📚 Year 9 OCR Music: Formula & Theorem Quick Reference | Year 9 OCR 音乐：公式定理速查手册
Musical mastery is built on patterns, rules, and structures that act just like mathematical formulas. From interval calculations to chord recipes and rhythmic divisions, these ‘theorems’ give you the power to read, write, and analyse music with confidence. This pocket guide collects the essential musical formulas you will need for your Year 9 OCR Music studies, presented in a clear, paired English-Chinese format to reinforce your learning.
音乐的精通建立在模式、规则和结构之上，它们的作用就像数学公式。从音程计算到和弦配方，再到节奏划分，这些“定理”赋予你自信地读谱、写谱和分析音乐的能力。这本口袋速查手册汇集了你在 Year 9 OCR 音乐学习中必备的音乐公式，以清晰的中英对照形式呈现，加深你的理解。
1. The Major Scale Formula | 大调音阶公式
A major scale is built using a fixed pattern of tones (T) and semitones (S). Starting on any note, apply the sequence: T – T – S – T – T – T – S. This gives you the familiar do-re-mi sound.
大调音阶使用固定的全音（T）和半音（S）模式建立。从任意音开始，应用序列：全 – 全 – 半 – 全 – 全 – 全 – 半。这就得到了熟悉的 do-re-mi 音响。
For example, C major: C (T) D (T) E (S) F (T) G (T) A (T) B (S) C. Each T equals two semitones (e.g., C to D), and each S equals one semitone (e.g., E to F).
例如，C 大调：C (全) D (全) E (半) F (全) G (全) A (全) B (半) C。每个全音等于两个半音（如 C 到 D），每个半音等于一个半音（如 E 到 F）。
Quick reference formula: Keynote + W W H W W W H (where W = whole step, H = half step).
速查公式：主音 + 全 全 半 全 全 全 半。
2. Natural Minor Scale Formula | 自然小调音阶公式
The natural minor scale also uses a tone-semitone pattern, but it is different from major: T – S – T – T – S – T – T. This creates a darker, more melancholic mood.
自然小调音阶也使用全音-半音模式，但与大小调不同：全 – 半 – 全 – 全 – 半 – 全 – 全。这创造出更暗淡、更忧郁的氛围。
For A natural minor (the relative minor of C major): A (T) B (S) C (T) D (T) E (S) F (T) G (T) A. Notice it uses the same notes as C major but starts on A.
以 A 自然小调（C 大调的关系小调）为例：A (全) B (半) C (全) D (全) E (半) F (全) G (全) A。注意它使用了与 C 大调相同的音符，但从 A 开始。
The formula is: Keynote + W H W W H W W. Relative minors share the same key signature.
公式为：主音 + 全 半 全 全 半 全 全。关系大小调共享同一个调号。
3. Major Chord Recipe (Root Position Triad) | 大三和弦配方（原位三和弦）
A major triad consists of a root, a major third (4 semitones above the root), and a perfect fifth (7 semitones above the root). This is your basic happy-sounding chord.
一个大三和弦由根音、大三度（根音上方 4 个半音）和纯五度（根音上方 7 个半音）组成。这是你最基本的欢快音响和弦。
On the keyboard, count up: root + 4 semitones = major third; root + 7 semitones = perfect fifth. For example, C major triad: C (root) – E (4 semitones up) – G (7 semitones up).
在键盘上，向上数：根音 + 4 半音 = 大三度；根音 + 7 半音 = 纯五度。例如，C 大三和弦：C（根音）– E（上行 4 半音）– G（上行 7 半音）。
Formula in semitones: [0, 4, 7] relative to the root. Notation: the chord symbol is just the capital letter, e.g., C.
半音公式：[0, 4, 7]（相对于根音）。记谱：和弦标记就是大写字母，如 C。
4. Minor Chord Recipe (Root Position Triad) | 小三和弦配方（原位三和弦）
A minor triad has a root, a minor third (3 semitones above the root), and a perfect fifth (7 semitones above the root). The lowered third gives it a sombre quality.
一个小三和弦包含根音、小三度（根音上方 3 个半音）和纯五度（根音上方 7 个半音）。降低的三音赋予了它一种阴郁的特质。
The semitone formula is: [0, 3, 7]. For A minor: A – C (3 semitones) – E (7 semitones). Listen for the difference in mood between C major and C minor.
半音公式为：[0, 3, 7]。A 小三和弦为例：A – C（3 半音）– E（7 半音）。倾听 C 大调与 C 小调之间情绪上的差异。
Chord symbol uses a small ‘m’, e.g., Am. This recipe is essential for building any minor triad.
和弦标记使用小写的 “m”，如 Am。这个配方是构建任何小三和弦的基础。
5. Diminished and Augmented Triad Formulas | 减三和弦与增三和弦公式
Beyond major and minor, two other triad qualities appear: diminished [0, 3, 6] and augmented [0, 4, 8]. Diminished stacks two minor thirds; augmented stacks two major thirds.
在大调与小调之外，还有另外两种三和弦性质：减三和弦 [0, 3, 6] 和增三和弦 [0, 4, 8]。减三是两个小三度的叠加；增三是两个大三度的叠加。
Diminished triad: root + 3 semitones (minor third) + 6 semitones (diminished fifth). Symbol is ° or dim, e.g., B°. Augmented triad: root + 4 semitones (major third) + 8 semitones (augmented fifth). Symbol is + or aug, e.g., C+.
减三和弦：根音 + 3 半音（小三度） + 6 半音（减五度）。标记为 ° 或 dim，如 B°。增三和弦：根音 + 4 半音（大三度） + 8 半音（增五度）。标记为 + 或 aug，如 C+。
These chords create tension and are often used to lead into more stable harmonies. Remember the numbers: 0-3-6 for diminished, 0-4-8 for augmented.
这些和弦制造紧张感，常用来导向更稳定的和声。记住数字：减三为 0-3-6，增三为 0-4-8。
6. Interval Size Formula (Counting Semitones) | 音程大小公式（半音计数法）
An interval’s quality and number can be calculated by counting semitones between two notes. Use the reference table below to identify common intervals up to an octave.
可以通过计算两个音之间的半音数量来确定一个音程的性质和度数。使用下面的参考表格来辨认一个八度内的常见音程。
| Semitones | Interval Name (Ascending) | Example from C |
|---|---|---|
| 0 | Perfect Unison | C – C |
| 1 | Minor 2nd | C – D♭ |
| 2 | Major 2nd | C – D |
| 3 | Minor 3rd | C – E♭ |
| 4 | Major 3rd | C – E |
| 5 | Perfect 4th | C – F |
| 6 | Tritone (Augmented 4th/Diminished 5th) | C – F♯/G♭ |
| 7 | Perfect 5th | C – G |
| 8 | Minor 6th | C – A♭ |
| 9 | Major 6th | C – A |
| 10 | Minor 7th | C – B♭ |
| 11 | Major 7th | C – B |
| 12 | Perfect Octave | C – C |
To determine an interval between two random notes, count the number of semitones from the lower note up to the higher one, then consult the table. Remember that the letter name distance (e.g., C to E is a third) must match the interval number; use enharmonic adjustments to name it correctly.
要确定任意两个音之间的音程，从较低的音向上数半音到较高的音，然后查阅上表。记住，字母名称之间的距离（如 C 到 E 是三度）必须与音程度数相匹配；使用等音调整来正确命名。
7. Time Signature Formula (Beats and Bar Length) | 拍号公式（拍子与小节长度）
A time signature is a fraction that tells you how beats are grouped. The top number indicates how many beats per bar; the bottom number indicates the note value that gets one beat (4 = crotchet, 8 = quaver, 2 = minim).
拍号是一个分数，告诉你拍子如何分组。上面的数字表示每小节有几拍；下面的数字表示以哪种音符为一拍（4 = 四分音符，8 = 八分音符，2 = 二分音符）。
For simple time signatures like 2/4, 3/4, 4/4, each beat divides naturally into two equal parts. In compound time like 6/8, each beat is a dotted crotchet that divides into three quavers.
对于简单的拍号，如 2/4、3/4、4/4，每一拍自然地分为两个均等的部分。在复合拍号如 6/8 中，每一拍是一个附点四分音符，分为三个八分音符。
Quick rule: top number = beats per measure; for compound, divide top number by 3 to get the number of dotted-beat groups.
速记规则：上方数字 = 每小节的拍数；对于复合拍号，上方数字除以 3 得到附点节拍群的组数。
8. Key Signature Sharp and Flat Order (Circle of Fifths Rule) | 调号升记号和降记号的顺序（五度圈规则）
Sharps in key signatures always appear in a fixed order: F♯, C♯, G♯, D♯, A♯, E♯, B♯. Flats appear in reverse order: B♭, E♭, A♭, D♭, G♭, C♭, F♭. This follows the circle of fifths.
调号中的升记号总是按固定顺序出现：F♯, C♯, G♯, D♯, A♯, E♯, B♯。降记号则按相反顺序出现：B♭, E♭, A♭, D♭, G♭, C♭, F♭。这遵循五度圈。
To find the major key with sharps: look at the last sharp and go up a semitone. For example, if the last sharp is D♯, the key is E major. For flats: the second-to-last flat in the key signature gives the major key name. For example, if the flats are B♭, E♭, A♭, the second-to-last is E♭, so the key is E♭ major.
要寻找有升记号的调：找到最后一个升记号，然后上行一个半音。例如，如果最后一个升记号是 D♯，那么调就是 E 大调。对于降记号：调号中倒数第二个降记号给出大调名称。例如，如果降记号为 B♭, E♭, A♭，倒数第二个是 E♭，因此调是 E♭ 大调。
Mnemonic for sharps: Father Charles Goes Down And Ends Battle. For flats: Battle Ends And Down Goes Charles’ Father.
升记号记忆口诀：Father Charles Goes Down And Ends Battle。降记号记忆口诀：Battle Ends And Down Goes Charles’ Father。
9. Triad Inversion Formulas (Figure Bass Shorthand) | 三和弦转位公式（数字低音简写）
A triad can be arranged in three positions. Root position stacks as root – 3rd – 5th. First inversion moves the root up an octave, so the 3rd is the lowest note; the intervals above the bass become a 3rd and a 6th (hence 6/3). Second inversion places the 5th in the bass; intervals are a 4th and a 6th (6/4).
一个三和弦可以有三种排列位置。原位排列为根音 – 三音 – 五音。第一转位将根音八度上移，使得三音成为最低音；低音上方的音程为三度和六度（因此标记为 6/3）。第二转位将五音放在低音部；音程为四度和六度（标记为 6/4）。
Formula for inversions: Root = 5/3 (often omitted); 1st inversion = 6/3 (often simplified to just 6); 2nd inversion = 6/4. These come from Baroque figured bass but are vital for understanding chord voicings.
转位公式：原位 = 5/3（常省略）；第一转位 = 6/3（常简写为 6）；第二转位 = 6/4。这些来源于巴洛克时期的数字低音，但对于理解和弦声部循环至关重要。
In OCR, you may be asked to identify or write chords in different inversions. Remember: check the bass note and then compare the intervals above it to the formula.
在 OCR 考试中，你可能会被要求识别或写出不同转位的和弦。记住：检查低音音名，然后将其上方的音程与公式比较。
10. Seventh Chord Formulas (Four-Note Chords) | 七和弦公式（四音和弦）
Adding a seventh above the root to a triad creates a seventh chord. The most common types use the major scale degrees: dominant 7th (major triad + minor 7th), major 7th (major triad + major 7th), minor 7th (minor triad + minor 7th).
在三和弦根音上方加上一个七度音便构成七和弦。最常用的类型使用大调音阶音级：属七和弦（大三和弦 + 小七度）、大七和弦（大三和弦 + 大七度）、小七和弦（小三和弦 + 小七度）。
Semitone formulas: Dominant 7th = [0, 4, 7, 10]; Major 7th = [0, 4, 7, 11]; Minor 7th = [0, 3, 7, 10]. For example, G7 (G-B-D-F) is a dominant 7th on G; Cmaj7 (C-E-G-B) is major 7th; Dm7 (D-F-A-C) is minor 7th.
半音公式：属七和弦 = [0, 4, 7, 10]；大七和弦 = [0, 4, 7, 11]；小七和弦 = [0, 3, 7, 10]。例如，G7 (G-B-D-F) 是 G 上的属七和弦；Cmaj7 (C-E-G-B) 是大七和弦；Dm7 (D-F-A-C) 是小七和弦。
These chords enrich harmonic progressions and appear in blues, pop, and classical music. They build on your triad knowledge.
这些和弦丰富了和声进行，出现在蓝调、流行音乐和古典音乐中。它们建立在你对三和弦的认识之上。
11. Relative Major/Minor Finder Formula | 关系大小调查找器公式
Every major key has a relative minor sharing the same key signature. To find the relative minor from a major key, count down three semitones from the major tonic. To find the relative major from a minor key, count up three semitones.
每个大调都有一个关系小调，它们共享同一个调号。要从大调找到关系小调，从大调主音向下数三个半音。要从小调找到关系大调，从小调主音向上数三个半音。
Example: C major → down 3 semitones = A minor. A minor → up 3 semitones = C major. This works for any key. G major → E minor; F major → D minor; D major → B minor.
例如：C 大调 → 下行 3 半音 = A 小调。A 小调 → 上行 3 半音 = C 大调。这适用于任何调。G 大调 → E 小调；F 大调 → D 小调；D 大调 → B 小调。
On the stave, you can also look at the last sharp or the second-to-last flat rule to work out either the major or minor key. Then apply the 3-semitone shift.
在五线谱上，你也可以根据升/降记号顺序规律先找出大调，然后应用 3 半音位移得到关系小调，反之亦然。
12. Diatonic Triad Pattern (Harmonised Major Scale) | 大小调自然三和弦模式（大调音阶和声化）
Building a triad on each degree of the major scale using only scale notes creates a pattern of chord qualities: I (major), ii (minor), iii (minor), IV (major), V (major), vi (minor), vii° (diminished).
在大调音阶的每个音级上，只使用音阶内的音来构建三和弦，就会产生一套和弦性质模式：I（大）、ii（小）、iii（小）、IV（大）、V（大）、vi（小）、vii°（减）。
In C major: C (I), Dm (ii), Em (iii), F (IV), G (V), Am (vi), B° (vii°). Use upper case for major, lower case for minor, and lower case with ° for diminished. This pattern is the same for any major key.
在 C 大调中：C (I)、Dm (ii)、Em (iii)、F (IV)、G (V)、Am (vi)、B° (vii°)。大写表示大和弦，小写表示小和弦，小写加 ° 表示减和弦。这个模式对任何大调都相同。
The formula for chord quality by scale degree: M, m, m, M, M, m, dim. This is the backbone of countless songs and progressions.
按音级排列的和弦性质公式：大、小、小、大、大、小、减。这是无数歌曲和进行的基础构架。
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