📚 AS Edexcel Music: Formula & Theorem Quick Reference | AS Edexcel 音乐：公式定理速查手册
Welcome to the AS Edexcel Music Quick Reference. In music, ‘formulas’ and ‘theorems’ appear as interval patterns, chord recipes, scale structures and notational rules. This handbook converts those building blocks into a rapid-access bilingual aid, helping you recall critical information instantly during analysis, dictation and composition tasks.
欢迎使用 AS Edexcel 音乐速查手册。在音乐中，“公式”与“定理”体现为音程模式、和弦配方、音阶结构以及记谱规则。这本手册将这些核心构件转化为中英双语速查工具，帮助你在分析、听写与创作中迅速调用关键信息。
1. Note Values and Their Formulas | 音符时值及其公式
Rhythmic notation follows precise proportional ‘formulas’. Each note value is exactly half the duration of the next longer one. The whole note (semibreve) acts as the base unit: it equals 2 half notes, 4 quarter notes, 8 eighth notes, or 16 sixteenth notes.
节奏记谱遵循精确的比例“公式”。每个音符时值恰好是下一个较长音符的一半。全音符（semibreve）作为基础单位：它等于2个二分音符、4个四分音符、8个八分音符或16个十六分音符。
The rest symbols mirror note durations. A whole rest hangs from the 4th line; a half rest sits on the 3rd line. Dotted notes add 50% of the original value: dotted half note = half note + quarter note.
休止符与音符时值一一对应。全休止符悬挂在第四线下方，二分休止符坐在第三线上。附点音符增加原时值的一半：附点二分音符 = 二分音符 + 四分音符。
½ → ¼ → ⅛ (each step halves the value)
½ → ¼ → ⅛（每步时值减半）
| English Name | 中文 | Beats (quarter as 1) | Rest Name |
|---|---|---|---|
| whole note | 全音符 | 4 | whole rest |
| half note | 二分音符 | 2 | half rest |
| quarter note | 四分音符 | 1 | quarter rest |
| eighth note | 八分音符 | 1/2 | eighth rest |
| sixteenth note | 十六分音符 | 1/4 | sixteenth rest |
2. Time Signatures and Rhythmic Grouping Rules | 拍号与音值组合规则
A time signature is a fraction-like sign: the top number shows beats per bar, the bottom number indicates which note gets one beat (4=quarter, 8=eighth, 2=half). Simple time has a top number of 2, 3 or 4; compound time uses 6, 9 or 12, where each beat divides into three subdivisions.
拍号是一个分数式标志：上方数字表示每小节的拍数，下方数字指明以何种音符为一拍（4代表四分音符，8代表八分音符，2代表二分音符）。单拍子拍号上方为2、3或4；复拍子使用6、9或12，其中每拍分为三个次分点。
Grouping formulas: in simple time, beams must not cross the middle of the bar and should reflect beats. In 4/4, you join eighth notes per beat; you cannot beam across beats 2 and 3. In compound time, beaming shows the dotted-crotchet beat.
组合公式：单拍子中，符杠不能跨越小节中线，必须按拍分组。在4/4中，按每拍组合八分音符；不能将第2拍和第3拍的音符连在一起。复拍子中，符杠要体现附点四分音符的拍子。
| Time Signature | Type | Beat Division |
|---|---|---|
| 2/4, 3/4, 4/4 | simple | beat = quarter, subdivide in 2s |
| 6/8, 9/8, 12/8 | compound | beat = dotted quarter, subdivide in 3s |
3. Key Signatures: The Circle of Fifths Formula | 调号：五度圈公式
Sharp keys: count upward by perfect 5ths from C major. Each new key adds one sharp; the tonic of a major key with sharps is a semitone above the last sharp. For example, the last sharp in E major (F♯, C♯, G♯, D♯) is D♯, so tonic is E.
升号调：从C大调向上按纯五度推算。每个新调增加一个升号；升号大调的主音是最后一个升号上方的小二度。例如E大调的升号为F♯、C♯、G♯、D♯，最后一个升号为D♯，主音即为E。
Flat keys: count downward by perfect 5ths. The tonic of a major key with flats is the second-to-last flat. In A♭ major (B♭, E♭, A♭, D♭), the second-to-last flat is A♭.
降号调：从C大调向下按纯五度推算。降号大调的主音是倒数第二个降号。在A♭大调（B♭、E♭、A♭、D♭）中，倒数第二个降号就是A♭。
| Major key | Sharps/Flats | Relative Minor |
|---|---|---|
| C major | 0 | A minor |
| G major | 1♯ (F♯) | E minor |
| D major | 2♯ | B minor |
| F major | 1♭ (B♭) | D minor |
| B♭ major | 2♭ | G minor |
Major tonic = last sharp + 1 semitone | Major tonic = 2nd-flat-from-end
大调主音 = 最后一个升号 + 1个半音 | 大调主音 = 倒数第二个降号
4. Interval Formulas: Semitone Counting and Inversions | 音程公式：半音计算与转位
Interval name = quality (perfect, major, minor, augmented, diminished) + number (2nd, 3rd, etc.). Work out the number from distance in letter names; then count semitones to determine quality. Perfect intervals (unison, 4th, 5th, octave) become augmented when expanded by a semitone, diminished when shrunk.
音程名称 = 性质（纯、大、小、增、减）+ 度数（二度、三度等）。先由音名字母距离确定度数，然后数半音确定性质。纯音程（同度、四度、五度、八度）扩大半音变为增，缩小半音变为减。
Major/minor intervals relate to scales: a major interval comes from the major scale; a minor interval is one semitone smaller. The semitone table below offers a quick reference.
大/小音程与音阶相关：大音程来自大调音阶；小音程比它小一个半音。下表提供快速参考。
| Interval | Semitones | Example |
|---|---|---|
| Minor 2nd | 1 | E-F |
| Major 2nd | 2 | C-D |
| Minor 3rd | 3 | D-F |
| Major 3rd | 4 | C-E |
| Perfect 4th | 5 | C-F |
| Perfect 5th | 7 | C-G |
| Minor 6th | 8 | E-C |
| Major 6th | 9 | C-A |
| Minor 7th | 10 | D-C |
| Major 7th | 11 | C-B |
| Octave | 12 | C-C |
Inversion formula: Interval number = 9 – original number. Quality flips: major ↔ minor, perfect ↔ perfect, augmented ↔ diminished.
转位公式：转位度数 = 9 – 原位度数。性质互换：大 ↔ 小，纯 ↔ 纯，增 ↔ 减。
5. Triad and Seventh Chord Recipes | 三和弦与七和弦配方
Triads are built by stacking two thirds (major or minor) above a root. The formula for a major triad is: root + 4 semitones (major 3rd) + 3 semitones (minor 3rd). The outer interval is a perfect 5th (7 semitones).
三和弦是在根音上叠加两个三度（大或小）构成的。大三和弦配方：根音 + 4个半音（大三度）+ 3个半音（小三度）。外围音程为纯五度（7个半音）。
Minor triad: root + 3 semitones (minor 3rd) + 4 semitones (major 3rd). Diminished: root + minor 3rd + minor 3rd (outer fifth is diminished, 6 semitones). Augmented: root + major 3rd + major 3rd (outer fifth is augmented, 8 semitones).
小三和弦：根音 + 3个半音（小三度）+ 4个半音（大三度）。减三和弦：根音 + 小三度 + 小三度（外围五度为减五度，6个半音）。增三和弦：根音 + 大三度 + 大三度（外围五度为增五度，8个半音）。
Seventh chords add a third above the fifth. Dominant 7th: major triad + minor 7th. Formula in semitones from root: 0-4-7-10. Major 7th: major triad + major 7th (0-4-7-11). Minor 7th: minor triad + minor 7th (0-3-7-10).
七和弦在五音之上再加一个三度。属七和弦：大三和弦 + 小七度。半音公式：0-4-7-10。大七和弦：大三和弦 + 大七度（0-4-7-11）。小七和弦：小三和弦 + 小七度（0-3-7-10）。
Triad = Root + (M3/m3) + (m3/M3); 7th = Triad + extra 3rd
三和弦 = 根音 +（大三度/小三度）+（小三度/大三度）；七和弦 = 三和弦 + 额外三度
6. Inversions and Figured Bass Shorthand | 转位与数字低音速记
Chord inversions are labeled with figured bass numbers showing intervals above the bass note. Root position: 5/3 (often omitted). First inversion: 6 (or 6/3). Second inversion: 6/4.
和弦转位用数字低音标记，表示低音上方音程。原位：5/3（常省略）。第一转位：6（或6/3）。第二转位：6/4。
For seventh chords, root position is 7; first inversion is 6/5; second inversion is 4/3; third inversion is 4/2 (or simply 2).
对于七和弦，原位为7；第一转位为6/5；第二转位为4/3；第三转位为4/2（或简写为2）。
| Chord type | Root | 1st inv. | 更多咨询请联系16621398022（同微信）
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