Year 8 Cambridge Music: Quick Reference Formulas and Theorems | Year 8 剑桥音乐：公式与定理速查手册

📚 Year 8 Cambridge Music: Quick Reference Formulas and Theorems | Year 8 剑桥音乐：公式与定理速查手册

This handbook provides a concise collection of the most important ‘formulas’ and ‘theorems’ of music theory that you need for Year 8 Cambridge Music. Just like in mathematics, music follows patterns and rules that can be memorised and applied. From scale formulas to chord-building patterns, from interval calculations to cadence types, this quick-reference guide will help you revise and reinforce the essential concepts.

本手册汇集了 Year 8 剑桥音乐课程中你需要掌握的最重要的音乐理论“公式”与“定理”。就像数学一样，音乐也遵循可以记忆和运用的模式与规则。从音阶公式到和弦构建模式，从音程计算到终止式类型，这份速查指南将帮助你复习和巩固核心概念。

1. The Major Scale Formula | 大调音阶公式

A major scale is built using a specific sequence of tones (whole steps) and semitones (half steps). The fixed pattern, starting from the tonic note, is: Tone, Tone, Semitone, Tone, Tone, Tone, Semitone. This is often abbreviated as T-T-S-T-T-T-S. This formula guarantees that every major scale has the same interval structure and characteristic bright sound, no matter which note you start on.

大调音阶是通过特定的全音（T）和半音（S）顺序构建而成的。从主音开始，固定模式为：全音、全音、半音、全音、全音、全音、半音，常缩写为 T-T-S-T-T-T-S。这个公式确保了每个大调音阶都具有相同的音程结构和典型明亮的音响，无论从哪个音开始。

T – T – S – T – T – T – S

To build a C major scale, simply apply the formula: C→D (T), D→E (T), E→F (S), F→G (T), G→A (T), A→B (T), B→C (S) – no accidentals needed. For G major, start on G: G→A (T), A→B (T), B→C (S), C→D (T), D→E (T), E→F♯ (T), F♯→G (S). Notice that F must be sharpened to F♯ to create a tone between E and F♯ and a semitone back to G. This necessity for accidentals gives rise to key signatures.

构建 C 大调时直接套用公式：C→D (T)，D→E (T)，E→F (S)，F→G (T)，G→A (T)，A→B (T)，B→C (S) —— 无需升降号。对于 G 大调，从 G 开始：G→A (T)，A→B (T)，B→C (S)，C→D (T)，D→E (T)，E→F♯ (T)，F♯→G (S)。注意 F 必须升高为 F♯ 才能构成 E 到 F♯ 的全音以及回到 G 的半音。这种对临时记号的需求正是调号产生的缘由。

2. Minor Scale Types and Patterns | 小调音阶类型与模式

There are three main forms of the minor scale, each with its own formula of tones and semitones. The natural minor follows the pattern T-S-T-T-S-T-T, identical to the Aeolian mode. The harmonic minor raises the 7th degree to create a leading tone, giving T-S-T-T-S-3 semitones-S (an augmented 2nd between the 6th and 7th). The melodic minor ascends with a raised 6th and 7th (T-S-T-T-T-T-S) and descends like the natural minor.

小调音阶主要有三种形式，每种都有各自的全音与半音公式。自然小调遵循 T-S-T-T-S-T-T 模式，与爱奥利亚调式相同。和声小调升高第 VII 级音以构成导音，模式为 T-S-T-T-S-3个半音-S（第 VI 与 VII 级之间为增二度）。旋律小调上行时升高第 VI 和第 VII 级（T-S-T-T-T-T-S），下行则同自然小调。

Natural minor: T – S – T – T – S – T – T
Harmonic minor: T – S – T – T – S – 3 – S
Melodic minor (ascending): T – S – T – T – T – T – S

For example, A natural minor uses all white notes from A to A: A-B (T), B-C (S), C-D (T), D-E (T), E-F (S), F-G (T), G-A (T). In A harmonic minor, the G becomes G♯, creating the characteristic interval of an augmented 2nd between F and G♯. A melodic minor ascending raises F to F♯ and G to G♯, then reverts on the descent.

以 A 自然小调为例，使用从 A 到 A 的全部白键：A-B (T)，B-C (S)，C-D (T)，D-E (T)，E-F (S)，F-G (T)，G-A (T)。A 和声小调将 G 变为 G♯，在 F 与 G♯ 之间形成标志性的增二度。A 旋律小调上行时升高 F 为 F♯、G 为 G♯，下行时则返回自然小调形式。

3. Interval Calculation Rules | 音程计算法则

An interval is the distance between two pitches, measured in semitones. The quality and number of an interval can be determined by counting how many letter names are involved (the interval number) and the exact count of semitones. The table below gives the most common intervals within an octave.

音程是两音之间的距离，以半音为单位计量。音程的性质和度数可以通过数清涉及几个音名（即几度）和确切的半音数来确定。下表列出了八度以内最常见的音程。

To find the interval between two notes, count the letter names for the number, then count the semitones between them. For example, C to E spans three letters (C-D-E) so it is a 3rd; the semitone count is 4, which corresponds to a Major 3rd. Remember that perfect intervals (unison, 4th, 5th

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