Year 8 CIE Music: Formula & Theorem Quick Reference Handbook | 公式定理速查手册

📚 Year 8 CIE Music: Formula & Theorem Quick Reference Handbook | 公式定理速查手册

This handbook compiles the essential formulas, patterns, and theoretical rules you need for Year 8 CIE Music. Use it to quickly recall note values, scale constructions, interval semitone counts, chord recipes, cadence progressions, and more.

本手册汇编了 Year 8 CIE 音乐所需的核心公式、模式与理论规则。你可以用它快速查阅音符时值、音阶构成、音程半音计数、和弦配方、终止式进行等内容。

1. Note Values & Rests | 音符时值与休止符

The semibreve (whole note) is the base unit; all other durations follow a simple doubling or halving pattern.

全音符是基本单位；所有其他时值遵循简单的加倍或减半模式。

1 semibreve = 2 minims = 4 crotchets = 8 quavers = 16 semiquavers = 32 demisemiquavers.

1 个全音符 = 2 个二分音符 = 4 个四分音符 = 8 个八分音符 = 16 个十六分音符 = 32 个三十二分音符。

The same ratios apply to rests: semibreve rest, minim rest, crotchet rest, quaver rest, etc.

相同的比例适用于休止符：全休止符、二分休止符、四分休止符、八分休止符等。

its original value. For example, a dotted minim = minim + crotchet (3 crotchets in total).

附点加在音符或休止符后，增加原有时值的一半。例如，附点二分音符 = 二分音符 + 四分音符（共3个四分音符）。

2. Time Signatures & Meter | 拍号与节拍

The top number of a time signature tells how many beats are in each bar; the bottom number tells which note value counts as one beat.

拍号的上方数字表示每小节有几拍；下方数字表示以哪种音符为一拍。

Simple time: each beat divides naturally into two equal parts. Simple duple: 2/4, 2/2; simple triple: 3/4, 3/2; simple quadruple: 4/4 (common time).

单拍子：每一拍自然分为两个等份。单二拍：2/4, 2/2；单三拍：3/4, 3/2；单四拍：4/4（普通拍子）。

Compound time: each beat divides into three equal parts. Compound duple: 6/8 (two dotted-crotchet beats); compound triple: 9/8; compound quadruple: 12/8.

复拍子：每一拍分为三个等份。复二拍：6/8（两个附点四分音符拍）；复三拍：9/8；复四拍：12/8。

To find the number of beats per bar in compound time, divide the top number by 3.

在复拍子中求每小节拍数，将上方数字除以3。

3. The Major Scale Formula | 大调音阶公式

All major scales follow the same pattern of tones (T) and semitones (S): T – T – S – T – T – T – S.

所有大调音阶遵循相同的全音（T）和半音（S）模式：T – T – S – T – T – T – S。

Using scale degrees, the pattern is: 1 (tonic), 2 (supertonic), 3 (mediant), 4 (subdominant), 5 (dominant), 6 (submediant), 7 (leading note), 8 (tonic).

用音级表示，模式为：1（主音）、2（上主音）、3（中音）、4（下属音）、5（属音）、6（下中音）、7（导音）、8（主音）。

Example: C major – C (T) D (T) E (S) F (T) G (T) A (T) B (S) C. No sharps or flats.

示例：C大调 – C（T）D（T）E（S）F（T）G（T）A（T）B（S）C。没有升降号。

Remember: half steps occur between scale degrees 3‑4 and 7‑8.

记住：半音出现在音级3-4和7-8之间。

4. Minor Scale Patterns | 小调音阶模式

Natural minor scale (pure form): T – S – T – T – S – T – T. It uses the same key signature as its relative major and starts on the 6th degree of the major scale.

自然小调（纯形式）：T – S – T – T – S – T – T。使用其关系大调的调号，并从大调第六级开始。

Harmonic minor scale: T – S – T – T – S – T+½ – S. The 7th degree is raised by a semitone, creating an augmented second (T+½) between the 6th and 7th degrees.

和声小调：T – S – T – T – S – T+½ – S。第七级升高半音，在第六级与第七级之间形成增二度（T+½）。

Melodic minor scale ascending: T – S – T – T – T – T – S (raised 6th and 7th). Descending: same as natural minor.

旋律小调上行：T – S – T – T – T – T – S（升高六级和七级）。下行：与自然小调相同。

Example in A minor (no sharps/flats): natural – A B C D E F G A; harmonic – A B C D E F G♯ A; melodic ascending – A B C D E F♯ G♯ A.

以A小调为例（无调号）：自然 – A B C D E F G A；和声 – A B C D E F G♯ A；旋律上行 – A B C D E F♯ G♯ A。

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

The order of sharps is always: F♯ C♯ G♯ D♯ A♯ E♯ B♯. Memorise it as: Father Charles Goes Down And Ends Battle.

升号出现的顺序总是：F♯ C♯ G♯ D♯ A♯ E♯ B♯。记忆口诀：Father Charles Goes Down And Ends Battle。

The order of flats is the reverse: B♭ E♭ A♭ D♭ G♭ C♭ F♭ (Battle Ends And Down Goes Charles’ Father).

降号顺序与升号相反：B♭ E♭ A♭ D♭ G♭ C♭ F♭（Battle Ends And Down Goes Charles’ Father）。

To find the relative minor of any major key, go down a minor third (3 semitones) from the major tonic. For example, C major’s relative minor is A minor; G major’s is E minor.

要找到任意大调的关系小调，从大调主音向下小三度（3个半音）。例如，C大调的关系小调是A小调；G大调的关系小调是E小调。

Key signature theorem: the last sharp in the key signature is the leading note (7th degree); raise it by a semitone to find the major tonic. For flat keys, the penultimate flat is the tonic.

调号定理：调号中最后一个升号是导音（第七级）；将其升高半音即得到大调主音。对于降号调，倒数第二个降号是主音。

6. Interval Formulas | 音程公式

Intervals are measured by the number of semitones between two notes. Use this table as a quick reference.

音程由两个音之间的半音数决定。使用下表作为快速参考。

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Interval Name (English/中文)	Semitones	Example
Perfect unison / 纯一度	0	C – C
Minor 2nd / 小二度	1	C – D♭
Major 2nd / 大二度	2	C – D
Minor 3rd / 小三度	3	C – E♭
Major 3rd / 大三度	4	C – E
Perfect 4th / 纯四度	5	C – F
Augmented 4th / Diminished 5th (Tritone) / 增四度/减五度（三全音）	6	C – F♯ / C – G♭
Perfect 5th / 纯五度	7	C – G
Minor 6th / 小六度	8	C – A♭
Major 6th / 大六度	9	C – A
Minor 7th / 小七度	10	C – B♭
Major 7th / 大七度	11	C – B
Perfect octave / 纯八度	12	C – C

Rule: major intervals become minor when lowered by a semitone; perfect intervals become diminished or augmented.

规则：大音程降低半音变为小音程；纯音程降低变为减音程，升高变为增音程。

7. Chord Construction: Triads | 三和弦构成

A triad is a three-note chord built from stacked thirds. The formula uses the number of semitones between the root, third, and fifth.

三和弦是由三度叠置的三个音构成的和弦。公式使用根音、三音、五音之间的半音数。

Major triad: root + 4 semitones + 3 semitones. Example: C – E – G (C major).

大三和弦：根音 + 4半音 + 3半音。示例：C – E – G（C大三和弦）。

Minor triad: root + 3 semitones + 4 semitones. Example: C – E♭ – G (C minor).

小三和弦：根音 + 3半音 + 4半音。示例：C – E♭ – G（C小三和弦）。

Diminished triad: root + 3 + 3. Example: C – E♭ – G♭ (C dim).

减三和弦：根音 + 3 + 3。示例：C – E♭ – G♭（C减三和弦）。

Augmented triad: root + 4 + 4. Example: C – E – G♯ (C aug).

增三和弦：根音 + 4 + 4。示例：C – E – G♯（C增三和弦）。

In a key, triads built on scale degrees are named with Roman numerals: I (tonic), ii (supertonic, minor in major keys), iii, IV, V, vi, vii° (diminished).

在调性内，建立在音级上的三和弦用罗马数字命名：I（主和弦）、ii（上主和弦，在大调中为小三和弦）、iii、IV、V、vi、vii°（减三和弦）。

8. Primary Chords & Cadences | 正三和弦与终止式

The primary chords in any major or minor key are I (tonic), IV (subdominant), and V (dominant). They contain all the notes of the scale and form the basis of harmonic progressions.

任何大小调的正三和弦是 I（主）、IV（下属）和 V（属）。它们包含了音阶中的所有音，构成和声进行的基础。

Cadences are musical punctuation formulas:

终止式是音乐的标点公式：

Perfect cadence: V – I. Sounds final and complete. In C major: G – C.

正格终止：V – I。听感结束而完整。在C大调中：G – C。

Plagal cadence: IV – I. Often called the ‘Amen’ cadence. In C major: F – C.

变格终止：IV – I。常被称为“阿门”终止。在C大调中：F – C。

Imperfect cadence: ends on V, creating an unfinished feeling. Common approach chords: I – V, ii – V, IV – V.

半终止：结束在 V 上，产生未完成感。常见的进行：I – V, ii – V, IV – V。

Interrupted (deceptive) cadence: V – vi. The ear expects I but gets vi instead. In C major: G – Am.

阻碍终止：V – vi。耳朵期待 I 却得到 vi。在C大调中：G – Am。

9. Rhythm: Dotted Notes & Ties | 节奏：附点与延音线

inal note + half its value. For a crotchet (1 beat), a dotted crotchet = 1 + ½ = 1½ beats.

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