📚 Year 7 Cambridge Music: Formula & Theorem Quick Reference Handbook | 剑桥Year 7音乐：公式定理速查手册
Music may not look like maths, but underneath the melodies and rhythms lies a world of patterns, proportions, and precise rules. This quick reference handbook collects all the essential “formulas” and “theorems” that a Year 7 Cambridge Music student needs to know — from note values and time signatures to scale formulas and chord spellings. Use it as a revision aid, a homework helper, or a pocket guide before your next listening test.
音乐看起来不像数学，但在旋律和节奏的背后，隐藏着模式、比例和精确的规则。这本速查手册汇集了剑桥Year 7音乐课程所有必备的“公式”与“定理”——从音符时值、拍号到音阶公式与和弦拼写。你可以用它来复习、做作业，或者在下次听力测验前当作掌中宝。
1. Note Values | 音符时值
In 4/4 time, a semibreve (whole note) lasts for 4 beats, a minim (half note) lasts for 2 beats, a crotchet (quarter note) lasts for 1 beat, a quaver (eighth note) lasts for ½ beat, and a semiquaver (sixteenth note) lasts for ¼ beat. The relationships follow powers of two: one semibreve = two minims = four crotchets = eight quavers = sixteen semiquavers.
在4/4拍中，全音符持续4拍，二分音符持续2拍，四分音符持续1拍，八分音符持续½拍，十六分音符持续¼拍。这些关系遵循2的幂次方：一个全音符 = 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。
| Note | Beats (4/4) | 符号 (英/中) |
|---|---|---|
| Semibreve | 4 | 𝄝 / 全音符 |
| Minim | 2 | 𝄞 / 二分音符 |
| Crotchet | 1 | ♩ / 四分音符 |
| Quaver | ½ | ♪ / 八分音符 |
| Semiquaver | ¼ | 𝅘 / 十六分音符 |
2. Dotted Notes | 附点音符
A dot placed after a note increases its duration by half of the original value. The formula: Dotted note = original note value × 1.5. For example, a dotted minim = 2 + 1 = 3 beats; a dotted crotchet = 1 + ½ = 1½ beats. Double dots add an extra quarter of the original value, but these are rarely required at Year 7 level.
附点加在音符后面，时值增加原有时值的一半。公式：附点音符 = 原有时值 × 1.5。例如，附点二分音符 = 2 + 1 = 3拍；附点四分音符 = 1 + ½ = 1½拍。双附点会增加原有时值的四分之一，但在Year 7阶段很少涉及。
3. Time Signatures | 拍号
A time signature looks like a fraction. The top number tells how many beats are in each bar, and the bottom number tells what kind of note gets one beat. The formula for bottom numbers: 4 = crotchet, 8 = quaver, 2 = minim. Common time signatures: 4/4 (4 crotchet beats per bar), 3/4 (3 crotchet beats), 2/4, and 6/8 (6 quaver beats per bar, usually in two dotted-crotchet pulses).
拍号看起来像一个分数。上方数字表示每小节有多少拍，下方数字表示以哪种音符为一拍。下方数字的公式：4 = 四分音符，8 = 八分音符，2 = 二分音符。常见拍号：4/4（每小节4个四分音符拍）、3/4（3个四分音符拍）、2/4，以及6/8（每小节6个八分音符拍，通常以两个附点四分音符为律动单位）。
4. Major Scale Formula | 大调音阶公式
All major scales follow the same pattern of tones (T) and semitones (S): T – T – S – T – T – T – S. A semitone is the smallest step on a piano (one key to the very next key), and a tone equals two semitones. Starting from any note and applying this formula yields the correct major scale. For example, C major: C D E F G A B C (all white keys, following T T S T T T S).
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。半音是钢琴上最小的距离（相邻两键），全音等于两个半音。从任何一个音出发，套用这个公式就能得出正确的大调音阶。例如，C大调：C D E F G A B C（全部白键，符合T T S T T T S）。
T – T – S – T – T – T – S
5. Minor Scale Formula (Natural Minor) | 小调音阶公式（自然小调）
The natural minor scale uses the pattern: T – S – T – T – S – T – T. This is equivalent to playing a major scale from its 6th degree. For example, A natural minor uses exactly the same notes as C major: A B C D E F G A. The formula works for any starting pitch.
自然小调音阶的模式是：T – S – T – T – S – T – T。这相当于从大调音阶的第六级开始演奏。例如，a自然小调与C大调使用完全相同的音符：A B C D E F G A。这个公式适用于任何起始音。
T – S – T – T – S – T – T
6. Interval Formulas | 音程公式
An interval is the distance between two notes, measured in semitones. Key intervals for Year 7: unison (0 semitones), minor 2nd (1 semitone), major 2nd (2 semitones), minor 3rd (3 semitones), major 3rd (4 semitones), perfect 4th (5 semitones), perfect 5th (7 semitones), perfect octave (12 semitones). The formula for a perfect 5th is always 7 semitones, no matter the starting note.
音程是两个音之间的距离，以半音为单位。Year 7需掌握的关键音程：同度（0个半音）、小二度（1个半音）、大二度（2个半音）、小三度（3个半音）、大三度（4个半音）、纯四度（5个半音）、纯五度（7个半音）、纯八度（12个半音）。纯五度的公式始终是7个半音，无论从哪个音开始。
7. Triad Chord Formulas | 三和弦公式
A triad is a three-note chord built in thirds. The formula for a major triad: root + 4 semitones (major 3rd) + 3 semitones (minor 3rd). For a minor triad: root + 3 semitones (minor 3rd) + 4 semitones (major 3rd). A diminished triad: root + 3 + 3. An augmented triad: root + 4 + 4. The root is the note that names the chord.
三和弦是由三个音按三度叠置构成的和弦。大三和弦的公式：根音 + 4个半音（大三度） + 3个半音（小三度）。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 + 3 + 3。增三和弦：根音 + 4 + 4。根音是给和弦命名的音。
| Chord Type | Formula (semitones) | Example on C |
|---|---|---|
| Major | 4 + 3 | C – E – G |
| Minor | 3 + 4 | C – E♭ – G |
| Diminished | 3 + 3 | C – E♭ – G♭ |
| Augmented | 4 + 4 | C – E – G♯ |
8. Seventh Chord Formulas | 七和弦公式
By adding a fourth note a seventh above the root to a triad, we create seventh chords. The dominant 7th formula: major triad + minor 7th (root + 4 + 3 + 3 semitones). The major 7th formula: major triad + major 7th (root + 4 + 3 + 4 semitones). The minor 7th formula: minor triad + minor 7th (root + 3 + 4 + 3 semitones). Year 7 students usually meet dominant 7ths in the context of V⁷ chords.
在三和弦上方添加一个距离根音七度的音，就构成了七和弦。属七和弦的公式：大三和弦 + 小七度（根音 + 4 + 3 + 3个半音）。大七和弦公式：大三和弦 + 大七度（根音 + 4 + 3 + 4个半音）。小七和弦公式：小三和弦 + 小七度（根音 + 3 + 4 + 3个半音）。Year 7学生通常在V⁷和弦中遇到属七和弦。
9. Key Signatures – Quick Reference | 调号速查
Key signatures are linked to the circle of fifths. For sharp keys: C major (0 sharps), G major (F♯), D major (F♯, C♯), A major (F♯, C♯, G♯). The order of sharps is Father Charles Goes Down And Ends Battle (F C G D A E B). For flat keys: F major (B♭), B♭ major (B♭, E♭), E♭ major (B♭, E♭, A♭). Order of flats is Battle Ends And Down Goes Charles Father (B E A D G C F). To find a major key from its sharps: go up a semitone from the last sharp. For flats: the second-to-last flat is the key note.
调号与五度圈相关。升号调：C大调（0个升号）、G大调（F♯）、D大调（F♯, C♯）、A大调（F♯, C♯, G♯）。升号顺序是：F C G D A E B。降号调：F大调（B♭）、B♭大调（B♭, E♭）、E♭大调（B♭, E♭, A♭）。降号顺序是：B E A D G C F。从升号调找主音：把最后一个升号升高半音。降号调：倒数第二个降号就是调的主音。
10. Circle of Fifths | 五度圈
The circle of fifths arranges the 12 pitches so that each step clockwise moves up a perfect 5th (7 semitones) and adds one sharp. Moving counterclockwise goes down a perfect 5th and adds one flat. It is a visual formula for key relationships, chord progressions, and modulation. Year 7 students can use a simplified version showing major keys up to 3 sharps and 3 flats.
五度圈将12个音高排列成一个圆圈，顺时针每走一步升高一个纯五度（7个半音）并增加一个升号；逆时针每走一步降低一个纯五度并增加一个降号。它是调性关系、和弦进行和转调的视觉公式。Year 7学生可使用简化版，涵盖最多3升3降的大调。
11. Dynamics and Tempo Marks | 力度与速度标记
Italian terms act as formulas for expression. 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). Gradual change: crescendo (cresc., gradually louder), diminuendo (dim., gradually softer). Tempo: Lento (slow), Andante (walking pace), Moderato (moderate), Allegro (fast), Presto (very fast). A metronome mark, e.g. ♩ = 120, gives the exact beats per minute.
意大利术语如同表情的公式。力度：pp（很弱）、p（弱）、mp（中弱）、mf（中强）、f（强）、ff（很强）。渐变：cresc.（渐强）、dim.（渐弱）。速度：Lento（慢板）、Andante（行板）、Moderato（中板）、Allegro（快板）、Presto（急板）。节拍器标记，如 ♩ = 120，给出了每分钟精确的拍数。
12. Transposition Formula | 移调公式
To transpose a melody up or down by a specific interval, add or subtract the same number of semitones to every note in the original. For example, transposing up a perfect 5th means adding 7 semitones to each pitch. In written music for transposing instruments, the formula is: written note + interval of transposition = sounding note. Year 7 students most commonly transpose between C, B♭, and F instruments.
要将旋律按特定音程上下移调，就给原乐谱中的每个音加上或减去同样数量的半音。例如，向上移调一个纯五度意味着每个音升高7个半音。在移调乐器的记谱中，公式是：记谱音 + 移调音程 = 实际音高。Year 7学生最常在C调、B♭调和F调乐器之间进行移调。
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