📚 Year 9 SQA Music: Formula & Theorem Quick Reference Handbook | Year 9 SQA 音乐公式定理速查手册
This handbook collects the essential formulas, theorems and structural rules that underpin the Year 9 SQA Music curriculum. From note values and scale patterns to chord construction and cadence formulas, every concept is presented as a clear, bite-sized statement – English first, then Chinese – so you can revise efficiently and play with confidence.
本手册汇编了 Year 9 SQA 音乐课程的核心公式、定理与结构规则。从音符时值、音阶模式到和弦构成与终止式，每个概念都以简短清晰的双语（先英后中）呈现，帮助你高效复习，自信演奏。
1. Note Values & Rhythm Formulas | 音符时值与节奏公式
A semibreve (whole note) in 4/4 time lasts 4 beats. The basic duration chain: 1 semibreve = 2 minims = 4 crotchets = 8 quavers = 16 semiquavers.
在4/4拍中，一个全音符持续4拍。基本时值链：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。
A dotted note adds half of its original value. Dotted minim = 2 + 1 = 3 beats. Dotted crotchet = 1 + 0.5 = 1.5 beats. A double dot adds half plus a quarter: double-dotted minim = 2 + 1 + 0.5 = 3.5 beats.
附点音符增加原有时值的一半。附点二分音符 = 2 + 1 = 3拍。附点四分音符 = 1 + 0.5 = 1.5拍。双附点增加一半再加四分之一：双附点二分音符 = 2 + 1 + 0.5 = 3.5拍。
A tie joins two notes of the same pitch, adding their durations: crotchet tied to a quaver = 1 + 0.5 = 1.5 beats. Triplets play three notes in the time of two: three quaver triplets = 2 normal quavers = 1 crotchet beat.
延音线连接相同音高的音符，时值相加：四分音符加八分音符 = 1 + 0.5 = 1.5拍。三连音用三个音替代两个音的时值：3个八分三连音 = 2个普通八分音符 = 1个四分音符的拍。
2. Time Signatures & Meter | 拍号与节拍
The top number tells how many beats are in a bar; the bottom number tells which note value gets one beat. In 4/4, a crotchet = 1 beat, and there are 4 beats per bar. In 2/2 (cut time), a minim = 1 beat; the bar has 2 minim beats.
上方数字表示每小节的拍数，下方数字表示以哪种音符为一拍。4/4拍中四分音符为一拍，每小节4拍。2/2拍（切分拍）中二分音符为一拍，每小节2个二分音符拍。
Compound time signatures have a dotted note as the beat. Formula: divide the top number by 3 to find the number of beats. 6/8 = 2 dotted-crotchet beats per bar. 9/8 = 3 beats, 12/8 = 4 beats.
复拍子以附点音符为基本拍。公式：上方数字除以3得到拍数。6/8拍 = 每小节2个附点四分音符拍。9/8 = 3拍，12/8 = 4拍。
Irregular time signatures (5/4, 7/8) combine simple and compound groupings, e.g. 5/4 = 3 + 2 or 2 + 3 crotchet beats.
混合拍子（5/4、7/8）结合单拍与复拍的分组，例如5/4拍 = 3+2 或 2+3 个四分音符拍。
3. Major Scale Formula | 大调音阶公式
The major scale follows the pattern of whole steps (W) and half steps (H): W – W – H – W – W – W – H. In terms of tones (T) and semitones (S): T – T – S – T – T – T – S.
大调音阶遵循全音（W）和半音（H）的模式：W – W – H – W – W – W – H。用全音（T）和半音（S）表示为：T – T – S – T – T – T – S。
Apply the formula from any starting note to build a major scale. C major: C – D – E – F – G – A – B – C. G major: G – A – B – C – D – E – F♯ – G (F is raised by a semitone to fit the pattern).
从任何起始音应用此公式即可构建大调音阶。C大调：C – D – E – F – G – A – B – C。G大调：G – A – B – C – D – E – F♯ – G（必须升高F以符合模式）。
4. Minor Scale Formulas (Natural, Harmonic, Melodic) | 小调音阶公式（自然、和声、旋律）
Natural minor: W – H – W – W – H – W – W (T – S – T – T – S – T – T). It uses the same notes as the relative major starting on the 6th degree. A natural minor: A – B – C – D – E – F – G – A.
自然小调：W – H – W – W – H – W – W（全-半-全-全-半-全-全）。它与关系大调使用相同音符，但从第6级开始。a自然小调：A – B – C – D – E – F – G – A。
Harmonic minor: raise the 7th degree by a semitone from the natural minor. Formula: W – H – W – W – H – aug.2nd – H (T–S–T–T–S–T+S–S). A harmonic minor: A – B – C – D – E – F – G♯ – A.
和声小调：将自然小调第7级升高半音。公式：W – H – W – W – H – 增二度 – H。a和声小调：A – B – C – D – E – F – G♯ – A。
Melodic minor (ascending): raise the 6th and 7th degrees. Formula: W – H – W – W – W – W – H (T–S–T–T–T–T–S). Descending reverts to natural minor: W – W – H – W – W – H – W.
旋律小调（上行）：升高第6、7级。公式：W – H – W – W – W – W – H。下行恢复为自然小调：W – W – H – W – W – H – W。
5. Intervals & Semitone Counting | 音程与半音计数
An interval is the distance between two pitches, measured in semitones. A perfect unison is 0 semitones; a perfect octave is 12 semitones. The quality (perfect, major, minor, augmented, diminished) depends on the number of semitones relative to the major scale of the lower note.
音程是两个音高之间的距离，以半音为单位。纯一度为0个半音；纯八度为12个半音。音程性质（纯、大、小、增、减）取决于与低音大调音阶相比的半音数。
| Interval 音程 | Semitones 半音数 | Example (from C) |
|---|---|---|
| Perfect unison 纯一度 | 0 | C – C |
| Minor 2nd 小二度 | 1 | C – D♭ |
| Major 2nd 大二度 | 2 | C – D |
| Minor 3rd 小三度 | 3 | C – E♭ |
| Major 3rd 大三度 | 4 | C – E |
| Perfect 4th 纯四度 | 5 | C – F |
| Augmented 4th/Diminished 5th 增四度/减五度 | 6 | C – F♯ |
| Perfect 5th 纯五度 | 7 | C – G |
| Minor 6th 小六度 | 8 | C – A♭ |
| Major 6th 大六度 | 9 | C – A |
| Minor 7th 小七度 | 10 | C – B♭ |
| Major 7th 大七度 | 11 | C – B |
| Perfect octave 纯八度 | 12 | C – C’ |
Augmented intervals are one semitone larger than major/perfect; diminished intervals are one semitone smaller than minor/perfect. For example, C – D♯ is an augmented 2nd (3 semitones), while C – G♭ is a diminished 5th (6 semitones).
增音程比大/纯音程多一个半音；减音程比小/纯音程少一个半音。例如C – D♯为增二度（3个半音），C – G♭为减五度（6个半音）。
6. Triad Construction | 三和弦构成
A triad is a three-note chord built by stacking two thirds. The quality is determined by the size of the thirds in semitones.
三和弦是由两个三度音程叠置而成的三音和弦。其性质由两个三度的半音数决定。
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: A – C – E.
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