升高第 7 级音以创造导音，使属和弦成为大三和弦，增强向主音的倾向。旋律小调上行时同时升高第 6 和第 7 级，避免生硬的增二度；下行时恢复为自然小调。在考试节选中，小调中升高的第 7 级常暗示和声小调，而上行时升高的第 6 级则指向旋律小调。
6. Triad Chord Building Rules | 三和弦构建规则
A triad is a three-note chord built by stacking two thirds. The combination of major and minor thirds determines the chord's quality. Being able to spell any triad from a given root is a core skill for OCR harmony questions.
三和弦是由两个三度叠置而成的三音和弦。大小三度的组合决定和弦的性质。从给定根音构建任何三和弦是 OCR 和声题的核心技能。
Major triad: root + Major 3rd (4 st) + Perfect 5th (7 st) or root + 4 st + 3 st
大三和弦：根音 + 大三度（4 半音） + 纯五度（7 半音）或根音 + 4 半音 + 3 半音
Minor triad: root + minor 3rd (3 st) + Perfect 5th (7 st)
小三和弦：根音 + 小三度（3 半音） + 纯五度（7 半音）
Diminished triad: root + minor 3rd + diminished 5th (6 st)
减三和弦：根音 + 小三度 + 减五度（6 半音）
Augmented triad: root + Major 3rd + augmented 5th (8 st)
增三和弦：根音 + 大三度 + 增五度（8 半音）
When working in a key, diatonic triads follow a pattern. In a major key, the triads built on each scale degree are: I major, ii minor, iii minor, IV major, V major, vi minor, vii° diminished. This Roman numeral formula is the same for every major key. For a minor key, the natural minor gives i, ii°, III, iv, v, VI, VII; however, with the harmonic minor's raised 7th, the V chord becomes major, creating a dominant seventh function that is crucial for cadences.
在特定调内，自然三和弦遵循固定模式。在大调中，各音级上的三和弦依次为：I 大三，ii 小三，iii 小三，IV 大三，V 大三，vi 小三，vii° 减三。这个罗马数字公式适用于所有大调。小调的自然形式产生 i, ii°, III, iv, v, VI, VII；但采用和声小调的升七级后，V 级和弦变为大三，形成属七功能，对终止式至关重要。
7. Seventh Chord Formulas | 七和弦公式
Adding another third on top of a triad creates four-note seventh chords, which add colour, tension, and a stronger sense of harmonic direction. The most common seventh chords in OCR Music are the dominant 7th, minor 7th, major 7th, half-diminished 7th, and diminished 7th.
在三和弦上方再叠加一个三度便构成四音的七和弦，为音乐增添色彩、张力和更强的和声方向感。OCR 音乐中最常见的七和弦有属七、小七、大七、半减七和减七和弦。
Dominant 7th: Major triad + minor 7th (10 st from root) – e.g. G-B-D-F
属七和弦：大三和弦 + 小七度（距根音 10 半音）– 例 G-B-D-F
Major 7th: Major triad + Major 7th (11 st) – e.g. C-E-G-B
大七和弦：大三和弦 + 大七度（11 半音）– 例 C-E-G-B
Minor 7th: minor triad + minor 7th – e.g. D-F-A-C
小七和弦：小三和弦 + 小七度 – 例 D-F-A-C
Half-dim. 7th: diminished triad + minor 7th – e.g. B-D-F-A
半减七和弦：减三和弦 + 小七度 – 例 B-D-F-A
Diminished 7th: diminished triad + diminished 7th (9 st) – e.g. B-D-F-Ab
减七和弦：减三和弦 + 减七度（9 半音）– 例 B-D-F-A♭
In a major key, the dominant 7th (V⁷) contains a tritone between the 3rd and 7th of the chord, which resolves naturally to the tonic. The diminished 7th chord is symmetrical: it stacks minor thirds and can belong to multiple keys at once, making it a popular pivot in modulation.
大调中，属七和弦（V⁷）在三音与七音之间包含一个三全音，该音程自然地解决到主和弦。减七和弦是对称的：它由小三度叠置而成，可同时属于多个调，使其成为转调中常用的中介和弦。
8. Perfect, Imperfect, Plagal & Interrupted Cadences | 终止式与和弦进行公式
Cadences are the punctuation marks of musical phrases. OCR expects you to recognise them aurally and notate the chords using Roman numerals. The four principal cadences each have a distinct formula and effect.
终止式是乐句的标点符号。OCR 要求通过听觉识别它们并用罗马数字标记和弦。四种主要终止式各有独特的公式和效果。
Perfect cadence: V → I (full close; sounds final and complete)
正格终止：V → I（完全终止；完满、结束感）
Imperfect cadence: I/ii/IV → V (half close; leaves music hanging, expecting continuation)
不完全终止（半终止）：I/ii/IV → V（半终止；悬而未决，期待继续）
Plagal cadence: IV → I (Amen cadence; softer, often used in hymns)
变格终止：IV → I（阿门终止；柔和，常用于赞美诗）
Interrupted cadence: V → vi (deceptive; the expected tonic is replaced by the submediant)
阻碍终止：V → vi（意外；期待的 I 被 vi 替换）
In minor keys, the perfect cadence often uses V-i, with the raised leading note in the dominant chord. Listen for the harmonic minor's characteristic augmented 2nd in the melody above a V-i cadence. Common chord progressions such as I-IV-V-I, ii-V-I, and the 12-bar blues pattern (I-I-I-I-IV-IV-I-I-V-IV-I-I) are built on these cadential formulas.
小调中，正格终止常用 V-i，属和弦带有升高的导音。注意倾听 V-i 终止式旋律中因和声小调而出现的增二度。常见的和弦进行如 I-IV-V-I、ii-V-I、以及 12 小节布鲁斯模式（I-I-I-I-IV-IV-I-I-V-IV-I-I）都建立在这些终止公式之上。
9. Circle of Fifths & Key Signature Calculation | 五度圈与调号计算
Key signatures are generated by the circle of fifths, a formula that orders sharps and flats in a never-ending spiral. For your OCR exam, you need to recall key signatures up to four sharps and four flats for both major and relative minor keys.
调号由五度圈生成，这是一个将升号和降号按顺序排列的螺旋公式。在 OCR 考试中，你需要记住多达四升四降的大调及其关系小调的调号。
