KS3 AQA Music: Formulas & Theorems Quick Reference | KS3 AQA 音乐：公式定理速查手册

📚 KS3 AQA Music: Formulas & Theorems Quick Reference | KS3 AQA 音乐：公式定理速查手册

This quick reference handbook compiles the essential formulas, rules, and theorems you will encounter in KS3 AQA Music. Understanding these building blocks will help you read, write, and analyse music with confidence. From note-value arithmetic to chord construction, each concept is presented as a clear ‘formula’ that you can memorise and apply in performing, composing, and listening tasks.

这本速查手册汇集了 KS3 AQA 音乐课程中必备的公式、规则和定理。理解这些基础模块将帮助你在读谱、创作与分析音乐时充满信心。从音符时值的算术规则到和弦构建方法，每一个概念都以清晰的“公式”呈现，方便你在演奏、作曲和听力练习中记忆并运用。

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1. Note Values & Formulas | 音符时值与公式

In Western notation, note durations follow a simple doubling and halving system. The semibreve (whole note) is the longest value we normally use; each shorter note is exactly half the duration of the previous one. These relationships allow you to calculate any rhythm as a fraction of a whole note.

在西方的记谱法中，音符时值遵循简单的加倍与减半规则。全音符（semibreve）是最长的常见单位，每一个更短的音符都恰好是前一个音符时值的一半。这些关系使你能够将所有节奏计算为全音符的若干分之一。

• Semibreve = 4 crotchet beats (whole note)

  全音符 = 4 个四分音符拍

• Minim = 2 crotchets (half note, 1/2 of a semibreve)

  二分音符 = 2 个四分音符（半音符）

• Crotchet = 1 beat (quarter note, 1/4 of a semibreve)

  四分音符 = 1 拍（四分之一音符）

• Quaver = 1/2 beat (eighth note, 1/8 of a semibreve)

  八分音符 = 1/2 拍（八分之一音符）

• Semiquaver = 1/4 beat (sixteenth note, 1/16 of a semibreve)

  十六分音符 = 1/4 拍（十六分之一音符）

Think of these values as a fraction tree: semibreve = 1, minim = 1/2, crotchet = 1/4, quaver = 1/8, semiquaver = 1/16. Every bar must contain the total number of beats shown by the time signature, so these fractions must add up exactly to the required sum.

这些时值可以看成一个分数树：全音符 = 1，二分音符 = 1/2，四分音符 = 1/4，八分音符 = 1/8，十六分音符 = 1/16。每个小节的音符时值总和必须等于拍号所规定的拍数，因此这些分数必须精确地加起来。

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2. Rests & Time Signatures | 休止符与拍号

For every note value there is an equivalent rest of the same duration. Rests show when you should not play, and they follow exactly the same doubling/halving rules. The semibreve rest hangs from the 4th line of the stave, the minim rest sits on the 3rd line, and other rests have their own distinctive symbols.

每个音符时值都有一个相对应的、同等长度的休止符。休止符表示你应当停止演奏的时长，并遵循完全相同的加倍/减半规则。全休止符悬挂在谱表第四线，二分休止符位于第三线，其他休止符也有各自独特的符号。

The time signature is a formula written at the start of a piece. The top number tells you how many beats are in each bar; the bottom number tells you which note value counts as one beat (4 = crotchet, 8 = quaver, 2 = minim).

拍号是写在乐曲开始的一个“公式”。上面的数字表示每小节有多少拍；下面的数字表示以何种音符为一拍（4 代表四分音符，8 代表八分音符，2 代表二分音符）。

• 4/4 time: 4 crotchet beats per bar

  4/4 拍：每小节 4 个四分音符拍

• 3/4 time: 3 crotchet beats per bar (waltz time)

  3/4 拍：每小节 3 个四分音符拍（圆舞曲拍子）

• 2/4 time: 2 crotchet beats per bar

  2/4 拍：每小节 2 个四分音符拍

• 6/8 time: 6 quaver beats per bar, often felt in two groups of three quavers

  6/8 拍：每小节 6 个八分音符拍，通常分成两组三拍来感觉

Time signatures thus set the whole mathematical framework for grouping notes and rests; always check the bottom number to know which note equals one ‘beat unit’.

拍号为音符和休止符的分组设定了数学框架；永远要查看下方数字以确定哪一个音符是“一拍单位”。

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3. Dotted Notes & Ties | 附点音符与连线

A dot placed after a note increases its length by half of the original value. This can be written as a formula: Dotted note = note + (note × ½). For example, a dotted minim = 2 + 1 = 3 crotchet beats, and a dotted crotchet = 1 + ½ = 1½ crotchet beats (or 3 quavers).

音符后的附点将它的时值增加原有时值的一半。公式可以写成：附点音符 = 音符 + (音符 × ½)。例如，附点二分音符 = 2 + 1 = 3 个四分音符拍；附点四分音符 = 1 + ½ = 1½ 个四分音符拍（即 3 个八分音符）。

A tie is a curved line that joins two notes of the same pitch. The durations are added together: tied note = note₁ + note₂. No new attack is played on the second note; it simply extends the sound. Ties are often used across bar lines when a note value cannot be shown by a single dotted note.

连线是一条连接两个同音高音符的弧线。其时值为两个音符相加：连线音符 = 音符₁ + 音符₂。第二个音符不需要重新演奏，只是延续声音。当附点音符不足以表示跨小节的长音时，常常使用连线。

These two devices are your tools for creating durations that do not fit neatly into the standard note‑value tree.

这两种工具让你能够创作出标准音符树无法直接表示的时间长度。

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4. Tempo & Dynamics | 速度与力度标记

Tempo is the speed of the beat, measured in beats per minute (BPM). The formula is: Tempo = number of beats / minute. In KS3 music you will often see Italian tempo terms, which act as a quick reference for approximate BPM ranges.

速度是节拍快慢的程度，以每分钟拍数（BPM）计量。公式为：速度 = 拍数 / 分钟。在 KS3 音乐中你常会看到意大利语速度术语，它们相当于大致 BPM 范围的快速参考。

• Largo – very slow (approx. 40–60 BPM)

  广板 – 非常慢（约 40–60 BPM）

• Adagio – slow and stately (approx. 66–76 BPM)

  柔板 – 缓慢而庄重（约 66–76 BPM）

• Andante – walking pace (approx. 76–108 BPM)

  行板 – 步行速度（约 76–108 BPM）

• Moderato – moderate speed (approx. 108–120 BPM)

  中板 – 中等速度（约 108–120 BPM）

• Allegro – fast, lively (approx. 120–168 BPM)

  快板 – 快速、活泼（约 120–168 BPM）

• Presto – very fast (approx. 168–200 BPM)

  急板 – 非常快（约 168–200 BPM）

Dynamics indicate how loud or soft to play. The standard scale from softest to loudest uses abbreviations: pp (pianissimo, very soft), p (piano, soft), mp (mezzo‑piano, moderately soft), mf (mezzo‑forte, moderately loud), f (forte, loud), ff (fortissimo, very loud). Crescendo (cresc.) means gradually getting louder, diminuendo (dim.) gradually softer.

力度标记指示演奏的强弱。从最弱到最强的标准力度级别为：pp（很弱），p（弱），mp（中弱），mf（中强），f（强），ff（很强）。渐强（cresc.）表示逐渐变强，渐弱（dim.）表示逐渐变弱。

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5. Pitch & Clefs | 音高与谱号

A clef is a symbol placed at the beginning of the stave to assign specific pitches to the lines and spaces. The treble clef (G clef) curls around the second line, fixing it as G above middle C. The bass clef (F clef) places its two dots around the fourth line, marking it as F below middle C.

谱号是放在谱表开头的符号，用以确定各条线和间所代表的音高。高音谱号（G 谱号）环绕第二线，将该线定为中央 C 之上的 G。低音谱号（F 谱号）的两个点夹住第四线，将其标记为中央 C 之下的 F。

Mnemonics help you read notes quickly. For treble clef lines: E G B D F (Every Good Boy Deserves Football); spaces: F A C E (spelling FACE). For bass clef lines: G B D F A (Great Big Dogs Fight Animals); spaces: A C E G (All Cows Eat Grass).

利用口诀可以帮你快速读谱。高音谱号线：E G B D F（Every Good Boy Deserves Football）；间：F A C E（拼成 FACE）。低音谱号线：G B D F A（Great Big Dogs Fight Animals）；间：A C E G（All Cows Eat Grass）。

Middle C sits on a ledger line between the two staves, acting as the pivot of the grand staff. Understanding clefs is the first formula for mapping written music to keyboard or instrument.

中央 C 位于两谱表之间的加线上，是整个大谱表的枢纽。理解谱号是将乐谱映射到键盘或乐器上的首要公式。

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6. Major Scale Formula | 大调音阶公式

Every major scale is built on exactly the same pattern of tones (T) and semitones (S). A tone equals two semitones. The formula is: T T S T T T S. In whole‑step / half‑step language: W W H W W W H.

任何大调音阶都由完全相同的全音（T）与半音（S）模式构成。全音等于两个半音。公式为：全 全 半 全 全 全 半。或写作：W W H W W W H。

• C major: C – D (T) – E (T) – F (S) – G (T) – A (T) – B (T) – C (S)

  C 大调：C–D（全）–E（全）–F（半）–G（全）–A（全）–B（全）–C（半）

• G major: G – A (T) – B (T) – C (S) – D (T) – E (T) – F♯ (T) – G (S) — one sharp required to keep the pattern

  G 大调：G–A–B–C–D–E–F♯–G，需要一个升号来保持模式

• F major: F – G (T) – A (T) – B♭ (S) – C (T) – D (T) – E (T) – F (S) — one flat required

  F 大调：F–G–A–B♭–C–D–E–F，需要一个降号来保持模式

This pattern is the fundamental formula from which all key signatures and major‑scale melodies are derived.

这个模式是产生所有调号和所有大调旋律的基础公式。

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7. Minor Scale Types & Formulas | 小调音阶类型与公式

Minor scales come in three main forms, each with its own interval formula. The natural minor is simply the major scale pattern starting on the 6th degree: T S T T S T T (W H W W H W W). For A natural minor (no sharps/flats): A – B (T) – C (S) – D (T) – E (T) – F (S) – G (T) – A (T).

小调音阶有三种主要形式，各有其独特的音程公式。自然小调就是从大调第六级开始的模式：全 半 全 全 半 全 全（W H W W H W W）。以 a 自然小调（无升无降）为例：A–B–C–D–E–F–G–A。

The harmonic minor raises the 7th degree by a semitone. Formula: T S T T S (T + S) S. In A harmonic minor, the G becomes G♯, creating an augmented second between the 6th and 7th degrees (F – G♯ is three semitones).

和声小调将第七级升高半音。公式：全 半 全 全 半 增二度 半。a 和声小调将 G 变为 G♯，在六级与七级之间产生一个增二度（F 到 G♯ 为三个半音）。

The melodic minor alters both the 6th and 7th degrees when ascending: T S T T T T S (W H W W W W H). Descending, it reverts to the natural minor pattern. So A melodic minor ascending: A – B – C – D – E – F♯ – G♯ – A; descending: A – G – F – E – D – C – B – A.

旋律小调在上行时升高六级和七级：全 半 全 全 全 全 半（W H W W W W H）。下行时恢复为自然小调。a 旋律小调上行：A–B–C–D–E–F♯–G♯–A；下行：A–G–F–E–D–C–B–A。

Recognising these three formulas helps you interpret minor‑key pieces and compose with emotional variety.

识别这三种公式有助于你理解小调作品，并能在作曲时表达丰富的情感变化。

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8. Key Signatures & Circle of Fifths | 调号与五度圈

The circle of fifths is a visual theorem that organises all major and minor keys. Moving clockwise from C major, each step adds one sharp; the order of sharps is F♯, C♯, G♯, D♯, A♯, E♯, B♯. Moving anticlockwise from C, each step adds one flat; the order of flats is B♭, E♭, A♭, D♭, G♭, C♭, F♭.

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