📚 Year 8 CAIE Music: Quick Reference Handbook of Formulas and Theorems | Year 8 CAIE 音乐：公式定理速查手册
This quick reference handbook brings together the essential 'formulas' and 'theorems' of music theory for Year 8 CAIE students. Just as mathematics relies on patterns, music is built upon scales, intervals, and rhythmic proportions. Use this guide to rapidly check note values, key signatures, chord structures, and Italian terms that regularly appear in listening, composing, and performing tasks.
这份速查手册汇集了 Year 8 CAIE 音乐课程中必不可少的“公式”和“定理”。正如数学依靠模式，音乐也建立在音阶、音程和节奏比例之上。使用本指南快速查阅音符时值、调号、和弦结构以及听力、创作和演奏中常见的意大利术语。
1. Note Values & Rests | 音符时值与休止符
A note's duration is determined by its shape. In 4/4 time, a semibreve lasts four beats, a minim two beats, a crotchet one beat, a quaver half a beat, and a semiquaver a quarter of a beat. Dots add half the original value.
音符的时值由其形状决定。在 4/4 拍中，全音符持续四拍，二分音符两拍，四分音符一拍，八分音符半拍，十六分音符四分之一拍。附点增加原时值的一半。
| English Name | 中文名称 | Symbol | Rest Symbol | Beats (4/4) |
|---|---|---|---|---|
| Semibreve | 全音符 | 𝅝 | 𝄻 | 4 |
| Minim | 二分音符 | 𝅗𝅥 | 𝄼 | 2 |
| Crotchet | 四分音符 | 𝅘𝅥 | 𝄽 | 1 |
| Quaver | 八分音符 | 𝅘𝅥𝅮 | 𝄾 | ½ |
| Semiquaver | 十六分音符 | 𝅘𝅥𝅯 | 𝄿 | ¼ |
| Dotted Minim | 附点二分音符 | 𝅗𝅥. | 𝄼. | 3 |
Rests indicate silence. Each note value has a matching rest of equal duration. A whole-bar rest (semibreve rest) hangs from the fourth line of the staff; a minim rest sits on the third line.
休止符表示无声。每种音符都有相等时值的休止符。全小节休止（全休止符）悬挂在五线谱第四线下方；二分休止符放置在第三线上。
2. Time Signatures | 拍号
beats per bar; the bottom number gives the beat unit (4 = crotchet, 8 = quaver, 2 = minim).
拍号出现在乐曲开头，表明每小节有几拍以及以何种音符为一拍。上方数字表示每小节拍数；下方数字表示拍的单位（4 代表四分音符，8 代表八分音符，2 代表二分音符）。
- Simple time: each beat divides into two equal parts. Common examples: 2/4, 3/4, 4/4 (often written as a C for common time).
- 简单拍子： 每拍可自然分为两个等份。常见：2/4、3/4、4/4（常用 C 表示，即 common time）。
- Compound time: each beat divides into three equal parts. Examples: 6/8 (two dotted-crotchet beats), 9/8, 12/8.
- 复拍子： 每拍可自然分为三个等份。例如：6/8（两个附点四分音符拍）、9/8、12/8。
When counting compound time, the pulse is felt on the dotted note, not the quaver. Thus 6/8 has two main beats, each worth three quavers.
在计算复拍子时，节拍重心在附点音符上，而非八分音符。因此 6/8 拍有两大拍，每拍相当于三个八分音符。
3. Clefs and the Grand Staff | 谱号与大谱表
The treble clef (G clef) circles the second line, indicating that this line is G above middle C. The bass clef (F clef) places its two dots around the fourth line, marking it as F below middle C. Together they form the grand staff, a system used for piano music.
高音谱号（G 谱号）环绕第二线，表明该线为中央 C 上方的 G。低音谱号（F 谱号）的两个点围绕第四线，标记为中央 C 下方的 F。两者共同构成大谱表，用于钢琴音乐。
Middle C sits on one ledger line below the treble staff or one ledger line above the bass staff. The mnemonic for treble lines is Every Good Boy Deserves Fruit (E-G-B-D-F); spaces spell FACE. For bass lines, Good Boys Deserve Fruit Always (G-B-D-F-A); spaces are All Cows Eat Grass (A-C-E-G).
中央 C 位于高音谱表下方加一线，或低音谱表上方加一线。高音谱表线的记忆口诀：Every Good Boy Deserves Fruit（E-G-B-D-F）；间为 FACE。低音谱表线：Good Boys Deserve Fruit Always（G-B-D-F-A）；间为 All Cows Eat Grass（A-C-E-G）。
4. Major Scales Pattern | 大调音阶模式
All major scales follow the same pattern of tones (T) and semitones (S): T-T-S-T-T-T-S. This interval formula is the 'theorem' behind every major key.
所有大调音阶都遵循相同的全音（T）与半音（S）模式：T-T-S-T-T-T-S。这一音程公式是每个大调的“定理”。
Starting on C, this gives all white notes: C-D (T), D-E (T), E-F (S), F-G (T), G-A (T), A-B (T), B-C (S). When building other major scales, accidentals are added to preserve the pattern. For G major, F must be raised to F♯; for D major, F♯ and C♯.
从 C 开始，得到全部白键：C-D（T）、D-E（T）、E-F（S）、F-G（T）、G-A（T）、A-B（T）、B-C（S）。在构建其他大调时，需添加临时升降号以保持模式。G 大调需将 F 升为 F♯；D 大调需 F♯ 和 C♯。
Scale degrees are numbered 1st (tonic) to 8th (octave). The tonic is the home note and gives the key its name.
音阶的级数从第 1 级（主音）到第 8 级（八度）。主音是中心音，并赋予该调名称。
5. Minor Scales Pattern | 小调音阶模式
There are three forms of the minor scale. The natural minor uses the pattern T-S-T-T-S-T-T. The harmonic minor raises the 7th degree by a semitone, creating a distinctive augmented 2nd between the 6th and 7th degrees. The melodic minor raises both the 6th and 7th degrees when ascending, but reverts to the natural minor when descending.
小调音阶有三种形式。自然小调模式为 T-S-T-T-S-T-T。和声小调将第 7 级升高半音，在第 6 与第 7 级之间形成增二度。旋律小调上行时升高第 6 和第 7 级，下行时回归自然小调。
A minor is the relative minor of C major, sharing the same key signature (no sharps or flats). The relative minor is always a minor third below the major tonic.
A 小调是 C 大调的关系小调，共用同一调号（无升降号）。关系小调的主音总是比大调主音低小三度。
| Form | 形式 | A Minor Example |
|---|---|---|
| Natural minor | 自然小调 | A B C D E F G A |
| Harmonic minor | 和声小调 | A B C D E F G♯ A |
| Melodic minor (ascending) | 旋律小调（上行） | A B C D E F♯ G♯ A |
6. Key Signatures (Major) | 调号（大调）
A key signature is a set of sharps or flats placed at the beginning of each staff, indicating which notes are consistently altered. The order of sharps is F♯, C♯, G♯, D♯, A♯, E♯, B♯. The order of flats is B♭, E♭, A♭, D♭, G♭, C♭, F♭.
调号是放置在每行谱表开头的一组升号或降号，表明哪些音被永久改变。升号顺序为：F♯、C♯、G♯、D♯、A♯、E♯、B♯。降号顺序为：B♭、E♭、A♭、D♭、G♭、C♭、F♭。
ind the major key from sharps, go up a semitone from the last sharp (e.g., last sharp is D♯ → key is E major). For flats, the second-to-last flat names the key (e.g., B♭, E♭, A♭ → key is E♭ major).
由升号找大调的方法是：从最后一个升号上行半音（如最后一个升号为 D♯ → 调为 E 大调）。对于降号，倒数第二个降号即为调名（如 B♭、E♭、A♭ → 调为 E♭ 大调）。
| Sharps/Flats | Major Key | 大调 |
|---|---|---|
| 0 | C major | C 大调 |
| 1♯ | G major | G 大调 |
| 2♯ | D major | D 大调 |
| 3♯ | A major | A 大调 |
| 1♭ | F major | F 大调 |
| 2♭ | B♭ major | 降 B 大调 |
7. Intervals | 音程
An interval is the distance between two pitches, counted in scale steps from the lower note to the higher note. The number is the count of letter names inclusive; the quality (perfect, major, minor, augmented, diminished) depends on the exact number of semitones.
音程是两个音高之间的距离，按音级从低音数到高音。度数包含两端音名的总个数；性质（纯、大、小、增、减）取决于具体的半音数量。
In a major scale, intervals from the tonic are all major or perfect: unison (P1), major 2nd (M2), major 3rd (M3), perfect 4th (P4), perfect 5th (P5), major 6th (M6), major 7th (M7), perfect octave (P8). A minor interval is one semitone smaller than major.
在大调音阶中，从主音开始的音程均为大音程或纯音程：纯一度（P1）、大二度（M2）、大三度（M3）、纯四度（P4）、纯五度（P5）、大六度（M6）、大七度（M7）、纯八度（P8）。小音程比大音程少一个半音。
The tritone (augmented 4th or diminished 5th) spans three whole tones and sits exactly halfway through the octave. It was historically called 'diabolus in musica'.
三全音（增四度或减五度）涵盖三个全音，正好把八度分成两半。历史上曾被称为“音乐中的魔鬼”。
8. Triads and Chords | 三和弦
A triad is a three-note chord stacked in thirds. The tonic triad (I) is built on the first degree of the scale and defines the key. In major keys, the tonic triad is major; in minor keys, the tonic triad is minor.
三和弦是由三个按三度叠置的音构成的和弦。主三和弦（I 级）建立于音阶的第一级，决定了调的属性。在大调中，主和弦为大三和弦；在小调中，主和弦为小三和弦。
A major triad consists of a root, major third, and perfect fifth (e.g., C-E-G). A minor triad has a root, minor third, and perfect fifth (e.g., A-C-E). The dominant triad (V) creates tension that resolves to the tonic.
大三和弦由根音、大三度和纯五度构成（如 C-E-G）。小三和弦由根音、小三度和纯五度构成（如 A-C-E）。属三和弦（V 级）制造紧张感，并倾向于解决到主和弦。
| Roman Numeral | Function | 功能 | Example in C major |
|---|---|---|---|
| I | Tonic | 主和弦 | C-E-G |
| IV | Subdominant | 下属和弦 | F-A-C |
| V | Dominant | 属和弦 | G-B-D |
9. Dynamics and Articulation | 力度与演奏法
Dynamics indicate the volume of music. The main symbols form a continuum from very soft to very loud: pp (pianissimo, very soft), p (piano, soft), mp (mezzo-piano, moderately soft), mf (mezzo-forte, moderately loud), f (forte, loud), ff (fortissimo, very loud). Gradual changes use < (crescendo, getting louder) and > (decrescendo/diminuendo, getting softer).
力度标记指示音乐的音量。主要符号由极弱至极强连续排列：pp（pianissimo，很弱）、p（piano，弱）、mp（mezzo-piano，中弱）、mf（mezzo-forte，中强）、f（forte，强）、ff（fortissimo，很强）。渐变力度使用 <（crescendo，渐强）和 >（decrescendo/diminuendo，渐弱）。
Articulation markings tell performers how to attack or connect notes. Staccato (dot above or below the note) means short and detached; legato (slur) means smooth and connected; accent (>) means stressed; tenuto (line) means held for full value.
演奏法标记告诉表演者如何起奏或连接音符。断奏（音符上或下的圆点）表示短促分离；连奏（连线）表示平滑连贯；重音（>）表示强调；保持音（横线）表示奏满时值。
10. Tempo Markings | 速度标记
ing pace), Moderato (moderate), Allegro (fast, lively), and Presto (very fast). Metronome marks give precise bpm, e.g., 𝅘𝅥 = 120.
速度即节拍快慢，通常用意大利语标记。常见术语：Largo（非常慢而宽广）、Adagio（缓慢而庄严）、Andante（行板，步行速度）、Moderato（中板）、Allegro（快板，活泼）、Presto（急板）。节拍器标记给出精确的每分钟拍数，如 𝅘𝅥 = 120。
Modifying words refine the tempo: 'molto' means very (Allegro molto = very fast), 'poco' ndo (rit.) means gradually slowing down; accelerando (accel.) means gradually speeding up.
修饰词进一步说明速度：'molto' 意为非常（Allegro molto 很快），'poco' 意为少许（poco rit. 稍慢）。Ritardando（rit.）表示渐慢；accelerando（accel.）表示渐快。
11. Ornaments | 装饰音
Ornaments are decorative notes that embellish a melody. The trill (tr) is a rapid alternation between the written note and the note above; the mordent (short squiggle) is a quick single alternation; the turn (sideways S) goes note above, main note, note below, main note; the acciaccatura (small note with a slash) is a crushed grace note played very quickly before the main note.
装饰音是为旋律增添色彩的附加音符。颤音（tr）是记写音与上方音的快速交替；波音（短波浪线）是快速单次交替；回音（侧 S 形）演奏为上方音-主音-下方音-主音；短倚音（带斜线的小音符）是在主音前极快奏出的碎音。
Grace notes (appoggiaturas) without a slash take half the value of the main note and create expressive dissonance. Knowing ornaments helps in both performance and in aural identification during the listening exam.
不带斜线的长倚音（appoggiatura）通常占主音一半时值，并制造富有表情的不协和感。掌握装饰音有助于演奏和听力测试中的识别。
12. Musical Terms Quick Reference | 音乐术语速查
This glossary collects essential Italian terms frequently encountered in Year 8 CAIE repertoire. They cover style, expression, and direction.
本词汇表汇总了 Year 8 CAIE 曲目中常见的意大利术语，涵盖风格、表情和演奏指示。
| Term | Meaning | 含义 |
|---|---|---|
| cantabile | In a singing style | 如歌地 |
| dolce | Sweetly | 甜美地 |
| espressivo | Expressively | 有表情地 |
| leggiero | Lightly | 轻巧地 |
| maestoso | Majestic | 庄严地 |
| sostenuto | Sustained | 保持地 |
| subito | Suddenly | 突然地 |
| poco a poco | Little by little | 逐渐地 |
| da capo (D.C.) | From the beginning | 从头再奏 |
| dal segno (D.S.) | From the sign | 从记号处再奏 |
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