📚 Year 9 CCEA Music: Formula & Theorem Quick Reference | 九年级CCEA音乐：公式定理速查手册
Welcome to your go-to handbook for all the essential music theory formulas and concepts in Year 9 CCEA Music. Whether you are deciphering note lengths, building scales, constructing chords, or recognising cadences, this revision resource presents each key idea as a clear, memorisable 'formula' or theorem. Keep it handy as you practise for exams, compose your own pieces, and analyse musical scores.
欢迎使用这份九年级CCEA音乐必备公式定理速查手册。不论是在解读音符长度、构建音阶、组合和弦，还是识别终止式，这份复习资料将每个关键概念都呈现为清晰、便于记忆的“公式”或定理。请随时查阅，帮助你备考、创作自己的乐曲和解析乐谱。
1. Note Values and Rest Equivalents | 音符时值与休止符等式
tchets = 8 quavers = 16 semiquavers. Their rests follow the same mathematical proportions.
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。对应的休止符也遵循相同的数学比例。
To calculate relative duration: the number of a note type in a semibreve equals its rhythmic 'denominator'; for example, there are 4 crotchet beats in a semibreve in simple time.
计算时值关系：一个全音符中包含某一音符的个数，就是该音符在节奏上的“分母”；例如，在单拍子中，一个全音符包含4个四分音符拍。
ote value + ½ original note value. So a dotted crotchet = 1 + ½ = 1½ beats in simple time.
附点音符将原时值延长一半。公式：附点音符时值 = 原音符时值 + ½原音符时值。因此在单拍子中，附点四分音符 = 1 + ½ = 1½拍。
e = original + ½ + ¼ of original. A double-dotted minim in 4/4 lasts 2 + 1 + ½ = 3½ beats.
双附点再增加原时值的四分之一。公式：双附点音符 = 原时值 + ½ + ¼原时值。在4/4拍中，双附点二分音符持续2 + 1 + ½ = 3½拍。
| Common Note‑Rest Equivalents | |
|---|---|
| Semibreve ⁄ rest | 4 beats |
| Minim ⁄ rest | 2 beats |
| Crotchet ⁄ rest | 1 beat |
| Quaver ⁄ rest | ½ beat |
| Semiquaver ⁄ rest | ¼ beat |
2. Time Signatures and Meter | 拍号与节拍
A time signature is a numerical formula written as two numbers stacked vertically. The top number tells how many beats per bar, the bottom number tells the type of note that gets one beat (4 = crotchet, 8 = quaver, 2 = minim).
拍号以分数形式纵向书写两个数字。上方数字表示每小节有几拍，下方数字表示以什么音符为一拍（4 = 四分音符，8 = 八分音符，2 = 二分音符）。
Simple time: each beat divides naturally into two equal parts. The top number is typically 2, 3 or 4. Formula for simple time: beat divides into 2 equal parts.
单拍子：每一拍自然均分为两部分。上方数字通常为2、3或4。单拍子公式：每一拍分为两个均等部分。
9, 12). Formula for compound time: beat = dotted note; beat divides into 3 smaller notes.
复拍子：每一拍分为三个均等部分。上方数字是3的倍数（6、9、12）。复拍子公式：拍单位 = 附点音符；每拍分为3个更小的音符。
r bar, each dividing into three quavers. The formula is: number of beats = top number ÷ 3.
识别复拍子的拍单位：在6/8拍中，每小节有2个附点四分音符拍，每个再分为3个八分音符。公式：拍数 = 上方数字 ÷ 3。
Irregular time signatures (5/4, 7/8) contain both 2-part and 3‑part groupings; their grouping formula is determined by the phrase structure of the music.
不规则拍号（5/4、7/8）包含二拍和三拍的混合组合；其组合公式取决于乐句结构。
3. Major Scale Formula | 大调音阶公式
Every major scale follows the same pattern of tones (T) and semitones (S): T – T – S – T – T – T – S. In C major (all white keys) this gives C–D–E–F–G–A–B–C.
每个大调音阶都遵循相同的全音（T）和半音（S）模式：T – T – S – T – T – T – S。在C大调（全部白键）中，音级为C–D–E–F–G–A–B–C。
Major Scale Formula: T · T · S · T · T · T · S
We can build a major scale starting on any note by applying this formula. Each scale degree is numbered 1 to 8, where 8 is the octave of 1.
以此公式，我们可以从任何一个音开始构建大调音阶。各音级编号为1至8，其中8是1的高八度音。
Key signatures arise from the sharps or flats needed to preserve the T‑T‑S‑T‑T‑T‑S formula. The order of sharps: F♯, C♯, G♯, D♯, A♯, E♯, B♯. The order of flats: B♭, E♭, A♭, D♭, G♭, C♭, F♭.
调号是根据保持T‑T‑S‑T‑T‑T‑S公式所需的升号或降号得出的。升号顺序：F♯, C♯, G♯, D♯, A♯, E♯, B♯。降号顺序：B♭, E♭, A♭, D♭, G♭, C♭, F♭。
4. Minor Scale Formulae | 小调音阶公式
There are three common forms of the minor scale, each with its own interval pattern formula. All start from the tonic (1) and ascend to the octave.
小调音阶有三种常见形式，每种都有各自固定的音程模式公式。所有小调都从主音（1）开始上行至八度。
Natural minor: T – S – T – T – S – T – T. (Same key signature as its relative major.)
自然小调：T – S – T – T – S – T – T。（与其关系大调共用同一调号。）
Natural Minor: T · S · T · T · S · T · T
Harmonic minor: raises the 7th degree of the natural minor by a semitone. Pattern: T – S – T – T – S – Augmented 2nd – S. (Aug. 2nd = 3 semitones.)
和声小调：将自然小调的第7级音升高半音。模式：T – S – T – T – S – 增二度 – S。（增二度 = 3个半音。）
Harmonic Minor: T · S · T · T · S · A2 · S
Melodic minor: ascending raises the 6th and 7th degrees of the natural minor; descending reverts to natural minor. Ascending pattern: T – S – T – T – T – T – S.
旋律小调：上行时升高自然小调的第6和第7级音；下行时还原为自然小调。上行模式：T – S – T – T – T – T – S。
Melodic Minor Ascending: T · S · T · T · T · T · S
5. Chord Construction Formulas | 和弦构成公式
A triad is a three‑note chord built by stacking two thirds above a root. The quality of the triad depends on the sizes of those thirds.
三和弦是由根音上方叠加两个三度音构成的三音和弦。和弦性质取决于这两个三度的大小。
Major triad formula: Root + major 3rd (4 semitones) + perfect 5th (7 semitones). Between bottom and middle note: major 3rd; between middle and top note: minor 3rd.
大三和弦公式：根音 + 大三度（4个半音）+ 纯五度（7个半音）。根音到三音为大三度，三音到五音为小三度。
Major: Root + M3 + m3 → P5 from root
Minor triad formula: Root + minor 3rd (3 semitones) + perfect 5th. Structure: minor 3rd plus major 3rd.
小三和弦公式：根音 + 小三度（3个半音）+ 纯五度。结构：小三度 + 大三度。
Minor: Root + m3 + M3 → P5 from root
Diminished triad formula: Root + minor 3rd + diminished 5th (6 semitones). Both intervals are minor 3rds.
减三和弦公式：根音 + 小三度 + 减五度（6个半音）。两个三度均为小三度。
Diminished: Root + m3 + m3 → d5 from root
Augmented triad formula: Root + major 3rd + augmented 5th (8 semitones). Both intervals are major 3rds.
增三和弦公式：根音 + 大三度 + 增五度（8个半音）。两个三度均为大三度。
Augmented: Root + M3 + M3 → A5 from root
6. Interval Formulas | 音程公式
An interval measures the distance in semitones between two notes and is named by two factors: the number (2nd, 3rd, 4th etc.) and the quality (perfect, major, minor, augmented, diminished).
音程衡量两音之间的半音数，由两个因素命名：度数（二度、三度等）和性质（纯、大、小、增、减）。
The numerical value is determined by counting letter names from the lower note to the upper, inclusive. The quality is determined by the exact number of semitones.
音程度数由从下方音到上方音包含的音名字母数目确定（含首尾）。性质由精确的半音数决定。
| Interval | Semitones | Common Example |
|---|---|---|
| Minor 2nd | 1 | E–F |
| Major 2nd | 2 | C–D |
| Minor 3rd | 3 | A–C |
| Major 3rd | 4 | C–E |
| Perfect 4th | 5 | G–C |
| Tritone (A4/d5) | 6 | F–B |
| Perfect 5th | 7 | C–G |
| Minor 6th | 8 | E–C |
| Major 6th | 9 | C–A |
| Minor 7th | 10 | G–F |
| Major 7th | 11 | C–B |
| Octave (P8) | 12 | C–c |
Formula for interval inversion: the new number = 9 – ginal number; quality flips from major ↔ minor, perfect ↔ perfect, augmented ↔ diminished.
音程转位公式：新度数 = 9 – 原度数；性质互换为大↔小，纯↔纯，增↔减。
7. Circle of Fifths and Key Signatures | 五度圈与调号
The Circle of Fifths is a diagram that organises all major and minor keys by ascending perfect 5ths (clockwise) and descending perfect 5ths (anticlockwise). Each step clockwise adds one sharp; each anticlockwise adds one flat.
五度圈是一个按照上行纯五度（顺时针）和下行纯五度（逆时针）将所有大调和小调排列的图表。顺时针每走一步增加一个升号，逆时针增加一个降号。
Formula to find the relative minor: the relative minor of a major key lies a minor 3rd (3 semitones) below the major tonic. Thus, C major ↔ A minor, G major ↔ E minor.
找到关系小调的公式：大调的关系小调位于大调主音下方小三度（3个半音）。所以，C大调 ↔ a小调，G大调 ↔ e小调。
Key signature identification: for sharp keys, the last sharp is the leading note (7th degree) – go up a minor 2nd to find the tonic. For flat keys, the second‑last flat is the tonic (except F major).
调号识别：升号调中，最后一个升号是该调的导音（第7级），上行一个半音得到主音。降号调中，倒数第二个降号就是主音（F大调除外）。
Formula to count intervals between key signatures: moving up by a perfect 5th (7 semitones) from any tonic yields the next sharp key; down by a perfect 5th yields the next flat key.
计算调号间隔的公式：从任一主音上行纯五度（7个半音）得到下一个升号调；下行纯五度得到下一个降号调。
8. Dynamic Markings | 力度记号
Dynamic markings govern the volume of music. They act like a volume 'formula' ranging from very quiet to very loud, expressed with Italian abbreviations.
力度记号控制音乐的音量。它们如同音量“公式”，从极弱到极强，用意大利语缩写表示。
| Abbreviation | Italian Term | Meaning |
|---|---|---|
| pp | pianissimo | very quiet |
| p | piano | quiet |
| mp | mezzo‑piano | moderately quiet |
| mf | mezzo‑forte | moderately loud |
| f | forte | loud |
| ff | fortissimo | very loud |
Gradual change formulas: crescendo (cresc.) means gradually getting louder; diminuendo (dim.) or decrescendo means gradually getting quieter.
渐变力度公式：crescendo（渐强）表示音量逐渐增大；diminuendo（渐弱）或decrescendo表示音量逐渐减小。
Sudden change emphasis: sforzando (sfz) indicates a strong, sudden accent on a single note or chord.
突强记号：sforzando（sfz）表示对单个音或和弦施加突然的强奏重音。
9. Tempo Markings | 速度标记
Tempo tells the performer how fast to play. It appears at the start of a piece, usually in Italian, and can be given as a metronome mark (beats per minute, bpm).
速度标记告诉演奏者演奏的快慢。通常写在乐曲开头，用意大利语表示，也可给出节拍器数字（每分钟拍数，bpm）。
Common tempo formulas from slowest to fastest: Largo (very slow, broad), Adagio (slow), Andante (walking pace), Moderato (moderate), Allegro (fast, cheerful), Vivace (lively, very fast), Presto (extremely fast).
由慢到快的常见速度公式：Largo（广板，很慢）、Adagio（柔板，慢）、Andante（行板，步行速度）、Moderato（中板，中速）、Allegro（快板，快速、欢快）、Vivace（活板，非常快）、Presto（急板，极快）。
Tempo change formulas: accelerando (accel.) – gradually getting faster; rallentando (rall.) or ritardando (rit.) – gradually getting slower; a tempo – return to the original speed.
速度变化公式：accelerando（渐快）– 逐渐加快；rallentando 或 ritardando（渐慢）– 逐渐变慢；a tempo – 回到原速。
10. Articulation and Expression | 演奏法与表情术语
Articulation marks tell musicians how to perform individual notes. The main formulas are:
演奏法记号告诉演奏者如何演奏单个音符。主要公式如下：
Staccato: dot above/below note; shorten the note, making it detached. Formula: play note for about half its written length with a crisp separation.
断奏（Staccato）：符头上下加点；把音符缩短，使其断开。公式：演奏大约原音符时值一半的长度，干净地分离。
Legato: curved slur line; play notes smoothly, connecting them without audible gaps. Formula: minimal separation; sustain each note until the next begins.
连奏（Legato）：圆滑的连线；将音符平滑连接，不留可闻间隙。公式：最小分离度，每个音持续到下一个音开始。
Accent: > mark above/below note; attack the note with extra emphasis, then return to normal volume.
重音（Accent）：音符上下标记>；以额外强调方式奏出该音，然后回复正常音量。
Tenuto: short horizontal line; hold the note for its full value, often with slight pressure or emphasis.
保持音（Tenuto）：短横线；将音符完全奏满时值，并常稍加压力或侧重。
Expression terms for mood: dolce – sweetly; cantabile – in a singing style; maestoso – majestically; espressivo – expressively.
表情术语（情绪）公式：dolce – 甜美地；cantabile – 如歌地；maestoso – 庄严地；espressivo – 富有表情地。
11. Ornaments | 装饰音公式
Ornaments add decoration to the melody. Each has a standard performance formula.
装饰音为旋律增添装饰效果。每种装饰音都有标准演奏公式。
Trill: rapid alternation between the written note and the note above (diatonic upper note). Formula: start on the main note (or upper note, depending on period), alternate quickly for the note's duration.
颤音（Trill）：在主音与其上方自然音级音之间快速交替。公式：从主音开始（或根据时期可从上方音开始），快速交替持续整个音长。
Turn: a curled symbol~; play the note above, the main note, the note below, then the main note quickly. Formula: upper – main – lower – main.
回音（Turn）：弯曲形符号~；快速演奏上方音 – 主音 – 下方音 – 主音。公式：上–主–下–主。
Mordent (upper): a short zigzag; play main note, quickly alternate with the note above, and return. Formula: main – upper – main.
波音（上波音）：短小锯齿线；演奏主音，快速与上方音交替，再回到主音。公式：主–上–主。
Lower mordent: zigzag with a vertical line through it; play main note, then the note below, then back. Formula: main – lower – main.
下波音：带有竖穿线的锯齿符号；演奏主音，然后下方音，再回到主音。公式：主–下–主。
Appoggiatura: small note before a main note; takes half the main note's value (for regular note) or two‑thirds (for dotted note), leaning on the beat.
倚音（Appoggiatura）：主音前的小音；占用主音一半时值（普通音符）或三分之二（附点音符），在拍上演奏。
Acciaccatura: small note with a stroke through the stem; crushed in as quickly as possible before the main note.
碎音（Acciaccatura）：符干上带斜线的小音符；尽可能快地在主音前“挤进”演奏。
12. Cadences | 终止式公式
A cadence is the chord progression that ends a musical phrase, like a punctuation formula. There are four main cadences, each creating a different sense of completeness.
终止式是结束乐句的和弦进行，如同标点符号公式。主要有四种终止式，每种营造不同的完结感。
Perfect cadence: V – I. Sounds final, complete. Formula: dominant to tonic, both chords in root position with the tonic in the soprano for extra finality.
正格终止（完全终止）：V – I。听感终结、完满。公式：属和弦到主和弦，两者均用原位上，女高音落到主音效果更圆满。
Plagal cadence: IV – I. Sounds like an 'Amen' ending. Formula: subdominant to tonic, often used at the end of hymns.
变格终止（阿门终止）：IV – I。听感如“阿门”。公式：下属和弦到主和弦，常出现于赞美诗结尾。
Imperfect cadence: any chord ending on V (e.g. I–V, II–V, IV–V). Sounds unfinished, resting on the dominant. Formula: end on V, giving a feeling of 'more to come'.
不正格终止（半终止）：任何终止于V的和弦进行（如 I–V、II–V、IV–V）。听感未完成，停留在属和弦上。公式：结束在V，产生“意犹未尽”的感觉。
Interrupted cadence: V – vi (or V – VI in minor). Formula: dominant moves to the relative minor chord instead of the expected tonic, creating a surprise deflection.
阻碍终止：V – vi（或小调中 V – VI）。公式：属和弦没有进行到预期的主动，而是到了关系小调和弦，产生意外转向感。
Cadence identification theorem: look at the final two chords of a phrase, identify their roman numerals within the key, then match the pattern to the cadence type.
终止式识别定理：观察乐句最后两个和弦，确定其在调内的罗马数字级数，然后与终止式类型匹配。
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