📚 Year 8 Edexcel Music: Formulas & Theorems Quick Reference | Year 8 Edexcel 音乐：公式定理速查手册
Welcome to your Year 8 Edexcel Music quick reference handbook! Just like maths and science, music has its own set of ‘formulas’ and ‘theorems’ that help you decode rhythm, scales, chords and keys. Master these rules, and you’ll find composing and analysing music much easier.
欢迎来到 Year 8 Edexcel 音乐公式定理速查手册！就像数学和科学一样，音乐也有一套自己的”公式”和”定理”，帮助你破译节奏、音阶、和弦与调性。掌握这些规则，你会在作曲与音乐分析中感到更加得心应手。
1. Note Value & Dotted Note Equations | 音符时值与附点音符方程式
In standard British terminology, the basic note value relationships form the first ‘formula’ you must memorise. In simple time, one semibreve equals two minims, four crotchets, eight quavers or sixteen semiquavers.
在标准的英式术语中，基本音符时值关系是你必须记住的第一条”公式”。在单拍子中，一个全音符等于两个二分音符、四个四分音符、八个八分音符或十六个十六分音符。
1 semibreve = 2 minims = 4 crotchets = 8 quavers = 16 semiquavers
1 个全音符 = 2 个二分音符 = 4 个四分音符 = 8 个八分音符 = 16 个十六分音符
A dotted note always adds half of its original value. The dotted minim (dotted half note) lasts for 2 + 1 = 3 crotchet beats. The dotted crotchet (dotted quarter note) lasts for 1 + ½ = 1½ beats, often paired with a quaver to complete the beat in compound time.
附点音符总是增加自身时值的一半。附点二分音符延续 2 + 1 = 3 个四分音符的拍数。附点四分音符延续 1 + ½ = 1½ 拍，常常与一个八分音符搭配，在复拍子中构成完整的拍子。
For any note value X, the dotted version equals X + 0.5X. Double-dotted notes add an additional quarter of the original value: X + 0.5X + 0.25X. These ‘equations’ keep your rhythmic calculations accurate in both performance and theory exams.
对于任意音符时值 X，附点版本等于 X + 0.5X。复附点音符再加原时值的四分之一：X + 0.5X + 0.25X。这些”方程式”能让你在演奏与理论考试中保持节奏计算的准确性。
2. Time Signature Formulas | 拍号公式
A time signature can be read as a simple fraction-like instruction. The top number tells you how many beats fill each bar, while the bottom number indicates the type of note that receives one beat — 2 stands for minim (half note), 4 for crotchet (quarter note) and 8 for quaver (eighth note).
拍号可以像简单的分数指令一样阅读。上方数字告诉每小节有多少拍，下方数字则表示以何种音符为一拍——2 代表二分音符，4 代表四分音符，8 代表八分音符。
Beats per bar / Note value unit = time signature
每小节的拍数 / 音符时值单位 = 拍号
For example, 3/4 means three crotchet beats per bar; 6/8 is a compound duple time with six quavers grouped into two dotted-crotchet beats. Always remember: in simple time the main beat divides into two equal parts; in compound time the main beat divides into three equal parts. Treat this as a theorem for classifying any time signature.
例如，3/4 拍表示每小节有三个四分音符的拍子；6/8 拍是复二拍子，六个八分音符被组合成两个附点四分音符的拍子。永远记住：在单拍子中主要拍子一分为二，在复拍子中主要拍子一分为三。将这个当作分类任何拍号的定理。
3. Semitone, Whole Tone & Interval Formula | 半音、全音与音程公式
The smallest distance between two notes in Western music is a semitone (half step). Two semitones make one whole tone (whole step). On a keyboard, adjacent keys — including any black-key neighbours — are a semitone apart. This forms the building-block formula for all scales and chords.
西方音乐中两个音之间的最小距离是半音。两个半音构成一个全音。在键盘上，相邻的琴键——包括黑键——相距一个半音。这构成了所有音阶与和弦的基石公式。
1 whole tone = 2 semitones
1 个全音 = 2 个半音
When measuring intervals, count the number of semitones from the lower note to the higher one. A minor 2nd = 1 semitone, a major 2nd = 2 semitones, a perfect 4th = 5 semitones and a perfect 5th = 7 semitones. Keep this interval formula chart handy to identify melodic and harmonic intervals instantly in any key.
测量音程时，从较低的音到较高的音数半音数量。小二度 = 1 个半音，大二度 = 2 个半音，纯四度 = 5 个半音，纯五度 = 7 个半音。熟记这份音程公式图表，你就能在任何调中迅速辨识旋律音程与和声音程。
4. Major Scale Formula | 大调音阶公式
Every major scale follows the same pattern of tones and semitones, no matter which note you start on. Applying this formula guarantees you build a correct major scale — one of the most powerful ‘theorems’ in Year 8 music theory.
每一条大调音阶都遵循相同的全音与半音模式，无论从哪个音开始。套用这个公式能确保你构建出正确的大调音阶——这也是 Year 8 音乐理论中最强大的”定理”之一。
Tone – Tone – Semitone – Tone – Tone – Tone – Semitone
全音 – 全音 – 半音 – 全音 – 全音 – 全音 – 半音
Using C major as an example: C–D (tone), D–E (tone), E–F (semitone), F–G (tone), G–A (tone), A–B (tone), B–C (semitone). When you write any major scale in an exam, start on the tonic and apply the T–T–S–T–T–T–S recipe. This will also help you insert the correct accidentals.
以 C 大调为例：C–D（全音）、D–E（全音）、E–F（半音）、F–G（全音）、G–A（全音）、A–B（全音）、B–C（半音）。当你在考试中书写任何大调音阶时，从主音开始并套用全-全-半-全-全-全-半的配方。这也会帮助你插入正确的临时记号。
5. Natural Minor Scale Formula | 自然小调音阶公式
The natural minor scale is derived from the major scale but starts on a different degree, which changes the tone–semitone layout. Learning its own formula gives you a second essential theorem for minor-key music.
自然小调音阶由大调音阶衍生而来，但从不同的音级开始，从而改变了全音-半音的排列。学会它自己的公式，你便拥有了小调音乐的第二条核心定理。
Tone – Semitone – Tone – Tone – Semitone – Tone – Tone
全音 – 半音 – 全音 – 全音 – 半音 – 全音 – 全音
A natural minor: A–B (tone), B–C (semitone), C–D (tone), D–E (tone), E–F (semitone), F–G (tone), G–A (tone). Notice the semitones fall between steps 2–3 and 5–6, giving the scale its characteristic, slightly darker sound. In Year 8 you may also meet the harmonic minor (raised 7th) and melodic minor (raised 6th and 7th ascending), but the natural minor formula remains the foundation.
A 自然小调：A–B（全音）、B–C（半音）、C–D（全音）、D–E（全音）、E–F（半音）、F–G（全音）、G–A（全音）。注意半音出现在第 2-3 级和第 5-6 级之间，赋予音阶独特、略带黯淡的音响。在 Year 8 你或许还会遇到和声小调（升高第 7 级）与旋律小调（上行升高第 6、7 级），但自然小调的公式仍是最根本的基础。
6. Triad Construction Formulas | 三和弦构成公式
A triad is a three-note chord built by stacking intervals of a third. The quality of the triad depends on the exact semitone distances between the root, the third and the fifth. These distances act as precise formulas you can apply to any root note.
三和弦是由三度音程堆叠而成的三音和弦。三和弦的性质取决于根音、三音和五音之间确切的半音距离。这些距离便是你可以套用在任何根音上的精确公式。
Major triad = root + 4 semitones (major 3rd) + 3 semitones (perfect 5th from root = 7 semitones total)
大三和弦 = 根音 + 4 个半音（大三度）+ 3 个半音（根音到五音总共 7 个半音）
Minor triad = root + 3 semitones (minor 3rd) + 4 semitones (perfect 5th from root = 7 semitones total)
小三和弦 = 根音 + 3 个半音（小三度）+ 4 个半音（根音到五音共 7 个半音）
For C major: C to E = 4 semitones, E to G = 3 semitones. For A minor: A to C = 3 semitones, C to E = 4 semitones. Once you know these formulas, you can work out any major or minor chord without memorising them all individually, which is especially handy when analysing chord symbols or composing short progressions.
C 大三和弦：C 到 E = 4 个半音，E 到 G = 3 个半音。A 小三和弦：A 到 C = 3 个半音，C 到 E = 4 个半音。一旦你掌握了这些公式，你就可以推导出任何大、小三和弦而无须死记硬背，这在分析和弦记号或创作短小的和弦进行时特别方便。
7. Key Signatures & Circle of Fifths Rules | 调号与五度循环规则
Key signatures follow predictable patterns that can be treated as mathematical sequences. Sharp keys: the last sharp in the key signature is the leading note (7th degree) of the major key, so the tonic is one semitone above that final sharp. Flat keys: the second-to-last flat in the key signature gives the name of the major key directly.
调号遵循可预测的模式，可视为数学序列。升号调：调号中最后一个升号是该大调的导音（第 7 级），因此主音比最后的升号高半音。降号调：调号中倒数第二个降号直接给出大调的名称。
Tonic of sharp major key = last sharp + 1 semitone up
升号大调主音 = 最后一个升号 + 向上半音
Tonic of flat major key = second-to-last flat in the signature
降号大调主音 = 调号中倒数第二个降号
The order of sharps follows Father Charles Goes Down And Ends Battle: F♯, C♯, G♯, D♯, A♯, E♯, B♯. The order of flats is the reverse: Battle Ends And Down Goes Charles Father: B♭, E♭, A♭, D♭, G♭, C♭, F♭. Commit both sequences to memory — they are your navigation tools for every key signature question in Year 8 and beyond.
升号出现的顺序是 Father Charles Goes Down And Ends Battle：F♯、C♯、G♯、D♯、A♯、E♯、B♯。降号的顺序正相反：Battle Ends And Down Goes Charles Father：B♭、E♭、A♭、D♭、G♭、C♭、F♭。请将这两个序列牢牢记住——它们是你应对 Year 8 乃至后续每个调号问题的导航工具。
8. Relative Keys & Chord Number Formulas | 关系大小调与和弦级数公式
Every major key has a relative minor key that shares the same key signature. To find it, simply move down three semitones (a minor 3rd) from the major tonic. For instance, C major’s relative minor is A minor; G major’s relative minor is E minor. This formula works in reverse: to find the relative major of a minor key, go up three semitones.
每一个大调都有一个与之共用同一调号的关系小调。要找到它，只需从大调主音向下移动三个半音（小三度）。例如，C 大调的关系小调是 A 小调；G 大调的关系小调是 E 小调。该公式也可反向运用：要找到小调的关系大调，向上移动三个半音即可。
Relative minor = major tonic − 3 semitones
关系小调 = 大调主音 − 3 个半音
When analysing harmony, we label chords with Roman numerals according to their scale degree. In any major key, the pattern of chord qualities is fixed: I (major), ii (minor), iii (minor), IV (major), V (major), vi (minor), vii° (diminished). Treat this as a theorem of diatonic harmony — once you know the key, you instantly know the quality of every triad built on each degree.
分析和声时，我们用罗马数字为和弦标记其所在的音级。在任何大调中，和弦性质的模式是固定的：I（大）、ii（小）、iii（小）、IV（大）、V（大）、vi（小）、vii°（减）。将此视为自然音和声的定理——一旦你知道了调，就能立刻知道建立在每一级上的三和弦的性质。
Memorising the primary chords I, IV and V (the tonic, subdominant and dominant) and their formulas speeds up both composition and theory tasks enormously. In C major, these are C major, F major and G major; in A minor, they are i (Am), iv (Dm) and V (E major, often with a raised leading note).
熟记 I、IV 和 V 级（主、下属与属）这三个正三和弦及其公式，能极大提升你作曲和完成理论作业的速度。在 C 大调中它们分别是 C 大三和弦、F 大三和弦和 G 大三和弦；在 A 小调中它们是 i（Am）、iv（Dm）和 V（E 大三和弦，通常带有升高的导音）。
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