📚 Year 11 CCEA Music: Formula & Theorem Quick Reference | CCEA 11年级音乐：公式定理速查手册
This quick reference guide compiles the essential ‘formulas’ and theoretical rules you need to master for Year 11 CCEA Music. While music may not have equations in the mathematical sense, the patterns behind scales, chords, intervals, and rhythm follow precise, repeatable formulas that every GCSE student must know. Use this handbook to speed up your recognition, reinforce your understanding, and prepare confidently for listening papers, composition tasks, and performance analysis.
这本速查手册汇集了 CCEA 11 年级音乐必须掌握的核心“公式”和理论法则。虽然音乐不像数学那样使用方程，但音阶、和弦、音程和节奏背后的模式都遵循精准、可重复的公式，这是每一位 GCSE 学生都必须熟悉的。使用本手册可以加快辨识速度，巩固理解，并为听力考试、作曲任务和演奏分析做好充分准备。
1. Major Scale Formula | 大调音阶公式
The major scale follows a fixed pattern of whole tones (T) and semitones (S): T T S T T T S. Starting on any tonic, you can build a major scale by applying this sequence. For example, C major: C–D (T), D–E (T), E–F (S), F–G (T), G–A (T), A–B (T), B–C (S). No accidentals are needed in C major, but other keys will require sharps or flats to maintain the formula.
大调音阶遵循固定的全音（T）和半音（S）模式：全全半全全全半。从任意主音开始，按照这个序列就能构建大调音阶。例如 C 大调：C–D（全），D–E（全），E–F（半），F–G（全），G–A（全），A–B（全），B–C（半）。在 C 大调中不需要升降号，但其他调号需要加入升号或降号来保持这一模式。
Use this formula to construct any major scale mentally. The pattern of intervals, measured in semitones from the tonic, is: 0, 2, 4, 5, 7, 9, 11, 12. This numeric approach helps with transposition and understanding scale degrees.
用这个公式可以在脑中构建任何大调音阶。从主音算起的音程半音数为：0, 2, 4, 5, 7, 9, 11, 12。这种数字方法有助于移调和理解音级。
2. Minor Scale Formulas | 小调音阶公式
There are three common forms of the minor scale. The natural minor uses the pattern: T S T T S T T. In semitones from the tonic: 0, 2, 3, 5, 7, 8, 10, 12. The harmonic minor raises the 7th degree by one semitone, giving the pattern: T S T T S T+half S. The melodic minor raises the 6th and 7th when ascending (T S T T T T S) and reverts to natural minor when descending.
常见的小调音阶有三种形式。自然小调的模式为：全半全全半全全。从主音算起的半音数为 0, 2, 3, 5, 7, 8, 10, 12。和声小调将第七级升高一个半音，模式变为：全半全全半增二度半。旋律小调上行时升高第六级和第七级（全半全全全全半），下行时恢复为自然小调。
Key signature alone does not tell you which minor form is used; you must listen for the raised leading note in harmonic minor and the raised 6th and 7th in melodic minor. These alterations often appear as accidentals in the music.
调号本身并不会告诉你用的是哪一种小调形式；必须通过听辨出和声小调中升高的导音，以及旋律小调中升高的六级和七级音来判断。这些变化音通常以临时记号的形式出现在乐谱中。
3. Interval Formula Table | 音程公式表
An interval is the distance between two pitches, measured in semitones and described by a quality (perfect, major, minor, augmented, diminished) and a number. The following table gives the core formulas for intervals within one octave. Use it as a quick lookup during analysis.
音程是两个音高之间的距离，以半音数来度量，并用性质（纯、大、小、增、减）和度数来描述。下表给出了一个八度内核心音程的公式，可作为分析时的速查表。
| Interval Name / 音程名称 | Semitones / 半音数 | Example (C up) / 示例 (C 向上) |
|---|---|---|
| Perfect Unison / 纯一度 | 0 | C–C |
| Minor 2nd / 小二度 | 1 | C–D♭ |
| Major 2nd / 大二度 | 2 | C–D |
| Minor 3rd / 小三度 | 3 | C–E♭ |
| Major 3rd / 大三度 | 4 | C–E |
| Perfect 4th / 纯四度 | 5 | C–F |
| Augmented 4th / Diminished 5th (Tritone) / 增四度 / 减五度 | 6 | C–F♯ / C–G♭ |
| Perfect 5th / 纯五度 | 7 | C–G |
| Minor 6th / 小六度 | 8 | C–A♭ |
| Major 6th / 大六度 | 9 | C–A |
| Minor 7th / 小七度 | 10 | C–B♭ |
| Major 7th / 大七度 | 11 | C–B |
| Perfect Octave / 纯八度 | 12 | C–C’ |
The quality of an interval can change if the note is altered by an accidental. A major interval lowered by a semitone becomes minor; a perfect interval raised by a semitone becomes augmented.
音程的性质会因升降号而改变。大音程降低一个半音变为小音程；纯音程升高一个半音变为增音程。
4. Chord Building Formulas | 和弦构建公式
Chords are built by stacking intervals of a third. The formula for a major triad is root + major 3rd + perfect 5th (0, 4, 7 semitones). A minor triad uses root + minor 3rd + perfect 5th (0, 3, 7). A diminished triad has a minor 3rd and diminished 5th (0, 3, 6), while an augmented triad has a major 3rd and augmented 5th (0, 4, 8).
和弦通过叠加三度音程构建。大三和弦的公式是根音 + 大三度 + 纯五度（0, 4, 7 半音）。小三和弦用根音 + 小三度 + 纯五度（0, 3, 7）。减三和弦包含小三度和减五度（0, 3, 6），增三和弦包含大三度和增五度（0, 4, 8）。
The dominant 7th chord adds a minor 7th to the major triad (0, 4, 7, 10). The formula for a minor 7th chord is 0, 3, 7, 10. Always work out these semitone stacks from the root — this method works regardless of key or accidentals.
属七和弦在大三和弦基础上增加一个小七度（0, 4, 7, 10）。小七和弦的公式是 0, 3, 7, 10。总是从根音开始按半音堆叠来计算，这种方法不受调号或临时记号的影响。
When writing chords in a given key, use the scale degrees harmonized with the key signature. For example, in C major, the chord built on the 1st degree is C–E–G (I), on the 2nd is D–F–A (ii), and on the 5th is G–B–D (V). Roman numerals indicate chord function.
在给定调号中写和弦时，要用调号下的音级来构建和声。例如，在 C 大调中，一级上构建的和弦是 C–E–G (I)，二级上是 D–F–A (ii)，五级上是 G–B–D (V)。罗马数字表示和弦功能。
5. Circle of Fifths & Key Signatures | 五度循环与调号公式
The circle of fifths is a visual formula for all key signatures. Moving clockwise, each new sharp is a perfect fifth higher (C–G–D–A–E–B–F♯–C♯). The new sharp is always the leading note (7th degree) of the new key. The order of sharps: F♯, C♯, G♯, D♯, A♯, E♯, B♯.
五度循环是所有调号的形象公式。顺时针方向，每增加一个新的升号，就是高一个纯五度（C–G–D–A–E–B–F♯–C♯）。新出现的升号总是新调的导音（第七级）。升号出现的顺序为：F♯, C♯, G♯, D♯, A♯, E♯, B♯。
Moving anticlockwise, each new flat is a perfect fifth lower (C–F–B♭–E♭–A♭–D♭–G♭–C♭). The new flat is the subdominant (4th degree) of the new key. Order of flats: B♭, E♭, A♭, D♭, G♭, C♭, F♭.
逆时针方向，每增加一个新的降号，就是低一个纯五度（C–F–B♭–E♭–A♭–D♭–G♭–C♭）。新出现的降号总是新调的下属音（第四级）。降号出现的顺序为：B♭, E♭, A♭, D♭, G♭, C♭, F♭。
To quickly find the relative minor, count down a minor 3rd from the major tonic (e.g., C major → A minor). The relative major of a minor key is found by counting up a minor 3rd. Both share the same key signature, so this is a powerful shortcut in the listening exam.
快速找到关系小调的方法是从大调主音向下数一个小三度（如 C 大调 → a 小调）。从小调找关系大调则向上数一个小三度。两者共享同一个调号，这在听力考试中是一个极为有用的捷径。
6. Time Signature Formulas | 拍号公式
A time signature looks like a fraction, but it is a formula indicating how many beats are in a bar and what note value counts as one beat. The top number of a simple time signature (2/4, 3/4, 4/4) tells you the number of beats; the bottom number tells you the beat value (4 = crotchet beat). In simple time, each beat divides into two equal notes.
拍号看起来像分数，但它是一个公式，表明每小节有多少拍，以及以什么音符为一拍。单拍子拍号（2/4, 3/4, 4/4）的上方数字表示拍数；下方数字表示以几分音符为一拍（4 代表四分音符为一拍）。在单拍子中，每一拍可以分成两个相等的音符。
Compound time signatures (6/8, 9/8, 12/8) have a top number divisible by 3. The beat is a dotted note, not the single note on the bottom. To find the number of beats, divide the top number by 3. To find the beat note, multiply the bottom note value by 1.5: e.g., 6/8 has 2 dotted-crotchet beats per bar. This formula avoids confusion in rhythm dictation.
复拍子拍号（6/8, 9/8, 12/8）的上方数字可被 3 整除。这时一拍写成附点音符，而不是下方数字代表的单个音符。要计算每小节的拍数，将上方数字除以 3；要找到拍子音符，将下方音符的时值乘以 1.5。例如，6/8 拍每小节有 2 个附点四分音符的拍子。这个公式可避免节奏听写中的混淆。
7. Rhythm Duration Formulas | 节奏时值公式
Rhythm values follow a simple doubling/halving rule. A semibreve equals 2 minims; a minim equals 2 crotchets; a crotchet equals 2 quavers; a quaver equals 2 semiquavers. A dot after a note increases its duration by half its original value: crotchet + dot = 1.5 crotchets (or 3 quavers). Double dot adds half of the first dot’s value. A triplet sign ‘3’ over three notes means those three notes are played in the time of two of the same type.
节奏时值遵循简单的倍增/减半法则。全音符等于 2 个二分音符；二分音符等于 2 个四分音符；四分音符等于 2 个八分音符；八分音符等于 2 个十六分音符。音符后面的附点将其时值增加原本的一半：一个附点四分音符等于 1.5 个四分音符（或 3 个八分音符）。双重附点再增加第一个附点时值的一半。三连音记号“3”表示三个音在原本两个相同类型音的时值内奏出。
When adding note stems, the rule is: stems go up if the note is below the middle line of the stave, and down if above; notes on the middle line may go either direction but usually follow the surrounding notes. Beams connect notes according to the beat grouping shown by the time signature.
添加符干时，规则是：音符在五线谱中线以下符干向上，中线以上符干向下；中线上的音符可向上或向下，通常跟随前后音符的方向。符杠的连接要依据拍号显示的节拍分组。
8. Cadence Formulas | 终止式公式
Cadences are the musical equivalent of punctuation marks. A perfect cadence is V–I (or V7–I), sounding final and conclusive. A plagal cadence is IV–I, often called the ‘Amen’ cadence. An imperfect cadence ends on V, leaving the music feeling unfinished (I–V, ii–V, IV–V). An interrupted cadence is V–vi (or V–VI in minor), creating a surprise by avoiding the expected tonic.
终止式好比音乐中的标点符号。完全终止是 V–I（或 V7–I），听感圆满结束。变格终止是 IV–I，常被称为“阿门终止”。不完全终止结束在 V 级上，造成未完结的感觉（I–V, ii–V, IV–V）。阻碍终止是 V–vi（小调为 V–VI），通过避开预期的主和弦制造意外感。
To identify cadences in a listening extract, focus on the bass line movement and the last two chords of a phrase. Always check the key and listen for the leading note resolving to the tonic in perfect cadences.
在听力选段中识别终止式时，要关注低音线条的进行和乐句的最后两个和弦。务必确认调性，并注意在完全终止中导音解决到主音的倾向。
9. Ornamentation Quick Reference | 装饰音速查
Ornaments are formulaic decorations that add expressiveness to a melody. The trill (tr) is a rapid alternation between the written note and the one above, usually starting on the upper note. The turn (𝄐) plays the upper, written, lower, written note in quick succession. The mordent (upper Mordent 𝆜) plays written, upper, written; the lower mordent (𝆝) plays written, lower, written. The appoggiatura is a leaning note that takes half the value of the main note and resolves by step. The acciaccatura (𝆞) is a crushed note played as quickly as possible before the main note.
装饰音是程式化的加花，为旋律增添表现力。颤音（tr）是在记谱音和上方音之间快速交替，通常从上方音开始。回音（𝄐）快速奏出上方音、记谱音、下方音、记谱音。上波音（𝆜）奏成记谱音、上方音、记谱音；下波音（𝆝）奏成记谱音、下方音、记谱音。倚音是一个依附于主干音的音，占主干音一半的时值，并级进解决。碎音（𝆞）是一个尽可能短促地奏出、然后立即进入主干音的装饰音。
In your CCEA set works and unseen extracts, ornaments may be written out in full or indicated only by symbols. Practise recognising both notations and hearing the difference between a trill and a turn.
在 CCEA 的规定作品和陌生选段中，装饰音可能被完整记谱，也可能只标出符号。要练习识别两种记谱方式，并听辨颤音与回音的区别。
10. Transposition Formulas for Instruments | 乐器移调公式
Many instruments are transposing instruments, meaning their written pitch differs from the sounding pitch. For a B♭ clarinet or trumpet, the written note sounds a whole tone lower; the formula to convert written pitch to concert pitch is ‘written note + whole tone down’. Effectively, these instruments add two flats to the key signature of the piece compared to concert pitch.
许多乐器是移调乐器，即乐谱上的记谱音与实际发音音高不同。对于 B♭ 单簧管或 B♭ 小号，记谱音要比实际发音音高高一个大二度；将记谱音转换为实际音高的公式是“记谱音向下一个大二度”。实际上，这类乐器的调号会比 concert pitch（实际音高）的调号多两个降号。
For F horn, the written note sounds a perfect 5th lower (or perfect 4th higher). Alto sax is in E♭ (written sounds a major 6th lower). To transpose a part for these instruments, first determine the target key by calculating the interval of transposition, then write the notes at the correct pitch relative to the new key signature.
对于 F 调圆号，记谱音比实际发音高一个纯五度（或者说发音低纯四度）。中音萨克斯是 E♭ 调（记谱音发音低大六度）。为这些乐器移调时，先通过计算移调音程确定目标调号，然后依据新调号在正确的音高上记谱。
11. Musical Terms & Signs Formula Sheet | 音乐术语与记号公式表
Candidates must be fluent in Italian, German, and French terms that appear in CCEA listening questions. Tempo markings follow predictable patterns: adagio (slow), andante (walking pace), moderato (moderate), allegro (fast), presto (very fast). Modifiers like ‘molto’ (very) and ‘poco’ (a little) can be attached to these. Dynamics: pp (pianissimo, very soft), p (piano, soft), mp (mezzo-piano, moderately soft), mf (mezzo-forte, moderately loud), f (forte, loud), ff (fortissimo, very loud), with cresc. (crescendo, gradually louder) and dim. (diminuendo, gradually softer).
考生必须熟悉出现在 CCEA 听力问题中的意大利语、德语和法语术语。速度标记遵循可预见的模式：adagio（慢板），andante（行板），moderato（中板），allegro（快板），presto（急板）。可以加上修饰词如 molto（很）和 poco（稍微）。力度术语：pp（pianissimo，很弱），p（piano，弱），mp（mezzo-piano，中弱），mf（mezzo-forte，中强），f（forte，强），ff（fortissimo，很强），以及 cresc.（渐强）和 dim.（渐弱）。
Articulation signs include legato (smooth, indicated by a slur), staccato (short and detached, shown by a dot above or below the note), accent (> or sfz, meaning sudden emphasis), and tenuto (held for full value, marked with a line). Use these ‘formulas’ to describe how a passage should be played.
演奏法记号包括连奏（legato，平滑，用连线表示），断奏（staccato，短促断开，用音符上下的圆点表示），重音（> 或 sfz，表示突然强调），以及保持音（tenuto，奏足时值，用短横线表示）。熟练使用这些“公式”可以准确描述乐段应有的演奏方式。
12. Compositional Devices Formula Toolkit | 作曲技法公式工具箱
Repetition, sequence, imitation, and inversion are structural formulas frequently examined. A sequence repeats a short melodic or rhythmic idea at a higher or lower pitch; if the intervals remain exactly the same, it is a real sequence; if they are adjusted to stay within the key, it is a tonal sequence. Imitation is when one part echoes another, as in a canon or fugue. Inversion turns a melody upside down — an ascending interval becomes descending by the same number of steps.
重复、模进、模仿和倒影是常考的结构性公式。模进是将一个短小的旋律或节奏动机在更高或更低的音高上重复；如果音程完全相同，那就是完全模进；如果为适应调性而调整了音程，则是调性模进。模仿是指一个声部对另一声部的回声式追随，如卡农或赋格。倒影是将旋律上下颠倒——原本上行的音程变为同度数的下行音程。
Other devices include pedal (a held or repeated note, usually in the bass, under changing harmonies), ostinato (a persistently repeated pattern), and augmentation/diminution (stretching or compressing note values by a factor of 2). These are your toolkit for both recognising set work features and answering ‘describe the music’ questions.
其他作曲技法包括持续音（在和声变化时保持或重复的低音）、固定音型（持续重复的模式），以及增值和减值（将音符时值按 2 的倍数拉长或缩短）。这些即是你辨识规定作品特征和回答“描述音乐”问题的工具箱。
Published by TutorHao | Music Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply