Music Theory Formula Cheat Sheet for KS3 | KS3 音乐理论公式速查手册

📚 Music Theory Formula Cheat Sheet for KS3 | KS3 音乐理论公式速查手册

Welcome to your quick-reference guide for KS3 CAIE Music theory. This article gathers the essential formulas, patterns and rules you need to read, write and understand music at this level. Use it as a handy revision tool whenever you need a reminder on note values, scales, intervals, chords and more.

欢迎使用 KS3 CAIE 音乐理论速查手册。本文汇总了此阶段所需的关键公式、模式和规则，帮助你阅读、写作和理解音乐。当需要复习音符时值、音阶、音程、和弦等内容时，可以随时查阅。

1. Note Value Formulas | 音符时值公式

In music, each note value is related to others by simple ratios. The whole note (semibreve) is the basic unit from which shorter notes are derived. A half note (minim) equals half of a whole note, a quarter note (crotchet) equals one quarter, and so on. These relationships can be expressed as division formulas: each larger note value can be split into two of the next smaller value.

音乐中，每个音符时值都通过简单的比率相互关联。全音符（semibreve）是基本单位，更短的音符由它派生而来。二分音符（minim）等于全音符的一半，四分音符（crotchet）等于四分之一，依此类推。这些关系可以用等分公式表示：每个较大的音符时值都可以分成两个次级的较小音符时值。

UK Term (US Term)	Relative Value Formula
Semibreve (Whole note)	= 2 minims = 4 crotchets = 8 quavers = 16 semiquavers
Minim (Half note)	= 2 crotchets = 4 quavers = 8 semiquavers
Crotchet (Quarter note)	= 2 quavers = 4 semiquavers
Quaver (Eighth note)	= 2 semiquavers
Semiquaver (Sixteenth note)	= 2 demisemiquavers

A dotted note adds half of its original value. The formula is: Dotted note = original value × 1.5. For example, a dotted minim (dotted half note) normally lasting 2 beats becomes 3 beats (2 × 1.5). Double dotted notes add a further quarter of the original value.

附点音符增加原时值的一半。公式为：附点音符 = 原时值 × 1.5。例如，附点二分音符通常为 2 拍，变成 3 拍（2 × 1.5）。双附点音符再增加原时值的四分之一。

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2. Time Signature Formulas | 拍号公式

The time signature appears at the start of a piece as two numbers. The top number tells you how many beats are in each bar. The bottom number tells you what type of note gets one beat. A bottom number of 4 means a crotchet (quarter note) gets one beat; an 8 means a quaver (eighth note) gets one beat. This can be summarised as: Beat unit = 1 / bottom number of a semibreve.

拍号以两个数字出现在乐曲开头。上方数字表示每小节有几拍。下方数字表示以哪种音符为一拍。下方数字为 4 表示以四分音符为一拍；为 8 表示以八分音符为一拍。可以概括为：拍子单位 = 全音符的 1/下方数字。

Time signatures fall into simple and compound categories. In simple time, each beat divides naturally into two equal parts (e.g., 2/4, 3/4, 4/4). In compound time, each beat divides into three equal parts (e.g., 6/8, 9/8, 12/8). The formula for compound time: number of beats per bar = top number ÷ 3, and the beat unit is a dotted note.

拍号分为单拍子和复拍子。单拍子中，每一拍自然分成两个等份（如 2/4、3/4、4/4）。复拍子中，每一拍分成三个等份（如 6/8、9/8、12/8）。复拍子公式：每小节拍数 = 上方数字 ÷ 3，拍子单位为附点音符。

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3. Dotted Rhythms and Tuplet Formulas | 附点节奏与连音符公式

The dotted rhythm formula is straightforward: a dotted note lasts 1.5 times the undotted note. Triplets are the most common tuplet, where three notes fit into the time usually taken by two notes of the same kind. The formula: triplet quarter notes = 2 regular quarter notes. You often see a bracket or ‘3’ written above or below the triplet group.

附点节奏的公式非常直接：附点音符时值为原音符的 1.5 倍。三连音是最常见的连音符，用三个音符占据通常两个相同音符的时值。公式：三连音四分音符 = 2 个常规四分音符。通常在三连音组上方或下方标有弧线和数字 ‘3’。

Other tuplets follow the same principle: a quintuplet (5 notes in the time of 4), a sextuplet (6 in the time of 4), and so on. For any tuplet, the number indicates how many notes are crammed into the space normally occupied by the base number of notes.

其他连音符遵循相同原则：五连音（5 个音符占据 4 个音符的时值）、六连音（6 个音符占据 4 个音符的时值）等。对于任何连音符，该数字表示在通常由基数音符占据的空间内挤入多少个音符。

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4. Major Scale Formula | 大调音阶公式

Every major scale follows the same pattern of tones (T) and semitones (S): T – T – S – T – T – T – S. This works from any starting note. For example, starting on C: C (T) D (T) E (S) F (T) G (T) A (T) B (S) C. The semitones fall between the 3rd–4th and 7th–8th degrees of the scale.

每个大调音阶都遵循相同的全音（T）和半音（S）模式：T – T – S – T – T – T – S。这适用于任何起始音。例如，从 C 开始：C (T) D (T) E (S) F (T) G (T) A (T) B (S) C。半音落在音阶的第 3-4 级和第 7-8 级之间。

You can also think of the formula using scale-degree numbers: 1 2 3 4 5 6 7 8, where semitones are between 3–4 and 7–8. When building a major scale on a new tonic, use the T-T-S-T-T-T-S pattern and apply sharps or flats as needed to maintain it.

你也可以用音级数字来记忆公式：1 2 3 4 5 6 7 8，其中半音位于 3-4 和 7-8 之间。在建立新调的大调音阶时，使用 T-T-S-T-T-T-S 模式，必要时添加升号或降号以维持该模式。

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5. Minor Scale Formulas | 小调音阶公式

The natural minor scale uses this pattern: T – S – T – T – S – T – T. In A natural minor: A (T) B (S) C (T) D (T) E (S) F (T) G (T) A. The semitones occur between the 2nd–3rd and 5th–6th degrees.

自然小调音阶使用以下模式：T – S – T – T – S – T – T。以 A 自然小调为例：A (T) B (S) C (T) D (T) E (S) F (T) G (T) A。半音发生于第 2-3 级和第 5-6 级之间。

The harmonic minor scale raises the 7th degree by a semitone, creating a step-and-a-half interval between the 6th and 7th notes. Formula: T – S – T – T – S – 1½ – S. Melodic minor ascending raises both the 6th and 7th degrees: T – S – T – T – T – T – S (descending it reverts to natural minor).

和声小调音阶将第 7 级升高半音，在第 6 和第 7 音之间形成增二度（一个半全音）。公式：T – S – T – T – S – 1½ – S。旋律小调上行同时升高第 6 和第 7 级：T – S – T – T – T – T – S（下行恢复为自然小调）。

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6. Interval Semitone Formulas | 音程半音公式

Intervals are measured by counting semitones between two notes. The common interval qualities and their semitone counts are:

音程通过计算两个音之间的半音数来衡量。常见的音程性质及其半音数如下：

Interval Name	Semitone Count
Perfect unison (P1)	0
Minor 2nd (m2)	1
Major 2nd (M2)	2
Minor 3rd (m3)	3
Major 3rd (M3)	4
Perfect 4th (P4)	5
Augmented 4th / Diminished 5th (A4/d5)	6
Perfect 5th (P5)	7
Minor 6th (m6)	8
Major 6th (M6)	9
Minor 7th (m7)	10
Major 7th (M7)	11
Perfect octave (P8)	12

To find an augmented interval, add one semitone to a major or perfect interval. To find a diminished interval, subtract one semitone from a minor or perfect interval. For example, an augmented 5th = 8 semitones, a diminished 4th = 4 semitones.

要找到增音程，将大音程或纯音程增加一个半音。要找到减音程，将小音程或纯音程减少一个半音。例如，增五度 = 8 个半音，减四度 = 4 个半音。

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7. Triad Construction Formulas | 三和弦构建公式

A triad is built by stacking two thirds on top of a root note. The quality of the triad depends on the exact semitone distances between the notes. The four basic triad formulas are:

三和弦是在根音上叠加两个三度音构成的。和弦的性质取决于音与音之间具体的半音距离。四种基本三和弦的公式如下：

• Major triad: root + 4 semitones (major 3rd) + 3 semitones (minor 3rd). Example: C – E – G.
  大三和弦：根音 + 4 半音（大三度）+ 3 半音（小三度）。例如：C – E – G。
• Minor triad: root + 3 semitones (minor 3rd) + 4 semitones (major 3rd). Example: C – E♭ – G.
  小三和弦：根音 + 3 半音（小三度）+ 4 半音（大三度）。例如：C – E♭ – G。
• Diminished triad: root + 3 semitones + 3 semitones (two minor 3rds). Example: C – E♭ – G♭.
  减三和弦：根音 + 3 半音 + 3 半音（两个小三度）。例如：C – E♭ – G♭。
• Augmented triad: root + 4 semitones + 4 semitones (two major 3rds). Example: C – E – G♯.
  增三和弦：根音 + 4 半音 + 4 半音（两个大三度）。例如：C – E – G♯。

Inversions change the bottom note. Root position: root in bass. First inversion: 3rd in bass (chord formula: 3rd + 4th/3rd intervals above). Second inversion: 5th in bass. The intervals above the bass follow specific patterns that can be derived from the root position spacings.

转位改变了最低音。原位：根音在低音部。第一转位：三音在低音部（和弦公式：低音上方为三度/四度音程）。第二转位：五音在低音部。低音上方的音程关系可由原位间距推导得出。

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8. Key Signatures and Circle of Fifths Formulas | 调号与五度圈公式

Key signatures are determined by the number of sharps or flats placed at the beginning of the staff. The order of sharps is always: F♯ C♯ G♯ D♯ A♯ E♯ B♯ (Father Charles Goes Down And Ends Battle). The order of flats is the reverse: B♭ E♭ A♭ D♭ G♭ C♭ F♭.

调号取决于谱表开始处升号或降号的数目。升号顺序永远是：F♯ C♯ G♯ D♯ A♯ E♯ B♯（可记为 Father Charles Goes Down And Ends Battle）。降号顺序与之相反：B♭ E♭ A♭ D♭ G♭ C♭ F♭。

To find the major key from a sharp key signature, take the last sharp and go up one semitone. For example, last sharp F♯ → G major; last sharp C♯ → D major. For flat key signatures, the second-to-last flat is the major key. E.g., flats B♭ E♭ → E♭ major. The relative minor is always a minor 3rd below the major tonic.

从升号调找大调：取最后一个升号，再升高半音即为大调主音。例如，最后一个升号为 F♯ → G 大调；C♯ → D 大调。对于降号调，倒数第二个降号就是大调主音。如降 B♭ 和 E♭ → E♭ 大调。关系小调总是位于大调主音下方小三度。

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9. Chord Progression Formulas | 和弦进行公式

Chords built on each scale degree of a major key follow a fixed pattern of quality. Using Roman numerals: I (major), ii (minor), iii (minor), IV (major), V (major), vi (minor), vii° (diminished). The most common progressions in KS3 music are based on these chords.

大调音阶各级上建立的和弦遵循固定的性质模式。用罗马数字表示为：I（大）、ii（小）、iii（小）、IV（大）、V（大）、vi（小）、vii°（减）。KS3 音乐中最常见的和弦进行都基于这些和弦。

• I – IV – V – I: a standard perfect cadence progression.
  I – IV – V – I：标准的正格终止进行。
• ii – V – I: a strong predominant–dominant–tonic formula.
  ii – V – I：强有力的下属-属-主公式。
• I – vi – IV – V: the ’50s progression, widely used in pop.
  I – vi – IV – V：50 年代进行，广泛用于流行音乐。
• I – V – vi – IV: another massively popular four-chord loop.
  I – V – vi – IV：另一种极流行的四和弦循环。

In a minor key, the chord qualities shift, but the function formulas remain similar: i (minor), iv (minor), V (major, often using harmonic minor) are the core chords.

在小调中，和弦性质有所变化，但功能公式类似：i（小）、iv（小）、V（大，常使用和声小调）是核心和弦。

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10. Transposition Formula | 移调公式

Transposition means shifting a piece of music to a new key while keeping the exact interval relationships between all notes. The formula requires two steps: first, determine the interval of transposition from the old key note to the new key note. For example, transposing from C major to G major is up a perfect 5th or down a perfect 4th.

移调是指将乐曲移到新的调上，同时保持所有音符之间精确的音程关系。公式需要两步：

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