📚 Year 7 CIE Music: Formula & Theorem Quick Reference Handbook | 公式定理速查手册
Music theory has its own set of ‘formulas’ – rules and patterns that allow us to read, write and compose music with confidence. This handbook brings together the most essential music‑theory formulas for Year 7 CIE Music. From note‑value equations to interval recipes and chord building blocks, you will find every core concept explained clearly and paired with a Chinese translation. Keep this guide at hand as you practise, and soon these patterns will become second nature.
音乐理论有着自己的一套“公式”——这些规则和模式让我们能够自信地读谱、记谱和作曲。本手册汇集了 Year 7 CIE 音乐最核心的音乐理论公式。从音符时值的等量关系到音程的组合配方、和弦的搭建模块，每个核心概念都有清晰的解释和中文对照。在练习时随身携带这份指南，很快你就会发现这些模式会成为你的第二天性。
1. Note‑Value Pyramid | 音符时值金字塔
In common time, note values relate to each other by simple division. A semibreve (whole note) equals two minims (half notes), a minim equals two crotchets (quarter notes), a crotchet equals two quavers (eighth notes), and a quaver equals two semiquavers (sixteenth notes). This 2:1 relationship is the fundamental rhythm formula.
在常规拍号下，音符时值之间通过简单的除法关系相连。一个全音符等于两个二分音符，一个二分音符等于两个四分音符，一个四分音符等于两个八分音符，一个八分音符等于两个十六分音符。这个 2:1 的关系是最基本的节奏公式。
- Semibreve = 4 beats (in 4/4) | 全音符 = 4 拍（在 4/4 拍中）
- Minim = 2 beats | 二分音符 = 2 拍
- Crotchet = 1 beat | 四分音符 = 1 拍
- Quaver = ½ beat | 八分音符 = ½ 拍
- Semiquaver = ¼ beat | 十六分音符 = ¼ 拍
1 semibreve = 2 minims = 4 crotchets = 8 quavers = 16 semiquavers
2. Dotted Note Length Formula | 附点音符时值公式
lasts for 1 beat + ½ beat = 1½ beats. The formula is: dotted value = original value × 1.5.
音符后面加一个附点，其时值增加原时值的一半。因此附点二分音符时值为 2 拍 + 1 拍 = 3 拍；附点四分音符时值为 1 拍 + ½ 拍 = 1½ 拍。公式为：附点时值 = 原时值 × 1.5。
Dotted note = note + ½ note
Double dots add half the value again of the first dot. A double‑dotted minim = 2 + 1 + ½ = 3½ beats. These patterns follow a geometric progression.
双附点再增加第一个附点时值的一半。双附点二分音符 = 2 + 1 + ½ = 3½ 拍。这些模式遵循几何级数。
3. Time Signature Formula | 拍号公式
A time signature looks like a fraction but acts as a two‑ inim, 4 = crotchet, 8 = quaver). The formula is: number of beats × beat unit = bar length.
拍号看起来像分数，但它的作用是两部分指令：上方数字指出每小节有多少拍；下方数字指出哪种音符作为一拍（2 = 二分音符，4 = 四分音符，8 = 八分音符）。公式为：拍数 × 拍子单位 = 小节长度。
In 4/4, you can fill each bar with any combination of notes and rests that add up to 4 crotchet beats. In 3/4, the total must be 3 crotchet beats. In 6/8, you have 6 quaver beats per bar, usually grouped in two dotted‑crotchet pulses.
在 4/4 拍中，你可以用任何达到 4 个四分音符时值的音符与休止符组合来填满每个小节。在 3/4 拍中，总数必须等于 3 个四分音符的时值。在 6/8 拍中，每小节有 6 个八分音符的拍子，通常分为两个附点四分音符的律动。
4. Major Scale Formula | 大调音阶公式
All major scales are built from a fixed pattern of whole tones (T) and semitones (S). The formula, starting from the tonic, is: T – T – S – T – T – T – S. This sequence of seven intervals produces the familiar joyful sound and is the same for every major key.
所有大调音阶都建立在固定的全音（T）和半音（S）模式上。从主音开始的公式为：T – T – S – T – T – T – S。这段七音程序列产生我们熟悉的明亮音响，适用于每一个大调。
For example, C major: C – D (T) – E (T) – F (S) – G (T) – A (T) – B (T) – C (S). When you apply the same pattern starting on G, you need an F♯ to keep the semitone step between the 7th and 8th degrees.
例如，C 大调：C – D（T）– E（T）– F（S）– G（T）– A（T）– B（T）– C（S）。当你从 G 开始套用同一模式时，需要 F♯ 来保持第 7 级与第 8 级之间的半音步。
Major scale = T T S T T T S
5. Natural Minor Scale Formula | 自然小调音阶公式
The natural minor scale uses a different interval pattern: T – S – T – T – S – T – T. This gives the minor scale its more sombre, melancholy character. It is the Aeolian mode, starting from the 6th degree of its relative major scale.
自然小调音阶使用不同的音程模式：T – S – T – T – S – T – T。这让小调音阶具有更忧郁、悲伤的色彩。它就是爱奥利亚调式，从其关系大调的第 6 级开始。
A natural minor (the relative minor of C major) uses all white keys: A – B – C – D – E – F – G – A. The formula ensures that between the 2nd‑3rd degrees and 5th‑6th degrees we have semitones, creating the characteristic minor tonality.
A 自然小调（C 大调的关系小调）全部使用白键：A – B – C – D – E – F – G – A。此公式保证第 2 级与第 3 级之间、第 5 级与第 6 级之间是半音关系，从而产生小调特有的音响。
Natural minor = T S T T S T T
6. Harmonic and Melodic Minor Adjustments | 和声与旋律小调的调整公式
The harmonic minor raises the 7th degree by a semitone to create a leading tone and an exotic augmented‑2nd step between the 6th and 7th. The formula becomes: T – S – T – T – S – 1½ tones – S. In A harmonic minor, G becomes G♯.
和声小调将第 7 级升高半音，产生导音，并在第 6 级与第 7 级之间形成一个异域的增二度。公式变为：T – S – T – T – S – 1½ 全音 – S。在 a 和声小调中，G 变成 G♯。
The melodic minor raises both the 6th and 7th degrees when ascending (to smooth out the augmented interval) but reverts to natural minor when descending. Ascending formula: T – S – T – T – T – T – S. Descending: T – T – S – T – T – S – T (natural minor).
旋律小调在上行时升高第 6 和第 7 级（以平滑增音程），下行时恢复为自然小调。上行公式：T – S – T – T – T – T – S。下行公式：T – T – S – T – T – S – T（自然小调）。
7. Interval Quality Formula | 音程性质公式
An interval is named by two elements: the number (distance in letter names) and the quality (perfect, major, minor, etc.). In a major scale, unisons, 4ths, 5ths and octaves are perfect; 2nds, 3rds, 6ths and 7ths are major. To find an interval above a given note, count the letter names and apply the major‑scale pattern of the lower note.
音程由两个要素命名：度数（字母名的距离）和性质（纯、大、小等）。在大调音阶中，同度、四度、五度和八度是纯音程；二度、三度、六度和七度是大音程。要找出某个音上方的音程，先数字母名，再应用下方音的大调音阶模式。
jor 6th = 9 semitones, major 7th = 11 semitones, octave = 12 semitones. Minor intervals are one semitone smaller than major; diminished intervals are one semitone smaller than perfect or minor; augmented intervals are one semitone larger than perfect or major.
半音数是最终的检查标准。大二度 = 2 个半音，大三度 = 4 个半音，纯四度 = 5 个半音，纯五度 = 7 个半音，大六度 = 9 个半音，大七度 = 11 个半音，八度 = 12 个半音。小音程比大音程少一个半音；减音程比纯或小音程少一个半音；增音程比纯或大音程多一个半音。
8. Triad (Chord) Building Formula | 三和弦构建公式
h). A minor triad = minor 3rd + major 3rd. A diminished triad = minor 3rd + minor 3rd; an augmented triad = major 3rd + major 3rd.
三和弦由根音、三音和五音构成。其性质取决于堆叠的音程。大三和弦 = 大三度 + 小三度（根音到五音为纯五度）。小三和弦 = 小三度 + 大三度。减三和弦 = 小三度 + 小三度；增三和弦 = 大三度 + 大三度。
d = 0 + 4 + 7 semitones; minor = 0 + 3 + 7; diminished = 0 + 3 + 6; augmented = 0 + 4 + 8.
以 C 大调和弦为例，取根音 C，加大三度（E）和纯五度（G）。以根音上方半音数表示的公式：大三和弦 = 0 + 4 + 7 半音；小三和弦 = 0 + 3 + 7；减三和弦 = 0 + 3 + 6；增三和弦 = 0 + 4 + 8。
Major chord: R + 4 + 3 | Minor chord: R + 3 + 4
9. Key Signature Identification Trick | 调号识别方法
For sharp keys, the last sharp is always the leading note (7th degree) of the major key. Go up one semitone from the last sharp to name the major key. For flat keys, the second‑to‑last flat names the major key. F major (one flat) is the exception that you just memorise.
对于升号调，最后一个升号总是大调的导音（第 7 级）。从最后一个升号往上走一个半音即得到大调主音。对于降号调，倒数第二个降号就是大调主音。F 大调（一个降号）是例外，直接记忆即可。
Example: three sharps – F♯, C♯, G♯. Last sharp is G♯; a semitone above is A, so the key is A major (or F♯ minor). Three flats – B♭, E♭, A♭. The second‑to‑last flat is E♭, so E♭ major (or C minor).
示例：三个升号——F♯, C♯, G♯。最后一个升号是 G♯，上方半音是 A，因此为 A 大调（或 F♯ 小调）。三个降号——B♭, E♭, A♭。倒数第二个降号是 E♭，因此是 E♭ 大调（或 c 小调）。
Sharp key = last ♯ + semitone | Flat key = second‑last ♭
10. Tempo and Expression Formulas | 速度与表情术语公式
Italian tempo markings follow a standard order from slow to fast: Largo (very slow), Adagio (slow), Andante (walking pace), Moderato (moderate), Allegro (fast), Presto (very fast). Combined with modifiers like molto (very) or -etto (a little), you can create precise performance instructions.
意大利术语的速度标记从慢到快有标准顺序：Largo（非常缓慢）、Adagio（慢）、Andante（行板）、Moderato（中速）、Allegro（快板）、Presto（急板）。搭配修饰词如 molto（非常）或后缀 -etto（稍微），可以生成精确的演奏指示。
Dynamics follow a similar pattern: pp (pianissimo, very soft), p (piano, soft), mp (mezzo‑piano, moderately soft), mf (mezzo‑forte, moderately loud), f (forte, loud), ff (fortissimo, very loud). Crescendo (cresc.) means gradually getting louder, diminuendo (dim.) or decrescendo means gradually softer.
力度遵循类似模式：pp（pianissimo，很弱）、p（piano，弱）、mp（mezzo‑piano，中弱）、mf（mezzo‑forte，中强）、f（forte，强）、ff（fortissimo，很强）。Crescendo（渐强）表示音量逐渐增大，diminuendo 或 decrescendo（渐弱）表示音量逐渐减小。
11. Relative Minor/Major Formula | 关系大小调公式
Every major key has a relative minor starting on the 6th degree (la) of the major scale. Conversely, every minor key has a relative major starting on the 3rd degree of the minor scale. This relationship means they share the same key signature and the same set of notes.
每个大调都有一个关系小调，从大调音阶的第 6 级（la）开始。反之，每个小调都有一个关系大调，从小调音阶的第 3 级开始。这种关系意味着它们共享相同的调号和音列。
to A minor = C down three semitones to A. A minor to C major = A up three semitones to C.
公式：关系小调 = 大调主音 − 3 个半音（或向下数 3 个字母名）。关系大调 = 小调主音 + 3 个半音。示例：C 大调到 a 小调 = C 向下 3 个半音到 A。a 小调到 C 大调 = A 向上 3 个半音到 C。
Relative minor = major tonic ↓ 3 semitones
12. Scale Degree Names Formula | 音阶音级名称公式
Each scale degree has a technical name that describes its function. The pattern is identical in major and minor keys (with slight adjustments for variable 6th and 7th degrees in minor). Learning these names helps you analyse cadences and harmonic progressions quickly.
音阶的每个音级都有一个技术名称来描述其功能。这个模式在大调和小调中完全相同（小调中可变第 6、7 级稍作调整）。掌握这些名称有助于你快速分析终止式与和声进行。
| Degree | 音级 | Name | 名称 | Function | 功能 |
|---|---|---|
| 1 (do) | Tonic | 主音 | Home, centre of key |
| 2 (re) | Supertonic | 上主音 | Above the tonic |
| 3 (mi) | Mediant | 中音 | Midway between tonic and dominant |
| 4 (fa) | Subdominant | 下属音 | Below the dominant |
| 5 (sol) | Dominant | 属音 | Strongest contrasting pole |
| 6 (la) | Submediant | 下中音 | Midway between tonic and subdominant |
| 7 (ti) | Leading note (major) / Subtonic (natural minor) | 导音（大调）/ 下主音（自然小调） | Leads back to tonic |
The dominant (5) and tonic (1) form the backbone of tonal harmony, while the leading note (7) creates the strongest pull toward the tonic. In the harmonic minor, the raised 7th always functions as a leading note.
属音（5）和主音（1）构成了调性和声的主干，而导音（7）产生向主音最强的倾向。在和声小调中，升高的第 7 级总是充当导音。
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