📚 Year 10 Edexcel Music: Quick-Reference Handbook of Formulas & Theorems | 公式定理速查手册
This handbook gathers the core formulas, construction patterns, and mathematical relationships that Year 10 Edexcel Music students need to use fluently for listening, performing, and composing. Each rule is presented in a clear bilingual pair—English followed by Chinese—so you can memorise the logic behind note values, intervals, scales, chords, cadences, and key signatures as a set of reliable 'theorems'.
本手册收录了 Edexcel 音乐 Year 10 学生必须灵活运用的核心公式、构建模式与数理关系，涵盖听辨、演奏与创作所需的原理。每条规则均以清晰的双语对照呈现——英文之后紧跟中文，帮助你像记忆定理一样掌握音符时值、音程、音阶、和弦、终止式与调号背后的逻辑。
1. Note Value & Rest Mathematics | 音符与休止符的时值运算
In common time, a semibreve (whole note) equals two minims (half notes), four crotchets (quarter notes), eight quavers (eighth notes), sixteen semiquavers (sixteenth notes), and thirty-two demisemiquavers. The same ratios hold for rests: a semibreve rest fills a whole bar of 4/4, while a minim rest lasts half as long.
在常规拍号中，一个全音符等于两个二分音符、四个四分音符、八个八分音符、十六个十六分音符、三十二个三十二分音符。休止符的比值相同：全休止符占满4/4拍的一个完整小节，二分休止符时值为其一半。
Dotted notes multiply the basic duration by 1.5: a dotted minim lasts three crotchets. A double-dotted note multiplies by 1.75 (original + half + quarter). A tie simply adds the two note values together.
附点音符将基本时值乘以1.5：附点二分音符持续三个四分音符的长度。双附点音符乘以1.75（原值 + 一半 + 四分之一）。延音线直接将两个音符的时值相加。
| Note/Rest | British Name | Crotchet Equivalents | American Equivalent |
|---|---|---|---|
| 𝅝 / 𝄻 | Semibreve | 4 | Whole note / Whole rest |
| 𝅗𝅥 / 𝄼 | Minim | 2 | Half note / Half rest |
| 𝅘𝅥 / 𝄽 | Crotchet | 1 | Quarter note / Quarter rest |
| 𝅘𝅥𝅮 / 𝄾 | Quaver | 1/2 | Eighth note / Eighth rest |
| 𝅘𝅥𝅯 / 𝄿 | Semiquaver | 1/4 | Sixteenth note / Sixteenth rest |
2. Time Signature Formula | 拍号公式
The top number tells you how many beats are in each bar; the bottom number tells you which note value counts as one beat. If the bottom number is 4, the beat unit is a crotchet; if it is 8, the beat unit is a quaver; if it is 2, a minim.
上方数字表示每小节有多少拍；下方数字表示哪种音符为一拍。若下方数字为4，拍子单位是四分音符；若为8，单位是八分音符；若为2，单位是二分音符。
Simple time signatures have beats that divide into two equal parts (e.g., 2/4, 3/4, 4/4). Compound time signatures have dotted-note beats that divide into three equal parts (e.g., 6/8, 9/8, 12/8). To find the number of dotted-beat pulses in compound time, divide the top number by 3.
单拍子的每一拍可平分为两个等份（如2/4、3/4、4/4）。复拍子的每一拍是一个附点音符，可均分为三等份（如6/8、9/8、12/8）。在复拍子中，用上方数字除以3即可得出附点拍的数量。
3. Major Scale Formula (The Tone–Semitone Pattern) | 大调音阶公式（全音-半音模式）
Every major scale follows the same fixed pattern of tones (T) and semitones (S):
所有大调音阶都遵循相同的全音（T）与半音（S）顺序：
T – T – S – T – T – T – S
Starting from any tonic, apply the pattern. In C major, the semitones fall naturally between E–F and B–C. When you start on G, you need F♯ to preserve the semitone between the seventh and eighth degrees; starting on F requires B♭ to create the semitone between the fourth and fifth degrees.
从任一主音出发套用此模式。C大调中，半音自然落在E–F与B–C之间。若从G开始，需要升F（F♯）来保持第七级与第八级之间的半音；从F开始则需要降B（B♭），以保证第四级与第五级之间的半音。
4. Minor Scale Formulae (Natural, Harmonic, Melodic) | 小调音阶公式（自然、和声、旋律）
Natural minor: T – S – T – T – S – T – T
Harmonic minor: T – S – T – T – S – T+S – S (an augmented 2nd appears between the 6th and 7th degrees)
Melodic minor (ascending): T – S – T – T – T – T – S (raised 6th and 7th); descending reverts to natural minor.
自然小调：T – S – T – T – S – T – T
和声小调：T – S – T – T – S – T+S – S（六级与七级之间为增二度）
旋律小调上行：T – S – T – T – T – T – S（升高六级与七级）；下行还原为自然小调。
You can derive any harmonic minor scale by taking the natural minor and raising the 7th degree by a semitone. For melodic minor, raise both the 6th and 7th by a semitone when ascending, and then lower them back when descending.
任何和声小调可由自然小调升高七级一个半音得到。旋律小调上行时同时升高六级与七级，下行时将它们还原。
5. Interval Calculation | 音程计算
An interval is named by counting letter names (the interval number) and then measuring the exact number of semitones to determine its quality (perfect, major, minor, augmented, diminished). Always count from the lower note upward.
音程的命名方法是先数音名字母的个数（度数），再计算具体的半音数，以判定其性质（纯、大、小、增、减）。始终从低音向上数。
| Interval Name | Short Form | Semitones |
|---|---|---|
| Perfect unison | P1 | 0 |
| Minor second | m2 | 1 |
| Major second | M2 | 2 |
| Minor third | m3 | 3 |
| Major third | M3 | 4 |
| Perfect fourth | P4 | 5 |
| Augmented fourth / Diminished fifth | A4 / d5 | 6 |
| Perfect fifth | P5 | 7 |
| Minor sixth | m6 | 8 |
| Major sixth | M6 | 9 |
| Minor seventh | m7 | 10 |
| Major seventh | M7 | 11 |
| Perfect octave | P8 | 12 |
mitone count against the table. If the semitone count is one less than a major or perfect interval, the interval becomes minor or diminished respectively.
快速识别音程的方法是：先包含首尾计算音名数量（如C到E为3，三度），再对照表格检查半音数。若半音数比大音程或纯音程少一个，则该音程变为小音程或减音程。
6. Triad Construction Formulas | 三和弦构成公式
All triads are built by stacking two thirds (three notes). The quality depends on the combination of major (4 semitones, M3) and minor (3 semitones, m3) thirds:
所有三和弦均由两个三度音程叠加（三个音）构成，其性质取决于大三度（4个半音，M3）和小三度（3个半音，m3）的组合方式：
- Major triad = M3 + m3 (e.g., C–E–G, 4+3 semitones)
- Minor triad = m3 + M3 (e.g., C–E♭–G, 3+4 semitones)
- Diminished triad = m3 + m3 (e.g., C–E♭–G♭, 3+3 semitones)
- Augmented triad = M3 + M3 (e.g., C–E–G♯, 4+4 semitones)
大三和弦 = 大三度 + 小三度（如C–E–G，半音数4+3）
小三和弦 = 小三度 + 大三度（如C–E♭–G，3+4）
减三和弦 = 小三度 + 小三度（如C–E♭–G♭，3+3）
增三和弦 = 大三度 + 大三度（如C–E–G♯，4+4）
In a major key, the diatonic triads built on each scale degree are: I (major), ii (minor), iii (minor), IV (major), V (major), vi (minor), vii° (diminished). In a harmonic minor key, the V chord becomes major and the vii° becomes diminished.
在大调中，各级自然三和弦为：I（大三），ii（小三），iii（小三），IV（大三），V（大三），vi（小三），vii°（减三）。在和声小调中，属和弦变为大三和弦，导和弦为减三和弦。
7. Seventh Chord Formulas | 七和弦公式
A seventh chord adds a third on top of a triad, creating a four-note chord. The quality of the seventh (major, minor, diminished) determines the chord type.
七和弦在三和弦上方再叠加一个三度，形成四音和弦。七度音的性质（大、小、减）决定了和弦的类型。
Dominant 7th = major triad + m3 (minor 7th) — e.g., G–B–D–F (V⁷)
Major 7th = major triad + M3 (major 7th) — e.g., C–E–G–B (I⁷)
Minor 7th = minor triad + m3 — e.g., D–F–A–C (ii⁷)
Half-diminished 7th = diminished triad + M3 — e.g., B–D–F–A (viiø⁷)
Diminished 7th = diminished triad + m3 — e.g., B–D–F–A♭ (vii°⁷)
属七和弦 = 大三和弦 + 小三度（小七度），如 G–B–D–F (V
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