Year 11 CAIE Music Quick Reference: Formulas & Theorems | IGCSE音乐公式定理速查手册

📚 Year 11 CAIE Music Quick Reference: Formulas & Theorems | IGCSE音乐公式定理速查手册

This quick reference handbook condenses the essential music theory ‘formulas’ and ‘theorems’ required for the CAIE IGCSE Music examination. From note values and intervals to chord construction and cadences, each section provides a clear, formulaic summary to help you master the structural principles of music. Keep it handy for revision and application in listening, performing and composing.

这本速查手册浓缩了CAIE IGCSE音乐考试必备的核心音乐理论“公式”与“定理”。从音符时值与音程，到和弦构建与终止式，每一个部分都以清晰的公式化总结，帮助您掌握音乐的结构原理。可随身携带用于复习，并应用于听力、演奏与作曲中。

1. Note Durations and Rests | 音符时值与休止符

The duration of notes follows a simple doubling and halving formula. One semibreve (whole note) equals two minims, four crotchets, eight quavers, and sixteen semiquavers. Rests mirror these relative durations precisely. A dot adds half of the original note’s value; a dotted minim, for example, lasts as long as a minim plus a crotchet. Triplets indicate three notes played evenly in the time of two; they are notated with a small ‘3’ above or below the note group.

音符时值遵循简单的倍增与减半公式。一个全音符等于两个二分音符、四个四分音符、八个八分音符和十六个十六分音符。休止符的相对时值与此完全相同。附点增加原音符时值的一半；例如，附点二分音符的时值等于二分音符加四分音符。三连音表示在原本两个音符的时值内均匀演奏三个音，在音符组上方或下方标记小“3”。

Rests must also respect the metre; a whole-bar rest uses a semibreve rest even in 3/4. Multiple rests in one bar are combined to expose the beat structure clearly.

休止符也必须遵循节拍；整小节休止即使在3/4拍中也使用全休止符。一小节内的多个休止符应组合起来以清晰呈现节拍结构。

2. Time Signatures and Rhythmic Grouping | 拍号与节奏组合

Simple time signatures (2/4, 3/4, 4/4) have a top number of 2, 3 or 4 indicating beats per bar, with the bottom number 4 showing a crotchet beat. Compound time signatures (6/8, 9/8, 12/8) use a dotted crotchet as the main beat. The time signature formula helps decide beaming: in simple time, beams connect notes within a single beat; in compound time, three quavers are beamed together to form one dotted crotchet beat.

简单拍号（2/4、3/4、4/4）的上方数字为2、3或4，表示每小节的拍数，下方数字4表示以四分音符为一拍。复合拍号（6/8、9/8、12/8）以附点四分音符为主要拍点。拍号公式决定了符杠的用法：在简单拍子中，符杠连接同一拍内的音符；在复合拍子中，三个八分音符用符杠连成一个附点四分音符拍组。

Irregular time signatures such as 5/4 and 7/8 group beats asymmetrically. In 5/4, the grouping is often 3+2 or 2+3, clearly shown by beams or ties.

不规则拍号如5/4与7/8，其拍子组合不对称。5/4拍通常按3+2或2+3分组，并通过符杠或连线清楚体现。

3. Key Signatures and the Circle of Fifths | 调号与五度圈

Sharps appear in this fixed order: F♯, C♯, G♯, D♯, A♯, E♯, B♯. To find the major key from a sharp key signature, take the last sharp and move up a semitone. For flat key signatures, the order is B♭, E♭, A♭, D♭, G♭, C♭, F♭. The penultimate flat names the major key; the exception is F major, which has only B♭.

升号出现顺序固定为：F♯、C♯、G♯、D♯、A♯、E♯、B♯。从升号调找出大调主音的方法：取最后一个升号并上行半音。降号调顺序为：B♭、E♭、A♭、D♭、G♭、C♭、F♭。倒数第二个降号即为该大调的名称；例外是F大调，只有一个降号B♭。

Relative minor keys lie a minor third (three semitones) below the major tonic. The circle of fifths illustrates that moving clockwise adds a sharp, while moving anticlockwise adds a flat.

关系小调位于大调主音下方小三度（三个半音）。五度圈显示顺时针每移动一步增加一个升号，逆时针移动则增加一个降号。

4. Intervals: Formula for Distance and Quality | 音程：距离与性质的公式

To name an interval, count the letter names from the lower note to the upper note inclusive to determine its number (e.g. C to E is a 3rd). For quality, build a major scale on the lower note. If the upper note matches the scale, the interval is major for 2nds, 3rds, 6ths and 7ths, or perfect for unisons, 4ths, 5ths and octaves. If the upper note is one semitone smaller than the major/perfect version, the interval becomes minor (for 2nds, 3rds, 6ths, 7ths) or diminished (for perfect intervals). An augmented interval is one semitone larger than major or perfect.

为音程命名时，先计算从低音到高音包含的所有字母名以确定度数（例如C到E为三度）。性质判断需以低音为根音构建大调音阶。若高音正好是音阶中的音，则二度、三度、六度、七度为“大”，同度、四度、五度、八度为“纯”。若高音比大/纯音程低半音，则对于二、三、六、七度变为“小”，对于纯音程变为“减”。增音程比大或纯音程高半音。

The interval inversion formula: new interval = 9 minus original number. Major becomes minor, minor becomes major, perfect stays perfect, and augmented becomes diminished.

音程转位公式：新音程度数 = 9 – 原度数。大与小互换，纯保持纯，增与减互换。

5. Major and Minor Scales: Construction Formulas | 大小调音阶构建公式

Major scale formula (in tones and semitones): T T S T T T S. The semitones occur between the 3rd–4th and 7th–8th degrees. Every major scale can be built from a tonic using this pattern.

大调音阶公式（全音与半音）：全 全 半 全 全 全 半。半音位于第3–4级与第7–8级之间。任何大调音阶都可以通过此模式从主音构建。

Natural minor: T S T T S T T. Harmonic minor raises the 7th degree, creating an augmented 2nd between the 6th and 7th. Melodic minor raises both the 6th and 7th degrees ascending, but reverts to natural minor descending.

自然小调：全 半 全 全 半 全 全。和声小调升高第7级，在第6–7级之间形成增二度。旋律小调上行时升高第6级和第7级，下行时还原为自然小调。

6. Triads and Seventh Chords: Building Rules | 三和弦与七和弦构建法则

A triad consists of a root, a 3rd and a 5th. Major triad formula: major 3rd + minor 3rd (4 semitones + 3 semitones). Minor triad: minor 3rd + major 3rd (3 + 4). Diminished triad: minor 3rd + minor 3rd (3

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