Year 10 CCEA Music: Quick-Reference Formulae & Theorems Handbook | CCEA 音乐公式定理速查手册

📚 Year 10 CCEA Music: Quick-Reference Formulae & Theorems Handbook | CCEA 音乐公式定理速查手册

Music theory is built on patterns that can be expressed as clear, repeatable formulas – from counting semitones in an interval to constructing chords. This handbook gathers the essential formulas, theorems and quick-reference rules that every Year 10 CCEA Music student needs for composing, listening and appraising. Work through each section to build a mental toolkit you can use instantly in the exam hall.

音乐理论建立在可以被清晰表达为可重复公式的模式之上——从数音程的半音到构建和弦。这本手册汇集了每一位 CCEA 10 年级音乐学生在作曲、听辨和评析中所需的关键公式、定理和速查规则。逐节攻克，你就能建立起一整套在考场中可以立刻派上用场的思维工具箱。

1. Interval Semitone Formula | 音程半音公式

Every interval is defined by two things: a number (the staff distance, e.g. 2nd, 3rd, 5th) and a quality (perfect, major, minor, augmented, diminished). The distance in semitones follows a fixed pattern based on the interval number. The table below gives the semitone count for the most common intervals built from a given tonic.

每一个音程都由两个因素定义：度数（谱表上的线间距离，如二度、三度、五度）和性质（纯、大、小、增、减）。以半音计的距离遵循着一个基于音程度数的固定模式。下表给出了从给定主音出发最常见的音程所对应的半音数。

As a quick theorem: the semitone count of a major 2nd, 3rd, 6th or 7th is always one semitone larger than the corresponding minor interval. Perfect intervals (unison, 4th, 5th, octave) have fixed semitone values; if you raise a perfect interval by a semitone it becomes augmented, if you lower it by a semitone it becomes diminished.

速记定理：大二度、三度、六度、七度的半音数总是比对应的小音程多一个半音。纯音程（一度、四度、五度、八度）有固定的半音值；将纯音程升高一个半音便成为增音程，降低一个半音则成为减音程。

2. Major Scale Formula | 大调音阶公式

All major scales share the same step pattern: Tone – Tone – Semitone – Tone – Tone – Tone – Semitone. Using T for a tone (2 semitones) and S for a semitone (1 semitone), the formula is written as:

所有大调音阶都共享相同的音级进行模式：全音 – 全音 – 半音 – 全音 – 全音 – 全音 – 半音。用 T 表示一个全音（2 个半音），S 表示一个半音（1 个半音），公式可写为：

T - T - S - T - T - T - S

sharps or flats are added unless the pattern demands them; this is why G major needs an F♯ to keep the T–S pattern between the 6th and 7th degrees.

从任意主音开始，依次套用这一序列即可。例如 C 大调音阶为：C (全→) D (全→) E (半→) F (全→) G (全→) A (全→) B (半→) C。除非模式本身要求加入升降号，否则无需添加；这就是为何 G 大调需要 F♯ 来保持第 6、7 级之间的全-半关系。

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3. Minor Scale Formulae | 小调音阶公式

There are three main forms of the minor scale, each with its own pattern of tones and semitones. For clarity, the following shows the step formulas starting from the tonic.

小调音阶有三种主要形式，每种形式都有其自身的全音与半音模式。为清晰起见，下面列出从主音开始的音级进行公式。

Natural minor: T - S - T - T - S - T - T (e.g. A–B–C–D–E–F–G–A).
自然小调：全 – 半 – 全 – 全 – 半 – 全 – 全（例如 A–B–C–D–E–F–G–A）。

Harmonic minor: T - S - T - T - S - augmented 2nd (3 semitones) - S. The 7th degree is raised, creating a characteristic gap of three semitones between the 6th and 7th degrees.
和声小调：全 – 半 – 全 – 全 – 半 – 增二度（3 个半音）– 半。第七级被升高，使得第六级与第七级之间形成一个标志性的三半音差距。

Melodic minor (ascending): T - S - T - T - T - T - S (both 6th and 7th raised). The descending form often reverts to natural minor.
旋律小调（上行）：全 – 半 – 全 – 全 – 全 – 全 – 半（第六和第七级均升高）。下行通常回到自然小调形式。

Use these formulae to construct any minor scale accurately: pick the tonic, count the semitones according to the chosen form, and add the necessary accidentals.

使用这些公式便能准确地构建任何小调音阶：选定主音，根据所选形式数出半音，并加上必要的临时记号。

4. Chord Construction Formulae | 和弦构成公式

Chords are built by stacking intervals on top of a root note. The most common triads and seventh chords follow precise semitone stacking rules.

和弦是通过在根音上方叠置音程而构成的。最常见的三和弦与七和弦遵循精确的半音叠置规则。

When you need to spell a chord, start from the root and count up the required semitones while keeping the letter names in the correct sequence (e.g. root–3rd–5th for triads, root–3rd–5th–7th for seventh chords).

当你需要写出某个和弦的音名时，从根音开始，向上数出所需半音，同时保持字母名称的正确顺序（例如三和弦是根音–三音–五音，七和弦是根音–三音–五音–七音）。

5. Key Signature Calculation | 调号计算

Key signatures indicate which notes are consistently sharp or flat throughout a piece. The order of sharps and flats follows a fixed cycle of fifths.

调号表明了全曲中哪些音需要持续升降。升号和降号出现的顺序遵循一个固定的纯五度循环。

Sharps: F♯ - C♯ - G♯ - D♯ - A♯ - E♯ - B♯ me for a sharp signature, take the last sharp and go up one semitone (e.g. last sharp is D♯ → E major). For the relative minor, go down 3 semitones from the major tonic.
升号调：升号顺序为 F♯ - C♯ - G♯ - D♯ - A♯ - E♯ - B♯。要找出升号调的大调名称，找到最后一个升号并向上移动一个半音（如最后一个升号为 D♯ → E 大调）。关系小调的主音则是从大调主音向下移动 3 个半音。

Flats: B♭ - E♭ - A♭ - D♭ - G♭ - C♭ - F♭. For major keys using flats, the penultimate flat is the tonic (except F major, which has one flat). Alternatively, the second-to-last flat tells you the major key name directly.
降号调：降号顺序为 B♭ - E♭ - A♭ - D♭ - G♭ - C♭ - F♭。对于使用降号的大调，倒数第二个降号就是主音（F 大调只有一个降号，须记忆）。也就是说，只需看倒数第二个降号，便可直接得出大调名称。

Memorise the relative minor formula: Relative minor tonic = Major tonic − 3 semitones.

记住关系小调公式：关系小调主音 = 大调主音 − 3 个半音。

6. Circle of Fifths Relationships | 五度圈关系

The circle of fifths arranges all 12 pitches so that each step clockwise adds a sharp (or removes a flat), moving up a perfect 5th (7 semitones). Moving anticlockwise adds a flat (or removes a sharp), moving down a perfect 5th (or up a perfect 4th).

五度圈将十二个音高排列起来，顺时针每走一步增加一个升号（或减少一个降号），向上移动一个纯五度（7 个半音）。逆时针每走一步增加一个降号（或减少一个升号），向下移动一个纯五度（或向上移动一个纯四度）。

Order of major keys circling clockwise: C – G – D – A – E – B – F♯ – C♯ (and so on). The number of sharps increases from 0 to 7; then the flats take over from 5 flats down to 0. Use this cycle to quickly drift between closely related keys in modulations.

大调顺时针顺序：C – G – D – A – E – B – F♯ – C♯（依此类推）。升号数量由 0 增加到 7；随后

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