📚 Year 9 CIE Music: Quick Reference Handbook of Formulas and Theorems | 九年级 CIE 音乐：公式定理速查手册
This handbook gathers the essential musical formulas and theorems you need for Year 9 CIE Music. It covers note values, time signatures, scale construction, intervals, chords, key signatures, cadences, and other core concepts, with clear definitions and practical examples to support quick revision.
这本手册汇集了九年级 CIE 音乐课程所需的全部核心公式与定理。内容包括音符时值、拍号、音阶构成、音程、和弦、调号、终止式及其他基础概念，并配有清晰的定义和实用例子，方便你快速复习。
1. Note Values and Rests | 音符时值与休止符
The durations of notes and rests are built on proportional relationships. In a 4/4 bar, a semibreve (whole note) fills the entire bar with 4 beats.
音符与休止符的时值建立在比例关系上。在 4/4 拍中，全音符占满整个小节，时为 4 拍。
A minim (half note) lasts 2 beats, two minims fit in a 4/4 bar.
二分音符持续 2 拍，两个二分音符填满一个 4/4 小节。
A crotchet (quarter note) equals 1 beat, so four crotchets make a 4/4 bar.
四分音符等于 1 拍，因此四个四分音符组成一个 4/4 小节。
A quaver (eighth note) lasts half a beat – two quavers fit into one beat.
八分音符持续半拍——两个八分音符占一拍。
A semiquaver (sixteenth note) equals a quarter of a beat, with four semiquavers filling one beat.
十六分音符等于四分之一拍，四个十六分音符占一拍。
doubling/halving chain: 1 semibreve = 2 minims = 4 crotchets = 8 quavers = 16 semiquavers.
时值关系遵循倍增/减半链：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。
Rests use equivalent symbols for silence. The semibreve rest hangs below a line, the minim rest sits on a line, and the crotchet rest is a squiggle, while quaver and semiquaver rests have flags or beams.
休止符用相应的符号表示安静。全休止符悬挂在线的下方，二分休止符贴在线上，四分休止符呈波浪形，而八分和十六分休止符带符尾或横梁。
by half. Thus a dotted minim = 2 + 1 = 3 beats, and a dotted crotchet = 1 + ½ = 1½ beats.
附点加在音符或休止符后将时值延长原有的一半。所以附点二分音符 = 2 + 1 = 3 拍，附点四分音符 = 1 + ½ = 1½ 拍。
Ties connect two notes of the same pitch, adding their durations. Rests are never tied.
延音线连接两个相同音高的音符，将其时值相加。休止符不使用延音线。
| UK Name | US Name | Duration (4/4) | Relative Value |
|---|---|---|---|
| Semibreve | Whole note | 4 beats | 1 |
| Minim | Half note | 2 beats | 1/2 |
| Crotchet | Quarter note | 1 beat | 1/4 |
| Quaver | Eighth note | 1/2 beat | 1/8 |
| Semiquaver | Sixteenth note | 1/4 beat | 1/16 |
This table summarises the core note values and their relationships. Memorising these fractions helps you calculate rhythms quickly.
此表总结了核心音符时值及其关系。记住这些分数能帮助你快速计算节奏。
2. Time Signatures | 拍号
om number tells which note value counts as one beat (4 = crotchet, 8 = quaver, 2 = minim).
拍号由两个数字组成。上方数字表示每小节的拍数；下方数字表示以何种音符为一拍（4 = 四分音符，8 = 八分音符，2 = 二分音符）。
Simple time signatures have a top number of 2, 3, or 4. In simple time, every beat naturally divides into two equal parts. Examples: 2/4 (two crotchet beats per bar), 3/4 (three crotchet beats), 4/4 (four crotchet beats).
简单拍子的上方数字为 2、3 或 4。在简单拍子中，每拍自然分成两个等份。例如：2/4（每小节 2 个四分音符拍）、3/4（3 个四分音符拍）、4/4（4 个四分音符拍）。
r instance, 6/8 usually has two dotted crotchet beats per bar (each beat = three quavers).
复合拍子的上方数字为 6、9 或 12。这里的拍子是附点音符，每拍分成三个等份。例如，6/8 通常每小节有 2 个附点四分音符拍（每拍 = 三个八分音符）。
top number = 2,3,4 (beat divides by 2); Compound top number = 6,9,12 (beat divides by 3).
快速识别公式：简单拍子上方数字 2,3,4（每拍分成 2 份）；复合拍子上方数字 6,9,12（每拍分成 3 份）。
Irregular time signatures like 5/4 or 7/8 mix simple and compound groupings; they are often felt as 2+3 or 3+2 etc.
不规则拍号如 5/4 或 7/8 结合了简单与复合的分组；它们常被感受为 2+3 或 3+2 等。
3. The Major Scale Formula | 大调音阶公式
All major scales follow the same interval pattern of tones (T) and semitones (S):
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：
全 – 全 – 半 – 全 – 全 – 全 – 半
A tone (whole step) spans two semitones. A semitone is the smallest distance on a keyboard – from any key to the very next neighbour, white or black.
全音跨两个半音。半音是键盘上最小的距离——从任一琴键到你下一个紧邻的琴键（白或黑）。
Built on C, the notes are C D E F G A B C. The semitones fall between E–F (3–4) and B–C (7–8).
以 C 为根音构建，得到 C D E F G A B C。半音位于 E–F（3–4 级）和 B–C（7–8 级）之间。
To build any major scale, start from the tonic and apply T T S T T T S. For G major: G (T) A (T) B (S) C (T) D (T) E (T) F♯ (S) G. The F♯ is required to keep the pattern.
构建任何大调，都从主音开始并套用 T T S T T T S。G 大调：G (T) A (T) B (S) C (T) D (T) E (T) F♯ (S) G。F♯ 是为了维持音阶模式。
The order of sharps in key signatures is F♯ C♯ G♯ D♯ A♯ E♯ B♯. For major keys, the last sharp is the leading note – so the major tonic is one semitone above.
升号调的调号顺序为 F♯ C♯ G♯ D♯ A♯ E♯ B♯。对于大调，最后的升号是导音——因此大调主音在它的上方半音。
4. Minor Scales | 小调音阶
There are three common forms of the minor scale. All use the same key signature as their relative major (the major scale starting a minor third higher).
常用的小调音阶有三种形式。它们都使用关系大调的同一个调号（关系大调即比小调主音高小三度的大调）。
The natural minor follows the pattern: T – S – T – T – S – T – T. For A natural minor (relative to C major), the notes are A B C D E F G A.
自然小调的模式为：全 – 半 – 全 – 全 – 半 – 全 – 全。a 自然小调（C 大调的关系小调）的音为 A B C D E F G A。
The harmonic minor raises the 7th degree by a semitone, creating an augmented 2nd (T+S) step between the 6th and 7th degrees. Pattern: T – S – T – T – S – T+S – S. A harmonic minor: A B C D E F G♯ A.
和声小调升高第 7 级半音，在第 6 与第 7 级之间产生一个增二度（全音加半音）。模式：全 – 半 – 全 – 全 – 半 – 全+半 – 半。a 和声小调：A B C D E F G♯ A。
The melodic minor raises both the 6th and 7th degrees when ascending, and reverts to natural minor when descending. Ascending pattern: T – S – T – T – T – T – S (identical to a major scale with a minor third). A melodic minor ascending: A B C D E F♯ G♯ A; descending: A G F E D C B A.
旋律小调在上行时升高第 6 和第 7 级，下行时还原为自然小调。上行模式：全 – 半 – 全 – 全 – 全 – 全 – 半（除小三度外与大调一样）。a 旋律小调上行：A B C D E F♯ G♯ A；下行：A G F E D C B A。
5. Intervals | 音程
An interval measures the distance between two notes. It is named by a number (1st, 2nd, 3rd, etc.) and a quality (perfect, major, minor, augmented, diminished).
音程衡量两个音符之间的距离。它的名称由度数（一度、二度、三度等）和性质（纯、大、小、增、减）组成。
Counting semitones gives the exact size. Use this reference table for the most common intervals within an octave:
数半音可得出精确的大小。使用下面的参考表来掌握八度内最常用的音程：
| Interval Name | Semitones | Example (C to...) |
|---|---|---|
| Perfect Unison | 0 | C – C |
| Minor 2nd | 1 | C – D♭ |
| Major 2nd | 2 | C – D |
| Minor 3rd | 3 | C – E♭ |
| Major 3rd | 4 | C – E |
| Perfect 4th | 广告 / Sponsored 2027伊犁师范大学333教育综合819音乐理论综合考研初试一本通真题笔记知识重点总结技巧题库学复习资料教材模拟卷 音乐 备考教辅 · 正版现货 · 与本文同科同级别 查看详情 / View on Taobao参考价 ¥6.8
更多咨询请联系16621398022（同微信） 备考资讯每日更新，关注不错过 考纲变化 · 科目分析 · 学习方法  在微信里长按二维码识别关注 或截图后用「扫一扫 → 相册」选择本图 公众号：tutorhao |