📚 Year 9 CAIE Music: Quick-Reference Handbook of Rules and Formulas | Year 9 CAIE 音乐：公式定理速查手册
In music, there isn't a formula in the mathematical sense, but there are many rules, patterns and 'recipes' that you need to remember. This quick-reference handbook collects all the essential 'formulas' for Year 9 CAIE Music – from note values and intervals to chord spellings and cadences. Think of it as your music theory cheat sheet.
在音乐中，虽然没有数学意义上的公式，但有许多规则、模式和“配方”需要记住。这本速查手册收集了 Year 9 CAIE 音乐的所有基本“公式”——从音符时值和音程到和弦拼写与终止式。你可以把它当作音乐理论的速查表。
1. Note and Rest Values | 音符与休止符时值
Each note value has a corresponding rest of exactly the same duration. Learning the proportional relationships between notes is like memorising a set of simple division equations.
每种音符时值都有对应时长相等的休止符。掌握音符之间的比例关系就像记忆一组简单的除法等式。
A semibreve (whole note) lasts for 4 beats in 4/4 time.
全音符（semibreve）在4/4拍中持续4拍。
A minim (half note) lasts for 2 beats.
二分音符（minim）持续2拍。
A crotchet (quarter note) lasts for 1 beat.
四分音符（crotchet）持续1拍。
A quaver (eighth note) lasts for 1/2 beat; two quavers make one crotchet.
八分音符（quaver）持续半拍；两个八分音符等于一个四分音符。
A semiquaver (sixteenth note) lasts for 1/4 beat.
十六分音符（semiquaver）持续四分之一拍。
d note adds half of its original value. For example, a dotted minim lasts 2 + 1 = 3 beats.
附点音符增加原时值的一半。例如，附点二分音符持续 2 + 1 = 3 拍。
The following table shows the most common note–rest relationships:
下表展示了最常见的音符与休止符关系：
| English Name | 中文名称 | Duration (simple time) |
|---|---|---|
| Semibreve (whole note) | 全音符 | 4 beats |
| Minim (half note) | 二分音符 | 2 beats |
| Crotchet (quarter note) | 四分音符 | 1 beat |
| Quaver (eighth note) | 八分音符 | 1/2 beat |
| Semiquaver (sixteenth note) | 十六分音符 | 1/4 beat |
2. Time Signatures and Rhythm | 拍号与节奏
The top number of a time signature tells you how many beats are in each bar. The bottom number tells you what kind of note gets one beat.
拍号的分子表示每小节有几拍，分母表示以什么音符为一拍。
In 2/4 time, there are 2 crotchet beats per bar.
在2/4拍中，每小节有2个四分音符拍。
In 3/4 time, there are 3 crotchet beats per bar.
在3/4拍中，每小节有3个四分音符拍。
In 4/4 time (common time, C), there are 4 crotchet beats per bar.
在4/4拍（普通拍子，标记为C）中，每小节有4个四分音符拍。
In 6/8 time, there are 2 dotted-crotchet beats per bar; each beat divides into three quavers.
在6/8拍中，每小节有2个附点四分音符拍；每拍可分成三个八分音符。
When beaming quavers and semiquavers, group them to show each beat clearly. In 2/4, two quavers are beamed together; in 3/4, three quavers may be beamed if they belong to the same beat, but usually you beam per beat.
连接八分音符和十六分音符的符尾时，要清晰地显示出每一拍。在2/4拍中，两个八分音符连在一起；在3/4拍中，若属于同一拍，三个八分音符可以连在一起，但通常按拍分开连接。
A triplet squeezes three equal notes into the time normally taken by two of the same kind. It is marked with a '3' above or below the notes.
三连音将三个等时值音符挤入原本由两个同类型音符占据的时值中，上方或下方标注数字“3”。
3. Clefs and Pitch | 谱号与音高
The treble clef (G clef) curls around the second line, fixing that line as G above middle C.
高音谱号（G谱号）环绕第二线，将该线定为中央C上方的G音。
The bass clef (F clef) has two dots that sit either side of the fourth line, fixing that line as F below middle C.
低音谱号（F谱号）的两个圆点跨骑在第四线两侧，将该线定为中央C下方的F音。
Middle C sits on one ledger line below the treble stave, and one ledger line above the bass stave.
中央C在五线谱中的位置：位于高音谱表下一线，以及低音谱表上一线。
An 8va sign above notes means play one octave higher; an 8va or 8vb below means play one octave lower.
音符上方标有8va记号表示高八度演奏；下方标8va或8vb表示低八度演奏。
Accidentals last through the bar unless cancelled: a sharp (♯) raises a note by one semitone, a flat (♭) lowers it, and a natural (♮) returns it to the original pitch.
临时变音记号在所在小节内有效，除非被取消：升号（♯）升高半音，降号（♭）降低半音，还原号（♮）回到原来音高。
4. Key Signatures and Scales | 调号与音阶
A major scale follows the pattern: tone, tone, semitone, tone, tone, tone, semitone (T T S T T T S).
大调音阶的模式为：全音、全音、半音、全音、全音、全音、半音（T T S T T T S）。
A natural minor scale uses the pattern: T S T T S T T.
自然小调音阶的模式为：T S T T S T T。
A harmonic minor scale has a raised 7th degree, creating an augmented 2nd between the 6th and 7th notes: T S T T S T+S S.
和声小调音阶升高第VII级音，在第VI级与第VII级之间形成一个增二度：T S T T S T+S S。
A melodic minor scale ascends with a raised 6th and 7th degree (T S T T T T S) and descends as natural minor (T T S T T S T).
旋律小调音阶上行时升高第VI、VII级音（T S T T T T S），下行时还原为自然小调（T T S T T S T）。
The order of sharps in key signatures is: F♯, C♯, G♯, D♯, A♯, E♯, B♯.
调号中升记号的顺序为：F♯、C♯、G♯、D♯、A♯、E♯、B♯。
The order of flats is: B♭, E♭, A♭, D♭, G♭, C♭, F♭.
降记号的顺序为：B♭、E♭、A♭、D♭、G♭、C♭、F♭。
To find the relative minor of a major key, go down three semitones from the tonic. For example, C major's relative minor is A minor.
寻找大调的关系小调，从主音向下移低三个半音。例如，C大调的关系小调是a小调。
5. Intervals | 音程
An interval measures the distance between two pitches in semitones. The naming of an interval depends on its number (e.g., 2nd, 3rd) and its quality (major, minor, perfect, augmented, diminished).
音程衡量两个音高之间以半音为单位的距离。音程的名称既取决于级数（如二度、三度），也取决于性质（大、小、纯、增、减）。
A perfect unison: 0 semitones.
纯一度：0个半音。
A minor 2nd: 1 semitone (e.g., E–F).
小二度：1个半音（如E–F）。
A major 2nd: 2 semitones (e.g., C–D).
大二度：2个半音（如C–D）。
A minor 3rd: 3 semitones (e.g., A–C).
小三度：3个半音（如A–C）。
A major 3rd: 4 semitones (e.g., C–E).
大三度：4个半音（如C–E）。
A perfect 4th: 5 semitones (e.g., C–F).
纯四度：5个半音（如C–F）。
A tritone (augmented 4th / diminished 5th): 6 semitones.
三全音（增四度/减五度）：6个半音。
A perfect 5th: 7 semitones (e.g., C–G).
纯五度：7个半音（如C–G）。
A minor 6th: 8 semitones (e.g., E–C).
小六度：8个半音（如E–C）。
A major 6th: 9 semitones (e.g., C–A).
大六度：9个半音（如C–A）。
A minor 7th: 10 semitones (e.g., D–C).
小七度：10个半音（如D–C）。
A major 7th: 11 semitones (e.g., C–B).
大七度：11个半音（如C–B）。
A perfect octave: 12 semitones.
纯八度：12个半音。
Interval shortcut: Perfect 5th = 7 semitones
纯五度公式：7个半音
6. Triads and Inversions | 三和弦与转位
A triad is a three-note chord built in thirds. The formula for a major triad is: root + major 3rd (4 semitones) + perfect 5th (7 semitones).
三和弦是由三个音按三度叠置构成的和弦。大三和弦的公式为：根音 + 大三度（4个半音）+
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