📚 Year 9 CCEA Music: Quick Reference Handbook of Formulae and Theorems | CCEA 九年级音乐：公式定理速查手册
This handy reference compiles the essential 'formulae' and 'theorems' of music theory required for Year 9 CCEA Music. From note values to cadences, use this guide to quickly recall the building blocks of musical language.
这份便捷手册汇集了CCEA九年级音乐所需的核心“公式”与“定理”。从音符时值到终止式，用本指南快速回顾音乐语言的基本构件。
1. Note Values & Rest Equivalences | 音符与休止符时值等式
Every note symbol stands for a duration relative to the beat. The semibreve is the longest common value; each shorter note is exactly half the length of the previous one. Rests follow the same hierarchy.
每个音符符号代表相对于拍子的特定时值。全音符是最长的常见音符；每个较短的音符恰好是其前一个音符长度的一半。休止符遵循同样的层级。
| Note symbol | Name | Equivalent rest | Value (in crotchets) |
|---|---|---|---|
| 𝄴 | Semibreve | 𝄻 | 4 |
| 𝅗𝅥 | Minim | 𝄼 | 2 |
| ♩ | Crotchet | 𝄽 | 1 |
| ♪ | Quaver | 𝄾 | 1/2 |
| 𝅘𝅥𝅮 | Semiquaver | 𝄿 | 1/4 |
A dot placed after a note extends its duration by half of the original value. For example, a dotted crotchet equals a crotchet plus a quaver (1 ½ beats in simple time).
音符后加附点会将其时值延长原时值的一半。例如，附点四分音符等于一个四分音符加一个八分音符（在单拍子中为1 ½拍）。
A second dot adds half of the first dot's value. Thus a double-dotted minim equals minim + crotchet + quaver (3 ½ beats).
复附点（第二个附点）增加第一个附点时值的一半。因此，复附点二分音符等于二分音符 + 四分音符 + 八分音符（3 ½拍）。
2. Time Signatures & Beat Grouping Rules | 节拍记号与拍子分组定理
The top number of a time signature tells you how many beats are in each bar; the bottom number tells you which note value gets one beat. A '4' at the bottom means a crotchet beat.
拍号的上方数字表示每小节有几拍；下方数字表示以何种音符为一拍。下方为“4”表示以四分音符为一拍。
Simple time signatures (2/4, 3/4, 4/4) have a basic beat that divides into two equal parts. In compound time (6/8, 9/8, 12/8), the beat divides into three equal parts, and the top number shows the total of those divisions.
单拍号（2/4、3/4、4/4）的基本拍子等分为两部分。复拍号（6/8、9/8、12/8）的拍子等分为三部分，上方数字表示这些细分单元的总数。
Grouping Rule Theorem: Notes must be beamed together to show each whole beat clearly. In 6/8, quavers are beamed in groups of three, never in two or six.
分组定理：音符的符尾必须按照每一整拍进行组合。在6/8拍中，八分音符按三个一组连写，绝不按两个或六个连写。
3. Major Scale Formula | 大调音阶公式
Every major scale follows the same interval pattern of tones (T) and semitones (S). This is the fundamental formula for constructing any major key.
每个大调音阶都遵循相同的全音（T）与半音（S）模式。这是构建任何大调音阶的基本公式。
T – T – S – T – T – T – S
Check the formula on C major: the notes C D E F G A B C produce the steps C–D (T), D–E (T), E–F (S), F–G (T), G–A (T), A–B (T), B–C (S). No sharps or flats are needed because the natural spacing fits the formula.
用C大调验证此公式：音符C D E F G A B C产生的音程为 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，因为自然音程符合该公式。
To build a different major scale, start on a chosen note and apply the T–T–S–T–T–T–S pattern. Add sharps or flats as necessary to fit the semitone steps.
要构建其他大调音阶，从所选音符开始应用 T–T–S–T–T–T–S 模式，必要时添加升号或降号以符合半音布局。
4. Minor Scale Formulae | 小调音阶公式
There are three primary forms of the minor scale, each with its own formula, but all share a minor third above the tonic.
小调音阶有三种主要形式，各自有特定公式，但都在主音上方构建小三度。
Natural minor: T – S – T – T – S – T – T
The natural minor uses only the key signature and is the descending form of the classical melodic minor. Example in A minor: A–B (T), B–C (S), C–D (T), D–E (T), E–F (S), F–G (T), G–A (T).
自然小调只使用调号中的升降号，也是古典旋律小调的下行形式。以a小调为例：A–B（T），B–C（S），C–D（T），D–E（T），E–F（S），F–G（T），G–A（T）。
Harmonic minor: T – S – T – T – S – A2 – S
Where A2 denotes an augmented second (three semitones). The harmonic minor raises the 7th degree from the natural minor, creating a distinctive 'exotic' gap and a strong leading note. In A harmonic minor: G♯. The step F–G♯ spans three semitones.
其中A2表示增二度（三个半音）。和声小调将自然小调的第七级音升高，形成特色“异域”间隔和强烈的导音。a和声小调中：升高G至G♯，F–G♯跨三个半音。
Melodic minor (ascending): T – S – T – T – T – T – S
The ascending melodic minor raises both the 6th and 7th degrees for smoother voice-leading. Its top half looks identical to the major scale. In A melodic minor ascending: F♯ and G♯.
旋律小调上行时升高第六级和第七级音，使声部进行更流畅。其上半部分与大调音阶结构相同。a旋律小调上行：F♯和G♯。
5. Interval Calculation Theorems | 音程计算定理
An interval is labelled by its number (2nd, 3rd, etc.) and quality (major, minor, perfect). The number is always counted from the lower note to the higher note inclusive of both letter names.
音程由其度数（二度、三度等）和性质（大、小、纯等）定义。度数始终从低音到高音包含两端字母名计数。
Half-step counting theorem: ones; perfect 4th = 5 semitones, perfect 5th = 7 semitones, perfect octave = 12 semitones.
半音计数定理：大二度 = 2个半音，小二度 = 1个半音；大三度 = 4个半音，小三度 = 3个半音；纯四度 = 5个半音，纯五度 = 7个半音，纯八度 = 12个半音。
Inversion theorem: When an interval is inverted (lower note moves up an octave), the new number sums to 9 (2nd becomes 7th, 3rd becomes 6th etc.), and the quality swaps: major becomes minor, minor becomes major, perfect stays perfect.
转位定理：当音程转位（低音移高八度），新度数与原度数之和为9（二度变七度，三度变六度等），性质互换：大变小，小变大，纯不变。
6. Triad Construction Formulae | 三和弦构成公式
A triad is a three-note chord built in stacked thirds. Its quality depends on the precise arrangement of semitones between the root, third and fifth.
三和弦是由三度叠置的三音和弦。其性质取决于根音、三音和五音之间半音的精确排列。
Major triad: Root + 4 semitones (major 3rd) + 3 semitones (perfect 5th from root)
The major triad formula is often remembered as '4 + 3' semitones. Example: C–E (4) + E–G (3) = C major.
大三和弦公式常记为 '4 + 3' 半音。例如：C–E (4) + E–G (3) = C大三和弦。
Minor triad: Root + 3 semitones (minor 3rd) + 4 semitones (perfect 5th from root)
So the pattern is '3 + 4'. A minor: A–C (3) + C–E (4) = A minor.
公式为 '3 + 4'。a小三和弦：A–C (3) + C–E (4) = a小三和弦。
Diminished triad: Root + 3 semitones + 3 semitones (3 + 3)
Both stacked thirds are minor; the outer interval is a diminished 5th. Augmented triad: Root + 4 semitones + 4 semitones (4 + 4); the outer interval is an augmented 5th.
减三和弦：根音+3半音+3半音（3+3），两个三度均为小三度，框架为减五度。增三和弦：根音+4半音+4半音（4+4），框架为增五度。
7. Chord Inversion & Figured Bass Shorthand | 和弦转位与数字低音速记
When the lowest note of a triad is not the root, the chord is an inversion. Each inversion can be described by the intervals formed above the bass note and labelled with Roman numerals plus figured bass symbols.
当三和弦的最低音不是根音时，该和弦处在转位。每种转位可由低音上方的音程描述，并用罗马数字加数字低音标记。
Root position: The root is in the bass. Intervals above the bass are a 3rd and a 5th. Figured bass shorthand: I (or simply ⁵₃, but often omitted).
原位：根音在低音部。低音上方形成三度和五度。数字低音速记：I（或⁵₃，通常省略）。
First inversion: The 3rd of the triad is in the bass. Intervals above are a 3rd and a 6th. Figured bass: I⁶₃, commonly shortened to I⁶.
第一转位：三和弦的三音在低音部。低音上方形成三度和六度。数字低音标记：I⁶₃，通常简写为I⁶。
Second inversion: The 5th of the triad is in the bass. Intervals above are a 4th and a 6th. Figured bass: I⁶₄.
第二转位：三和弦的五音在低音部。低音上方为四度和六度。数字低音标记：I⁶₄。
8. Cadence Patterns | 终止式模式
A cadence is a pair of chords that ends a musical phrase. Each type follows a predictable formula; the pattern is the 'theorem' that creates a sense of closure or expectation.
终止式是结束乐句的一对和弦。每种终止式遵循可预测的进行模式；该模式正是制造收束感或期待感的“定理”。
Perfect cadence: V – I (both in root position, often with chord I in root position and an octave leap in the bass)
The strongest formula, sounding like a full stop. In C major: G major to C major. The leading note (B) rises to the tonic (C).
最强的终止式，听感如句号。C大调：G大和弦到C大和弦，导音B上行至主音C。
Plagal cadence: IV – I
Often called the 'Amen' cadence. In C major: F major to C major. Both chords share a common tone (C).
常称“阿们”终止。C大调：F大和弦到C大和弦，两和弦的共同音为C。
Imperfect cadence: I – V, ii – V, or IV – V
Any chord moving to V sounds unfinished, like a comma. The most common pattern is I–V.
任何和弦进行到V听起来未完成，如同逗号。最常见的模式为I–V。
Interrupted cadence: V – vi
The dominant resolves to the submediant instead of the tonic, creating a deceptive surprise. In C major: G major to A minor.
属和弦解决到下中音而非主音，产生暧昧的意外感。C大调：G大和弦到a小三和弦。
9. Tempo Marks & Metronome Conversion | 速度标记与节拍器换算定理
Italian tempo terms indicate a speed range measured in beats per minute (bpm). Remembering the approximate bpm is a useful conversion formula for performance.
意大利语速度术语表示以每分钟节拍数（bpm）衡量的速度范围。记住近似的bpm值是演奏时实用的转换公式。
| Term | Meaning | Approx. bpm |
|---|---|---|
| Largo | Very slow, broad | 40–60 |
| Adagio | Slow, stately | 66–76 |
| Andante | At a walking pace | 76–108 |
| Moderato | Moderate | 108–120 |
| Allegro | Fast, lively | 120–168 |
| Presto | Very fast | 168–200 |
Modifiers enlarge the range: '-issimo' intensifies (Prestissimo = extremely fast, 200+ bpm); '-etto' lightens the meaning (Allegretto = slightly less fast than Allegro).
修饰词可扩大范围：后缀“-issimo”加强程度（Prestissimo极快，200+ bpm）；“-etto”减轻含义（Allegretto稍慢于Allegro）。
10. Dynamics & Expression Terms | 力度与表情术语
Dynamic markings prescribe volume levels and their changes; they are essential formulae for shaping a performance.
力度记号规定音量层级及其变化；它们是塑造演奏效果的基本公式。
| Abbreviation | Italian term | Meaning |
|---|---|---|
| pp | pianissimo | very soft |
| p | piano | soft |
| mp | mezzo-piano | moderately soft |
| mf | mezzo-forte | moderately loud |
| f | forte | <
