📚 OCR Year 7 Music Formula & Theorem Quick Reference Handbook | OCR 七年级音乐公式定理速查手册
Music might feel like an art of emotion and instinct, but beneath every melody lies a hidden structure governed by mathematical patterns, acoustic laws, and notational rules. This handbook collects the essential 'formulas and theorems' every Year 7 OCR Music student needs – from the circle of fifths relationship to the mathematical ratio that defines an octave. Think of these as your cheat codes for reading, writing, and understanding music with precision and confidence.
音乐或许像是一门依赖情感和直觉的艺术，但在每一条旋律之下，都隐藏着由数学模式、声学规律和记谱规则支配的结构。本手册汇集了每位七年级 OCR 音乐学生所需的基本“公式和定理”——从五度循环圈的关系，到定义八度的数学比率。把这些当作你精准而自信地阅读、书写和理解音乐的秘籍。
1. The Stave Formula: 5 Lines, 4 Spaces | 五线谱公式：五条线，四个间
The musical stave is built on a simple counting rule: five parallel horizontal lines create four spaces between them. Notes can be placed on any line or in any space, and their vertical position determines pitch. When notes fall outside this range, short extra lines called ledger lines are added above or below.
五线谱建立在一个简单的计数规则上：五条平行的水平线在它们之间形成了四个间。音符可以放置在任何一条线上或任何一个间里，其垂直位置决定了音高。当音符超出此范围时，会在上方或下方添加称为加线的短附加线。
Counting from the bottom up, the lines and spaces follow alphabetical order when assigned a clef. With the treble clef, the lines spell E – G – B – D – F (memorised as 'Every Good Boy Deserves Football'), and the spaces spell F – A – C – E. These mnemonics are the foundation of note-reading literacy.
从下往上数，线和间在指定谱号后按字母顺序排列。使用高音谱号时，线上的音拼作 E – G – B – D – F（记作“Every Good Boy Deserves Football”），间里的音拼作 F – A – C – E。这些记忆法是音符阅读能力的基础。
2. The Octave Ratio Theorem: 2:1 | 八度比率定理：2:1
An octave is the most fundamental interval in music, and it is defined by an exact physical ratio. When one pitch vibrates at exactly twice the frequency of another, we hear them as the same note name, just higher or lower. For example, the A above middle C vibrates at 440 Hz, meaning the A one octave higher vibrates at 880 Hz, and the A one octave lower vibrates at 220 Hz.
八度是音乐中最基本的音程，它由一个精确的物理比率定义。当一个音高的振动频率恰好是另一个音高的两倍时，我们听到它们为相同的音名，只是更高或更低。例如，中央 C 上方的 A 以 440 Hz 振动，这意味着高一个八度的 A 以 880 Hz 振动，而低一个八度的 A 则以 220 Hz 振动。
OCR students should memorise this 2:1 ratio as the scientific basis for octave equivalence. It explains why doubling the length of a vibrating string halves its frequency, and why instruments across all cultures organise pitches into repeating octave cycles.
OCR 学生应记住这个 2:1 比率，作为八度等价的科学基础。它解释了为什么振动弦的长度加倍，其频率就会减半，也解释了为什么所有文化中的乐器都将音高组织成重复的八度循环。
3. Note Duration Mathematics: Powers of Two | 音符时值数学：二的幂次
Western rhythmic notation is built entirely on binary division. Starting from a semibreve (whole note), each shorter note divides the duration by two: a minim is ½ of a semibreve, a crotchet is ½ of a minim (so ¼ of a semibreve), a quaver is ½ of a crotchet (⅛ of a semibreve), and a semiquaver is ½ of a quaver (⅟₁₆ of a semibreve). This is the binary subdivision rule.
西方节奏记谱完全建立在二分法之上。从全音符开始，每个更短的音符将其时值除以二：二分音符是全音符的 ½，四分音符是二分音符的 ½（故为全音符的 ¼），八分音符是四分音符的 ½（全音符的 ⅛），十六分音符是八分音符的 ½（全音符的 ⅟₁₆）。这就是二分法细分规则。
m lasts for 2 + 1 = 3 crotchet beats, and a dotted crotchet lasts for 1 + ½ = 1½ crotchet beats. Ties perform a similar function by joining two notes of the same pitch into one continuous sound, adding their durations together.
附点音符巧妙地修改了这一规则。音符后添加的附点会将其时值增加恰好原始值的一半。因此，附点二分音符持续 2 + 1 = 3 个四分音符拍，附点四分音符持续 1 + ½ = 1½ 个四分音符拍。延音线通过将两个相同音高的音符连接成一个连续的声音，将其时值相加，从而执行类似的功能。
4. Time Signature Code: Top = Beats, Bottom = Beat Unit | 拍号密码：上方数字 = 拍数，下方数字 = 拍单位
A time signature is displayed as two numbers, one above the other, placed at the start of the first stave. The top number states how many beats are in each bar. The bottom number indicates the type of note that receives one beat, using a code where 4 represents a crotchet, 2 represents a minim, and 8 represents a quaver.
拍号显示为两个数字，一个在上，一个在下，置于第一行五线谱的开头。上方数字表明每小节有多少拍。下方数字使用一个代码表示接收一拍的音符类型，其中 4 代表四分音符，2 代表二分音符，8 代表八分音符。
Simple time signatures have top numbers of 2, 3, or 4, meaning each beat naturally divides into two equal quavers. Compound time signatures have top numbers of 6, 9, or 12, meaning each beat naturally divides into three equal quavers. This distinction helps OCR students identify whether a piece feels marching (simple) or lilting (compound).
单拍子的上方数字为 2、3 或 4，意味着每一拍自然地等分为两个八分音符。复拍子的上方数字为 6、9 或 12，意味着每一拍自然地等分为三个八分音符。这一区别帮助 OCR 学生识别一首乐曲给人的感觉是进行曲式的（单拍子）还是带有摇曳感的（复拍子）。
5. Major Scale Formula: T – T – S – T – T – T – S | 大调音阶公式：全 – 全 – 半 – 全 – 全 – 全 – 半
Every major scale follows an identical pattern of intervals between consecutive notes. Starting from the tonic (first note), the formula is: Tone, Tone, Semitone, Tone, Tone, Tone, Semitone. On a piano keyboard, a tone (whole step) skips exactly one key, while a semitone (half step) moves to the immediately adjacent key.
每个大调音阶在相邻音符之间都遵循相同的音程模式。从主音（第一个音）开始，公式为：全音，全音，半音，全音，全音，全音，半音。在钢琴键盘上，全音跳过恰好一个琴键，而半音移动到紧邻的琴键。
You can check this formula against C major (all white keys from C to C) — the natural semitones fall between E–F and B–C, exactly where the formula places them. To build any other major scale, apply the formula starting on the chosen tonic, adding sharps or flats as needed to maintain the pattern.
你可以用 C 大调（从 C 到 C 全部白键）来检验这个公式——自然的半音恰好落在 E–F 和 B–C 之间，正是公式所规定的位置。要构建任何其他大调音阶，从所选的主音开始应用此公式，根据需要添加升号或降号以维持此模式。
6. Chord Construction Theorem: Root + 3rd + 5th | 和弦构成定理：根音 + 三度音 + 五度音
A triad is the fundamental chord type in Western harmony, and its construction follows a strict stacking rule. Starting on any note (the root), add the note that is a third above it, then add the note that is a fifth above the root. In scale-degree numbers: 1 – 3 – 5. For a C major triad, this produces the notes C – E – G.
三和弦是西方和声中的基本和弦类型，其构成遵循严格的叠加规则。从任意一个音（根音）开始，在其上方叠加一个三度音，然后在根音上方再叠加一个五度音。用音阶级数表示为：1 – 3 – 5。对于 C 大调三和弦，这产生了 C – E – G 三个音。
The quality of a triad depends on the exact interval sizes. A major triad has a major third (4 semitones) followed by a minor third (3 semitones). A minor triad reverses this: minor third (3 semitones) then major third (4 semitones). Both span a perfect fifth (7 semitones) from root to fifth.
三和弦的性质取决于精确的音程大小。大三和弦由一个三度音（4 个半音）后接一个小三度（3 个半音）组成。小三和弦则相反：小三度（3 个半音）后接大三度（4 个半音）。两者从根音到五度音都跨越一个纯五度（7 个半音）。
7. Interval Counting Rule: Count Letter Names First, Then Semitones | 音程计算规则：先数字母名，再数半音
To identify any interval, start by counting the letter names involved, inclusive of both starting and ending notes. C to G covers five letters (C, D, E, F, G), so it is some kind of fifth. This gives you the interval number. Then count the exact number of semitones to determine the quality: perfect, major, minor, augmented, or diminished.
要识别任何音程，首先数所涉及的字母名数量，包括起始音和结束音。C 到 G 覆盖了五个字母（C、D、E、F、G），所以它是某种五度。这给出了音程的度数。然后计算确切的半音数以确定性质：纯、大、小、增或减。
third, sixth, seventh) which have a brighter or darker quality. The semitone counts for key intervals should be memorised: major second = 2, major third = 4, perfect fourth = 5, perfect fifth = 7, major sixth = 9, major seventh = 11.
OCR 学生将会遇到纯音程（同度、四度、五度、八度），它们具有纯净、开阔的音响效果，以及大/小音程（二度、三度、六度、七度），它们具有较明亮或较暗的特质。关键音程的半音数应该记住：大二度 = 2，大三度 = 4，纯四度 = 5，纯五度 = 7，大六度 = 9，大七度 = 11。
8. Dynamics Decoding Chart: Italian Abbreviation System | 力度解码表：意大利语缩略系统
re p (piano = soft) and f (forte = loud). The letter m placed before either means mezzo or 'moderately' : mp is moderately soft, mf is moderately loud. Repeating the letter intensifies the degree: pp (pianissimo) is very soft, ff (fortissimo) is very loud.
力度记号使用标准化的意大利语缩略词，形成一个响度的分级尺度。两个基本极点是 p（piano = 弱）和 f（forte = 强）。放在任一字母前的 m 表示 mezzo 或“中等”：mp 是中弱，mf 是中强。重复字母会强化程度：pp（pianissimo）是非常弱，ff（fortissimo）是非常强。
Gradual changes are indicated by elongated terms: crescendo (cresc.) means gradually getting louder, and diminuendo (dim.) or decrescendo (decresc.) means gradually getting softer. These are often paired with hairpin symbols that widen or narrow to match the change visually.
渐变通过拉长的术语表示：crescendo（cresc.）意味着逐渐变强，diminuendo（dim.）或 decrescendo（decresc.）意味着逐渐变弱。这些常与扩张或缩窄的喇叭形符号配对使用，以在视觉上与变化相匹配。
9. Tempo Speed Equation: BPM and Italian Terms | 速度公式：BPM 与意大利术语
Tempo is measured scientifically in beats per minute (BPM), but OCR scores mostly use Italian tempo words that convey both speed and mood. The core terms form a speed ladder from slowest to fastest: Largo (broadly, ~40–60 BPM), Adagio (slow and stately, ~66–76 BPM), Andante (walking pace, ~76–108 BPM), Moderato (moderate, ~108–120 BPM), Allegro (fast and lively, ~120–168 BPM), and Presto (very fast, ~168–200 BPM).
速度在科学上以每分钟节拍数（BPM）来衡量，但 OCR 乐谱大多使用能够同时传达速度和情绪的意大利语速度词。这些核心术语形成了一个从最慢到最快的速度阶梯：Largo（宽广地，约 40–60 BPM），Adagio（缓慢而庄严地，约 66–76 BPM），Andante（步行速度，约 76–108 BPM），Moderato（中速，约 108–120 BPM），Allegro（快速活泼地，约 120–168 BPM），Presto（极快，约 168–200 BPM）。
-etto softens (Allegretto = moderately fast). The word molto placed before any term means 'very', and non troppo means 'not too much', allowing precise expressive control.
速度修饰词调整这些基础速度：后缀 -issimo 会强化（Prestissimo = 极快），后缀 -etto 则会缓和（Allegretto = 稍快）。置于任何术语前的 molto 一词表示“非常”，non troppo 表示“不过分”，从而实现了精确的表现力控制。
10. Key Signature Identification: Sharp Order FCGDAEB | 调号识别：升号顺序 FCGDAEB
Key signatures place sharps or flats at the start of each stave to indicate which notes should be consistently raised or lowered. The sharps always appear in a fixed order: F♯, C♯, G♯, D♯, A♯, E♯, B♯. Memorise the phrase 'Father Charles Goes Down And Ends Battle' to recall this sequence. Flats appear in the exact reverse order: B♭, E♭, A♭, D♭, G♭, C♭, F♭ ('Battle Ends And Down Goes Charles Father').
调号在每行五线谱开头放置升号或降号，以指示哪些音符应持续升或降。升号总是以固定顺序出现：F♯, C♯, G♯, D♯, A♯, E♯, B♯。记住这句话“Father Charles Goes Down And Ends Battle”来回忆这个序列。降号以完全相反的顺序出现：B♭, E♭, A♭, D♭, G♭, C♭, F♭（“Battle Ends And Down Goes Charles Father”）。
You can quickly determine a major key when you see sharps: the key note is one semitone above the last sharp. For example, two sharps (F♯ and C♯) — the last sharp is C♯, so the major key is D major. For flats, the major key is the second-to-last flat in the sequence. One flat (B♭) uniquely signals F major.
当你看到升号时，可以快速确定大调：主音是最后一个升号上方一个半音的音。例如，两个升号（F♯ 和 C♯）——最后一个升号是 C♯，所以大调是 D 大调。对于降号，大调是降号序列中倒数第二个降号。一个降号（B♭）唯一地表示 F 大调。
11. Relative Minor Theorem: Down Three Semitones | 关系小调定理：向下三个半音
Every major key has a relative minor key that shares the identical key signature. The tonic of the relative minor is always three semitones (or a minor third) below the tonic of its relative major. For C major (no sharps or flats), counting down three semitones — C, B, B♭ (enharmonic to A♯), A — gives A minor, which indeed also has no sharps or flats.
每个大调都有一个共享相同调号的关系小调。关系小调的主音总是在其关系大调主音下方三个半音（或小三度）的位置。对于 C 大调（无升号和降号），向下数三个半音——C、B、B♭（与 A♯ 等音）、A——得出 A 小调，它确实也没有升号和降号。
This theorem works in both directions: to find the relative major of a minor key, count up three semitones from the minor tonic. This relationship helps OCR students recognise that a piece with one sharp (F♯) could be in G major or its relative E minor, and clues from the musical content (such as raised leading notes D♯) confirm which mode is active.
这一定理双向皆可应用：要查找小调的关系大调，从小调主音向上数三个半音。这种关系有助于 OCR 学生认识到，一首有一个升号（F♯）的乐曲可能是 G 大调或其关系小调 E 小调，而来自音乐内容的线索（如升高的导音 D♯）将确认哪种调式正在使用。
12. Articulation and Expression Quick-Reference Table | 演奏法与表情速查表
| Marking / 记号 | Meaning / 含义 | Visual Symbol / 视觉符号 |
|---|---|---|
| Staccato | Detached, short and separated / 断奏，短促而分离 | Dot above or below the note / 音符上方或下方的点 |
| Legato | Smoothly connected, no silence between notes / 连奏，音符间平滑连接无间隙 | Curved slur line / 弧形连音线 |
| Accent | Play the note with extra force, stronger attack / 演奏时额外加力，更强攻击性 | > above or below the note / 音符上方或下方的 > |
| Tenuto | Hold the note for its full value, slightly stressed / 保持音符时值饱满，稍加压力 | Short horizontal line / 短横线 |
| Fermata (Pause) | Hold the note or rest longer than written, at performer's discretion / 根据演奏者判断，延长音符或休止符 | ⌒ with a dot underneath / ⌒ 下方加一点 |
These articulation marks modify how individual notes are attacked, sustained, and released. Combined with dynamics and tempo, they form the expressive palette that turns accurate note-reading into genuine musical performance.
这些演奏法记号调整了单个音符如何发声、保持和释放。结合力度和速度，它们构成了表现力的调色板，将准确的音符阅读转化为真正的音乐演奏。
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