📚 Year 7 OCR Music: Formula & Theorem Quick Reference Handbook | 七年级OCR音乐：公式定理速查手册
Music is often seen as a creative art, but at its core it is built on patterns, rules and relationships that work just like formulas in mathematics. This quick reference handbook gathers the essential ‘formulas’ and ‘theorems’ you will meet in Year 7 OCR Music. From note durations and scale patterns to chord building and cadences, every concept is presented as a clear, memorable rule. Use it to revise, check your understanding, and build a solid foundation for composing and performing.
音乐常被视为一种创造性的艺术，但它的核心建立在模式、规则和关系之上，这些就像数学中的公式一样。这本速查手册汇集了你在七年级OCR音乐课程中会遇到的关键“公式”和“定理”。从音符时值和音阶模式到和弦构成与终止式，每个概念都以清晰易记的规则呈现。用它来复习、检查你的理解，并为作曲和表演打下坚实的基础。
1. Note Duration Formulas | 音符时值公式
Every note you read or play has a fixed length, called its duration. The relationships between different note values follow simple division formulas, always halving or doubling.
你读到的或演奏的每个音符都有固定的长度，这就是时值。不同音符时值之间的关系遵循简单的分割公式，总是减半或加倍。
1 whole note (semibreve) = 2 half notes (minims)
1个全音符 = 2个二分音符
1 half note = 2 quarter notes (crotchets)
1个二分音符 = 2个四分音符
1 quarter note = 2 eighth notes (quavers)
1个四分音符 = 2个八分音符
1 eighth note = 2 sixteenth notes (semiquavers)
1个八分音符 = 2个十六分音符
This chain means that a whole note lasts for 4 quarter-note beats, a half note for 2 beats, and so on. The same rule applies to rests: a whole rest equals 2 half rests, a half rest equals 2 quarter rests, etc.
这条链条意味着一个全音符持续4个四分音符的拍子，二分音符持续2拍，依此类推。同样的规则也适用于休止符：一个全休止符等于2个二分休止符，二分休止符等于2个四分休止符，等等。
2. Dotted Notes and Ties | 附点与延音线公式
A dot placed after a note increases its duration by exactly half of its original value. A tie joins two notes of the same pitch to add their lengths together, creating one longer sound.
放在音符后面的附点会使该音符的时值增加原时值的一半。延音线将两个音高相同的音符连接起来，把它们的时值加在一起，形成一个更长的音。
Dotted note duration = original note duration + ½ of original note duration
附点音符时值 = 原音符时值 + 原音符时值的二分之一
Example: a dotted half note (minim) in 4/4 time equals 2 beats + 1 beat = 3 beats. A dotted quarter note equals 1½ beats. A double dotted note adds a further quarter of the original value on top of the first dot.
例如：在4/4拍中，附点二分音符等于2拍 + 1拍 = 3拍。附点四分音符等于1½拍。复附点音符在第一个附点的基础上再增加原时值的四分之一。
Tie formula: Total duration = duration of note A + duration of note B
延音线公式：总时值 = 音符A的时值 + 音符B的时值
Ties work across bar lines and do not require the notes to be re-articulated. Use them whenever you need a duration that cannot be written by a single note and dot combination.
延音线可以跨小节线使用，并且被连接的音不需要再次发音。当你需要的时值无法用单个音符加上附点来表示时，就可以使用延音线。
3. Time Signature Rules | 拍号定则
The time signature appears at the start of a piece and tells you two things: how many beats are in each bar (top number) and what type of note counts as one beat (bottom number).
拍号出现在乐曲的开头，它告诉你两件事：每小节有几拍（上方数字），以及哪种音符算作一拍（下方数字）。
Common bottom numbers work as a code: 4 stands for a quarter note beat, 8 for an eighth note beat, and 2 for a half note beat. Simple time signatures have beats that divide naturally into two equal parts; compound time signatures have beats that divide into three.
常见的下方数字就像一个代码：4代表以四分音符为一拍，8代表以八分音符为一拍，2代表以二分音符为一拍。单拍子每拍可以自然地分成两个相等的部分；复拍子每拍可以分成三个部分。
By formula, simple time: duple (2/4, 2/2), triple (3/4, 3/2), quadruple (4/4). Compound time: duple (6/8), triple (9/8), quadruple (12/8). In 6/8, there are 6 eighth notes per bar, but they are felt in two groups of three, giving 2 dotted-quarter beats.
按照公式，单拍子包括：二拍子（2/4、2/2）、三拍子（3/4、3/2）、四拍子（4/4）。复拍子包括：二拍子（6/8）、三拍子（9/8）、四拍子（12/8）。在6/8拍中，每小节有6个八分音符，但它们被感受为两组（每组三个），因此形成了2个附点四分音符的拍感。
4. Major Scale Formula | 大调音阶公式
All major scales follow the same pattern of tones (T) and semitones (S), no matter which note they start on. Once you learn this sequence, you can build any major scale.
所有大调音阶都遵循相同的全音（T）与半音（S）模式，无论从哪个音开始。一旦你学会这个序列，你就能构建任何大调音阶。
Major scale formula: T – T – S – T – T – T – S
大调音阶公式：全 – 全 – 半 – 全 – 全 – 全 – 半
Using this formula, you can work out the notes of C major (C-D-E-F-G-A-B-C) or check that G major contains an F♯ to keep the pattern of tones and semitones correct. The semitones always fall between the 3rd-4th degrees and the 7th-8th degrees.
利用这个公式，你可以推算出C大调（C-D-E-F-G-A-B-C），或者检查G大调是否包含了升F（F♯）以保持全音半音模式的正确。半音总是出现在第3-4级音和第7-8级音之间。
Remember that the formula works upwards (ascending). A descending major scale simply reverses the order. For keyboard players, the pattern of steps helps you find the correct black and white keys.
请记住，这个公式适用于上行（音阶上行）。下行大调音阶只是将顺序反过来。对于键盘演奏者来说，音程的模式可以帮助你找到正确的黑键和白键。
5. Minor Scale Formulas | 小调音阶公式
Minor scales come in three main forms. The natural minor follows a fixed tone-semitone pattern. The harmonic minor raises the 7th degree to create a stronger pull back to the tonic. The melodic minor raises both the 6th and 7th degrees when ascending.
小调音阶有三种主要形式。自然小调遵循固定的全音半音模式。和声小调升高第VII级音，以创造出更强的主音倾向性。旋律小调在上行时同时升高第VI级和第VII级音。
Natural minor: T – S – T – T – S – T – T
自然小调：全 – 半 – 全 – 全 – 半 – 全 – 全
To find the natural minor scale starting on A, you can simply play all the white notes from A to A: A-B-C-D-E-F-G-A. No sharps or flats are needed.
要找到从A开始的自然小调音阶，只需弹奏从A到A的全部白键：A-B-C-D-E-F-G-A。不需要任何升降号。
Harmonic minor: raise the 7th degree by a semitone
和声小调：将第VII级音升高半音
Example: A harmonic minor = A-B-C-D-E-F-G♯-A. The leap between F and G♯ creates a distinctive ‘Middle Eastern’ sound and an augmented 2nd interval.
例如：A和声小调 = A-B-C-D-E-F-G♯-A。F和G♯之间的跳跃产生了一个独特的、“中东”风格的声音，并形成了一个增二度音程。
Melodic minor: ascending raise 6th and 7th; descending is natural
旋律小调：上行升高第VI和第VII级；下行还原为自然
In A melodic minor, ascending: A-B-C-D-E-F♯-G♯-A; descending: A-G-F-E-D-C-B-A. This shape smooths out the awkward leap found in the harmonic version.
在A旋律小调中，上行：A-B-C-D-E-F♯-G♯-A；下行：A-G-F-E-D-C-B-A。这种形式消除了和声小调中那个别扭的跳跃。
6. Interval Formulas | 音程公式
An interval is the distance between two notes. Every interval can be measured in semitones. Knowing these numbers helps you identify, build and spell intervals quickly.
音程是两个音之间的距离。每个音程都可以用半音来测量。知道这些数字可以帮助你快速识别、构建和拼写音程。
| Interval name | Semitones | Example from C |
| Perfect Unison | 0 | C – C |
| Minor 2nd | 1 | C – D♭ |
| Major 2nd | 2 | C – D |
| Minor 3rd | 3 | C – E♭ |
| Major 3rd | 4 | C – E |
| Perfect 4th | 5 | C – F |
| Augmented 4th / Diminished 5th | 6 | C – F♯ / C – G♭ |
| Perfect 5th | 7 | C – G |
| Minor 6th | 8 | C – A♭ |
| Major 6th | 9 | C – A |
| Minor 7th | 10 | C – B♭ |
| Major 7th | 11 | C – B |
| Perfect Octave | 12 | C – C (higher) |
These semitone counts are absolute. When naming an interval, always consider the letter names involved (a 3rd must span three letter names, e.g. C to E). The quality (major, minor, perfect, etc.) depends on the exact number of semitones.
这些半音数是绝对的。在命名音程时，一定要考虑所涉及的音名字数（三度必须跨越三个音名，例如C到E）。音程的性质（大、小、纯等）取决于确切的半音数量。
7. Triad Chord Formulas | 三和弦公式
Triads are three-note chords built by stacking intervals of a third. The type of triad is determined by the quality of the thirds used. All formulas are given from the root note upwards.
三和弦是由三个音叠置而成的和弦，按三度关系构建。三和弦的类型取决于所使用的三度的性质。所有公式都是从根音向上计算。
Major triad: Root + 4 semitones + 3 semitones
大三和弦：根音 + 4个半音 + 3个半音
This creates a major 3rd on the bottom and a minor 3rd on top. Example: C major = C (root) – E (4 semitones up) – G (3 semitones up). It sounds bright and happy.
这形成了底部大三度加顶部小三度的结构。例如：C大三和弦 = C（根音）– E（上方4个半音）– G（上方3个半音）。听起来明亮、快乐。
Minor triad: Root + 3 semitones + 4 semitones
小三和弦：根音 + 3个半音 + 4个半音
A minor triad has a minor 3rd on the bottom and a major 3rd above it. Example: A minor = A – C – E. It sounds darker or sadder.
小三和弦底部为小三度，上方为大三度。例如：A小三和弦 = A – C – E。听起来更阴暗或悲伤。
Diminished triad: Root + 3 + 3 semitones
减三和弦：根音 + 3 + 3个半音
Two stacked minor 3rds produce a diminished 5th. Example: B diminished = B – D – F. It sounds tense and unstable.
两个叠加的小三度产生减五度。例如：B减三和弦 = B – D – F。听起来紧张而不稳定。
Augmented triad: Root + 4 + 4 semitones
增三和弦：根音 + 4 + 4个半音
Two major 3rds give an augmented 5th. Example: C augmented = C – E – G♯. It has a dreamy, floating quality.
两个大三度产生增五度。例如：C增三和弦 = C – E – G♯。具有梦幻、漂浮的感觉。
8. Circle of Fifths & Key Signature Formulas | 五度圈与调号公式
The circle of fifths organises key signatures by the number of sharps or flats. Each step clockwise adds one sharp; each step anticlockwise adds one flat. The order of sharps and flats is fixed.
五度循环圈按照升降号的数量组织调号。顺时针每走一步增加一个升号，逆时针每走一步增加一个降号。升降号出现的顺序是固定的。
Order of sharps: F♯ – C♯ – G♯ – D♯ – A♯ – E♯ – B♯
升号顺序：F♯ – C♯ – G♯ – D♯ – A♯ – E♯ – B♯
A mnemonic to remember is ‘Father Charles Goes Down And Ends Battle’. For flats, the order is reversed: B♭ – E♭ – A♭ – D♭ – G♭ – C♭ – F♭ (‘Battle Ends And Down Goes Charles’ Father’).
记忆口诀是 ‘Father Charles Goes Down And Ends Battle’ （爸爸查尔斯走下去并结束了战斗）。降号的顺序则相反：B♭ – E♭ – A♭ – D♭ – G♭ – C♭ – F♭（’Battle Ends And Down Goes Charles’ Father’）。
To find the major key from a sharp key signature, take the last sharp and go up a semitone. Example: last sharp is D♯ → one semitone higher is E, so the key is E major. For flat keys, the second-to-last flat names the key. Example: key signature has B♭, E♭ and A♭ → second-to-last is E♭, so the key is E♭ major.
要从升号调号找出大调，看最后一个升号，再向上走一个半音。例如：最后一个升号是D♯ → 高半音是E，所以调是E大调。对于降号调，看倒数第二个降号，那就是调名。例如：调号有B♭、E♭和A♭ → 倒数第二个是E♭，所以是E♭大调。
Relative minors share the same key signature. The relative minor is always 3 semitones below the major tonic. Example: C major (0 sharps) → A minor; G major (1 sharp) → E minor.
关系小调共用同一个调号。关系小调的主音总是在大调主音下方3个半音处。例如：C大调（无升降）→ A小调；G大调（1个升号）→ E小调。
9. Cadence Formulas | 终止式公式
Cadences are like punctuation marks at the end of musical phrases. They use fixed chord progressions to create a sense of ending, interruption or surprise.
终止式就像乐句末尾的标点符号。它们使用固定的和弦进行来营造收束、中断或意外感。
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