Year 8 CCEA Music: Quick Reference Formula & Theorem Handbook | Year 8 CCEA 音乐：公式定理速查手册

📚 Year 8 CCEA Music: Quick Reference Formula & Theorem Handbook | Year 8 CCEA 音乐：公式定理速查手册

Music theory is built on a set of reliable formulas and rules, just like maths or science. This handbook brings together the essential rhythmic, melodic, and harmonic 'theorems' you will meet in Year 8 CCEA Music. Keep it handy for quick revision and to strengthen your understanding of how music is constructed.

音乐理论像数学和科学一样，建立在一套可靠的公式和规则之上。这本手册汇集了你在 CCEA Year 8 音乐课程中会遇到的重要节奏、旋律与和声“定理”，方便你随时速查，加深对音乐结构方式的理解。

1. Note Values & Rhythmic Equations | 音符时值与节奏等式

In any simple time signature, note values relate to each other through clear mathematical ratios. The basic formula is: one semibreve (whole note) equals two minims, four crotchets, eight quavers, and sixteen semiquavers. This chain of equivalence is the foundation of rhythm reading and writing.

在任何单拍子中，音符时值之间有着清晰的数学比例关系。基本公式为：一个全音符等于两个二分音符、四个四分音符、八个八分音符和十六个十六分音符。这一连串的等值关系是节奏读写的基础。

A dot placed after any note adds exactly half of its original value. For example, a dotted minim lasts for 3 crotchet beats because a minim (2 beats) plus half of it (1 beat) equals 3 beats. The dotted note rule applies to all note values and is essential for working with uneven rhythms.

附点加在任何音符后面，会为该音符增加原时值的一半。例如，附点二分音符持续 3 拍，因为二分音符（2 拍）加上它的一半（1 拍）等于 3 拍。这一附点规则适用于所有音符时值，是处理非对称节奏的基础。

The same durational logic extends to rests: each rest symbol matches a note value and follows the same proportional equations. A semibreve rest hangs from the fourth line; a minim rest sits on the third line; and crotchet, quaver, and semiquaver rests have their own distinct symbols. The rests are silent beats that obey the same rhythmic formulas.

同样的时值逻辑也适用于休止符：每个休止符符号都对应一种音符时值，并遵循相同的比例等式。全休止符挂在第四线下方；二分休止符坐在第三线上；四分休止符、八分休止符和十六分休止符则各有其独特形状。休止符是保持时值公式的无声节拍。

2. Time Signatures and Beat Rules | 拍号与节拍规则

A time signature is a fraction-like symbol that encodes two rules: the top number tells you how many beats are in each bar, and the bottom number tells you which note value counts as one beat. In 4/4, the '4' on top means four beats per bar, and the bottom '4' signals that a crotchet gets one beat.

拍号是一个类似分数的符号，它包含两条规则：上方的数字表示每小节有几拍，下方的数字表示以何种音符为一拍。在 4/4 拍中，上方的“4”代表每小节四拍，下方的“4”则表示以四分音符为一拍。

The beat-division rule separates simple time from compound time. In simple time signatures (2/4, 3/4, 4/4), each beat naturally divides into two equal parts. In compound time signatures (6/8, 9/8, 12/8), each beat divides into three equal parts, creating a lilting, swung feel. The bottom number in compound time often represents a dotted beat, so 6/8 means two dotted-crotchet beats per bar.

拍子分割规则区分了单拍子与复拍子。在单拍子（2/4、3/4、4/4）中，每一拍自然地均分为两份。在复拍子（6/8、9/8、12/8）中，每一拍均分为三份，产生摇曳的摇摆感。复拍子的下方数字通常代表附点节拍，因此 6/8 拍表示每小节有两组附点四分音符的拍子。

al note-value capacity of a bar, multiply the top number by the value of the bottom number' k of the bar as holding 6 quavers, grouped into two dotted-crotchet beats. The rule: each bar must be filled with a combination of notes and rests that exactly matches this total.

要计算一个小节能容纳的总时值，可以用上方数字乘以下方数字代表的音符时值。在 3/4 拍中，一小节容纳 3 × 1 个四分音符 = 3 个四分音符。在 6/8 拍中，可以认为一小节容纳 6 个八分音符，并分为两组附点四分音符的拍子。规则是：每小节必须用恰好等于该总时值的音符和休止符组合来填满。

3. Tones and Semitones: The Building Blocks | 全音与半音：构建基石

The smallest interval used in Western music is the semitone (half step). On a keyboard, moving from any key to the immediately adjacent key – whether white to black, black to white, or white to white where there is no black key in between – produces a semitone. Two semitones make one whole tone (whole step).

西方音乐中使用的最小音程是半音。在键盘上，从任何一个键移动到紧接着的相邻键——无论白键到黑键、黑键到白键，还是中间没有黑键的白键到白键——都构成一个半音。两个半音合为一个全音。

1 Tone (T) = 2 Semitones (S)

1 个全音 (T) = 2 个半音 (S)

Semitones are the measuring tape for all scales, intervals, and chords. When you build a major scale, you use a pattern of tones and semitones; when you measure the distance between two notes to name an interval, you count semitones. Understanding this fundamental relationship turns abstract note names into exact pitch distances.

半音是衡量所有音阶、音程和和弦的“卷尺”。构建大调音阶时，你使用的是全音和半音的模式；测量两个音之间的距离来命名音程时，你数的是半音。理解这一基本关系，能将抽象的音名转化为精确的音高距离。

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4. Major Scale Formula | 大调音阶公式

Every major scale follows the same step pattern: Tone – Tone – Semitone – Tone – Tone – Tone – Semitone. This formula, often remembered as T-T-S-T-T-T-S, is the theorem that generates the familiar do–re–mi–fa–sol–la–ti–do sound regardless of the starting note.

每个大调音阶都遵循相同的步进模式：全音 – 全音 – 半音 – 全音 – 全音 – 全音 – 半音。这个公式常被记作 T-T-S-T-T-T-S，它是生成我们熟悉的 do–re–mi–fa–sol–la–ti–do 音响的定理，无论起始音是什么。

Major Scale Formula: T – T – S – T – T – T – S

大调音阶公式：T – T – S – T – T – T – S

Applying the formula: start on C, and you get C–D (T), D–E (T), E–F (S), F–G (T), G–A (T), A–B (T), B–C (S). This yields the C major scale with no sharps or flats. To construct G major, begin on G and follow the same pattern: G–A (T), A–B (T), B–C (S), C–D (T), D–E (T), E–F♯ (T), F♯–G (S). Notice that F must be sharpened to F♯ to preserve the T-T-S-T-T-T-S pattern. This is how key signatures are born.

应用公式：从 C 开始，便得到 C–D (T)、D–E (T)、E–F (S)、F–G (T)、G–A (T)、A–B (T)、B–C (S)，这就是没有升降号的 C 大调。要构建 G 大调，从 G 开始并遵循同一模式：G–A (T)、A–B (T)、B–C (S)、C–D (T)、D–E (T)、E–F♯ (T)、F♯–G (S)。注意，必须把 F 升高为 F♯，才能保持 T-T-S-T-T-T-S 的模式。这就是调号的由来。

5. Minor Scale Formulas | 小调音阶公式

The natural minor scale uses the pattern: T – S – T – T – S – T – T. If you play all the white notes on a keyboard from A to A, you will hear this pattern. It is often described as a major scale with lowered 3rd, 6th, and 7th degrees compared with the parallel major.

自然小调音阶使用的模式为：T – S – T – T – S – T – T。如果你在键盘上从 A 到下一个 A 弹奏所有白键，你听到的就是自然小调。与同主音大调相比，它常被描述为降低了第 3、第 6 和第 7 级音的大调音阶。

Natural Minor: T – S – T – T – S – T – T

自然小调：T – S – T – T – S – T – T

The harmonic minor modifies the natural minor by raising the 7th degree by a semitone, creating a distinctive three-semitone step (augmented 2nd) between the 6th and 7th degrees. Its formula is: T – S – T – T – S – T+S – S. The raised 7th provides a strong leading note that pulls powerfully back to the tonic.

和声小调通过将自然小调的第 7 级音升高半音而得到，在第 6 级和第 7 级之间产生一个独特的三半音距离（增二度）。其公式为：T – S – T – T – S – 全音+半音 – S。升高的第 7 级音构成强烈的导音，有力地倾向回到主音。

6. Interval Formulas: Counting Semitones | 音程公式：数半音

An interval measures the pitch distance between two notes. The number of semitones determines the interval's quality and type. The table below gives the fundamental interval-building blocks: perfect, major, and minor intervals up to an octave. These formulas allow you to identify and construct any interval accurately.

音程衡量的是两个音之间的音高距离。半音的数量决定了音程的性质和类型。下表列出了八度以内的基本音程构成模块：纯音程、大音程与小音程。这些公式能让你准确地识别和构建任何音程。

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