📚 Music Theory Quick Reference & Formulas for Year 10 Eduqas Music | 10年级Eduqas音乐理论公式速查
This handbook compiles the essential formulas, definitions, and rules needed for the Year 10 Eduqas GCSE Music course. Use it to revise scale patterns, interval measurements, chord construction, rhythmic values, key signatures, and other fundamental theory elements that underpin listening, performing, and composing tasks. Each section presents the core concept as a concise formula, followed by a clear explanation.
本手册汇编了10年级Eduqas GCSE音乐课程所需的关键公式、定义及规则。你可以用它来复习音阶模式、音程计算、和弦构成、节奏时值、调号以及其他支撑听辨、表演与创作的基础理论知识。每个小节将核心概念提炼为简洁公式，并附上清晰的解释。
1. Scale Formulas | 音阶公式
A major scale is built using the pattern of whole tones (T) and semitones (S): T-T-S-T-T-T-S. In semitone steps from the tonic, the distances are 0, 2, 4, 5, 7, 9, 11, 12.
大调音阶由全音（T）和半音（S）的模式构建：全-全-半-全-全-全-半。从主音开始的半音距离为 0, 2, 4, 5, 7, 9, 11, 12。
The natural minor scale uses T-S-T-T-S-T-T, corresponding to semitones 0, 2, 3, 5, 7, 8, 10, 12. The harmonic minor raises the 7th degree, producing T-S-T-T-S-3S-S (semitones 0, 2, 3, 5, 7, 8, 11, 12). The melodic minor ascending raises both the 6th and 7th: T-S-T-T-T-T-S (0, 2, 3, 5, 7, 9, 11, 12); descending, it returns to the natural minor.
自然小调用全-半-全-全-半-全-全，半音数为 0, 2, 3, 5, 7, 8, 10, 12。和声小调升高第 VII 级音，形成 T-S-T-T-S-增二度-半音（0,2,3,5,7,8,11,12）。旋律小调上行升高第 VI 和第 VII 级：T-S-T-T-T-T-S（0,2,3,5,7,9,11,12）；下行还原为自然小调。
The whole-tone scale consists entirely of whole tones: T-T-T-T-T-T. The chromatic scale is built from twelve consecutive semitones.
全音音阶完全由全音构成：T-T-T-T-T-T。半音音阶则由十二个连续的半音组成。
2. Interval Formulas | 音程公式
An interval is named by its size in scale degrees (second, third, fourth, etc.) and its quality (perfect, major, minor, augmented, diminished). The number of semitones determines the exact quality. These formulas let you identify any interval quickly.
音程的名称由度数（二度、三度、四度等）和性质（纯、大、小、增、减）决定。半音的数量决定具体性质。以下公式可帮你快速识别任何音程。
| Interval | Semitones | 音程 | 半音数 |
|---|---|---|---|
| Minor 2nd | 1 | 小二度 | 1 |
| Major 2nd | 2 | 大二度 | 2 |
| Minor 3rd | 3 | 小三度 | 3 |
| Major 3rd | 4 | 大三度 | 4 |
| Perfect 4th | 5 | 纯四度 | 5 |
| Augmented 4th / Diminished 5th | 6 | 增四度/减五度 | 6 |
| Perfect 5th | 7 | 纯五度 | 7 |
| Minor 6th | 8 | 小六度 | 8 |
| Major 6th | 9 | 大六度 | 9 |
| Minor 7th | 10 | 小七度 | 10 |
| Major 7th | 11 | 大七度 | 11 |
| Perfect 8ve | 12 | 纯八度 | 12 |
To invert an interval, subtract its semitone size from 12. A perfect 5th (7 semitones) inverts to a perfect 4th (5 semitones). Major intervals become minor, and diminished intervals become augmented.
将音程转位，用12减去它的半音数。纯五度（7个半音）转位变成纯四度（5个半音）。大音程转位变成小音程，减音程转位变成增音程。
3. Chord Construction Formulas | 和弦构成公式
Chords are built by stacking intervals on a root note. The semitone distances between successive notes define the chord quality. Memorise these fundamental triads and seventh chords as stacking formulas of semitones.
和弦由根音上叠加音程构成。相邻音之间的半音数决定了和弦的性质。熟记以下三和弦与七和弦的半音叠加公式。
Triads – Major: root + 4 semitones (3rd) + 3 semitones (5th). Minor: root + 3 + 4. Augmented: root + 4 + 4. Diminished: root + 3 + 3.
三和弦 – 大三和弦：根音 + 4个半音（三音） + 3个半音（五音）。小三和弦：根音 + 3 + 4。增三和弦：根音 + 4 + 4。减三和弦：根音 + 3 + 3。
Seventh chords – Dominant 7th: major triad + minor 7th (semitone stack 4 + 3 + 3). Major 7th: major triad + major 7th (4 + 3 + 4). Minor 7th: minor triad + minor 7th (3 + 4 + 3). Half-diminished 7th: diminished triad + major 6th enharmonic minor 7th (3 + 3 + 4). Diminished 7th: diminished triad + diminished 7th (3 + 3 + 3).
七和弦 – 属七和弦：大三和弦 + 小七度（半音叠加 4 + 3 + 3）。大七和弦：大三和弦 + 大七度（4 + 3 + 4）。小七和弦：小三和弦 + 小七度（3 + 4 + 3）。半减七和弦：减三和弦 + 大六度（实际等音小七度）（3 + 3 + 4）。减七和弦：减三和弦 + 减七度（3 + 3 + 3）。
Inversions are named by the lowest sounding note: first inversion has the 3rd in the bass, second inversion the 5th, and third inversion (for seventh chords) the 7th. Figured bass numbers (e.g. 6, 6/4, 4/2) indicate intervals above the bass, but remember the formulas above to construct them from root position.
转位由最低音命名：第一转位以三音为低音，第二转位以五音为低音，七和弦的第三转位以七音为低音。数字低音记号（如 6, 6/4, 4/2）表示低音上方的音程，但记住上述根音位置公式就能构建出来。
4. Key Signatures & The Circle of Fifths | 调号与五度圈
The circle of fifths arranges keys by the number of sharps or flats in their key signatures, ascending by perfect fifths. Going clockwise adds one sharp each step; going anticlockwise adds one flat. The order of sharps is F♯, C♯, G♯, D♯, A♯, E♯, B♯. The order of flats is the reverse: B♭, E♭, A♭, D♭, G♭, C♭, F♭.
五度圈根据调号中升降号的数量排列各调，向上纯五度进行。顺时针每步增加一个升号；逆时针增加一个降号。升号出现的顺序为 F♯, C♯, G♯, D♯, A♯, E♯, B♯。降号的顺序与之相反：B♭, E♭, A♭, D♭, G♭, C♭, F♭。
To quickly identify a sharp key, look at the last sharp in the signature; the key is a semitone above that note. For example, if the last sharp is D♯, the major key is E. For flat keys, the second-to-last flat in the signature names the major key; the key of B♭ major has two flats (B♭, E♭), so the second-to-last flat is B♭.
快速识别升号调：看调号中的最后一个升号，上移半音即为主音。例如最后一个升号为 D♯，则大调为 E。对于降号调，看倒数第二个降号，即为大调主音；B♭ 大调有两个降号（B♭, E♭），倒数第二个降号 B♭ 即为主音。
The relative minor key shares the same key signature and is found a minor third (3 semitones) below the major tonic. The tonic major key of a minor key is a minor third above.
关系小调与主调共用同一个调号，其主音位于大调主音下方小三度（3个半音）。小调的关系大调则位于其上方小三度。
5. Note & Rest Value Equivalents | 音符与休止符时值换算
In simple time, note values are binary multiples. Use these formulas to relate durations within a bar of 4/4. The whole note (semibreve) is the reference value.
在简单拍子中，音符时值呈二进制倍数关系。以下公式帮助你在4/4拍的小节内关联各时值。全音符（semibreve）为基准值。
| Note/Rest | Relative duration | 音符/休止符 | 相对时值 |
|---|---|---|---|
| Semibreve (whole) | 1 (4 beats in 4/4) | 全音符 | 1（4/4拍中4拍） |
| Minim (half) | ½ (2 beats) | 二分音符 | ½（2拍） |
| Crotchet (quarter) | ¼ (1 beat) | 四分音符 | ¼（1拍） |
| Quaver (eighth) | 1/8 (½ beat) | 八分音符 | 1/8（½拍） |
| Semiquaver (sixteenth) | 1/16 (¼ beat) | 十六分音符 | 1/16（¼拍） |
Rests follow the same relative durations and simply indicate silence. A whole-bar rest, regardless of the time signature, is represented by a semibreve rest hanging below the line.
休止符的时值对应关系相同，仅表示静默。全小节休止符无论拍号均用全休止符标记，悬挂在线下方。
6. Dotted Notes, Double Dots & Tuplets | 附点、复附点与连音
A dot increases a note's or rest' a is: dotted value = original value × 1.5. A double dot adds another half of the first dot's value, giving a total factor of 1.75 (original + 0.5 + 0.25).
附点将音符或休止符的时值增加原时值的一半。公式为：附点时值 = 原时值 × 1.5。复附点再增加第一个附点时值的一半，总倍数为 1.75（原值 + 0.5 + 0.25）。
e quavers). A double-dotted minim equals 3.5 crotchet beats (minim = 2, plus 1, plus 0.5).
例如，附点四分音符等于 1.5 个四分音符的拍值（三个八分音符）。复附点二分音符等于 3.5 个四分音符（二分=2，加1，加0.5）。
Tuplets are irregular divisions of a beat. A triplet means 'three notes in the space of two' ⅔ of the regular note value. A crotchet triplet fits into one minim beat; a quaver triplet fits into one crotchet beat.
连音是对节拍的非均匀划分。三连音表示“在原本两个音的时值内演奏三个音”。公式为：三连音单音时值 = 原单音时值 × 2/3。四分三连音占一个二分音符的时值；八分三连音占一个四分音符的时值。
Other tuplets include duplets (2 in the time of 3), quintuplets, and sextuplets, all defined by the ratio of the number of notes to the normal number they replace.
其他连音包括二连音（以二对三）、五连音、六连音等，均由替换音符数与常规音符数之比确定。
7. Time Signatures & Metre | 拍号与节拍
otchet, 8 = quaver, 2 = minim). Simple metres have a top number of 2, 3, or 4 and each beat divides into two equal halves.
拍号写作两个数字。上方数字表示每小节的拍数，下方数字表示以何种音符为一拍（4代表四分音符，8代表八分音符，2代表二分音符）。简单拍子的上方数字通常为2、3或4，每拍可均匀分为两半。
Compound metres have a top number of 6, 9, or 12 and each beat divides into three dotted rhythms. The beat is a dotted note. For example, 6/8 means two dotted crotchet beats per bar; 9/8 means three; 12/8 means four.
复合拍子的上方数字为6、9或12，每拍由三个均分的音组成，拍子本身是附点音符。例如 6/8 拍表示每小节有两个附点四分音符的拍子；9/8 拍有三个；12/8 拍有四个。
Irregular metres have beat groupings that are not consistent throughout. 5/4 may be grouped as 3+2 or 2+3. 7/8 may be 2+2+3 or 3+2+2. Always look for beaming and accent patterns to determine the grouping.
不规整拍子的节奏组合不恒定。5/4 拍可能组合为 3+2 或 2+3。7/8 拍可能为 2+2+3 或 3+2+2。要根据符尾连接和重音模式判断组合方式。
8. Dynamics & Tempo Markings | 力度与速度术语
Dynamics indicate volume. The standard Italian terms used from soft to loud are: 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 include crescendo (cresc., getting louder) and diminuendo/dim. (dim., getting softer). sforzando (sfz) indicates a sudden strong accent.
力度标记表示音量。从弱到强的标准意大利术语为：pp (pianissimo, 很弱)、p (piano, 弱)、mp (mezzo-piano, 中弱)、mf (mezzo-forte, 中强)、f (forte, 强)、ff (fortissimo, 很强)。渐强用 crescendo (cresc.) 表示，渐弱用 diminuendo / dim. 表示。sforzando (sfz) 表示突强重音。
derato (moderately), Allegretto (slightly lively). Fast: Allegro (fast, cheerful), Vivace (lively, quick), Presto (very fast). Metronome marks give beats per minute, e.g. ♩ = 120.
速度标记设定节奏快慢。慢速术语：Largo（宽广地，很慢）、Adagio（从容的慢板）、Lento（缓慢）。中速：Andante（行板）、Moderato（中板）、Allegretto（稍快的小快板）。快速：Allegro（快板）、Vivace（活泼的快板）、Presto（急板）。节拍器标记给出每分钟拍数，如 ♩ = 120。
Tempo changes: accelerando (accel., gradually faster), ritardando/ritenuto (rit., gradually slower), rubato (expressive freedom in tempo), a tempo (return to the original tempo).
速度变化：accelerando (accel., 渐快)、ritardando/ritenuto (rit., 渐慢)、rubato（弹性速度）、a tempo（恢复原速）。
9. Cadences & Harmonic Progressions | 终止式与和声进行
A cadence is a formula of two chords that ends a phrase. The four principal cadences are defined by the chords used. Perfect cadence: V–I (or V7–I), sounding final and complete. Plagal cadence: IV–I, the 'Amen' cadence. Imperfect cadence: I–V, II–V, or IV–V, ending on V and sounding unfinished. Interrupted/deceptive cadence: V–vi (in major) or V–VI (in minor), a surprise move.
终止式是结束乐句的两个和弦组成的公式。四种主要终止式由所用和弦定义。正格终止：V–I（或 V7–I），听起来完满结束。变格终止：IV–I，即“阿们”终止。不完全终止：I–V、II–V 或 IV–V，停在 V 上，听起来未结束。阻碍终止：V–vi（大调）或 V–VI（小调），是一种意外进行。
Chord progressions often follow standard patterns. In a major key, the primary triads (I, IV, V) form the backbone. A common formula is I–vi–IV–V–I. The 12-bar blues uses I–I–I–I, IV–IV–I–I, V–IV–I–I (or with V at bar 10). Simplify by thinking in Roman numerals and remembering that minor chords ii, iii, vi are also available in the key.
和弦进行常遵循固定模式。在大调中，正三和弦（I, IV, V）构成骨架。常见公式如 I–vi–IV–V–I。12小节蓝调使用 I–I–I–I, IV–IV–I–I, V–IV–I–I（或第10小节用 V）。用罗马数字思考，并记住在该调中同样可以使用小三和弦 ii、iii、vi。
10. Ornaments & Articulation | 装饰音与演奏法
Ornaments are abbreviated symbols that add decoration to a note. The tr
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