📚 Year 9 SQA Music: Quick-reference Handbook of Formulas and Theorems | Year 9 SQA 音乐：公式定理速查手册
This handbook collects essential formulas, patterns and theoretical 'theorems' for Year 9 SQA Music. It covers key signatures, scales, intervals, chords, rhythm and transposition in a concise bilingual format to help you revise quickly.
本手册汇编了 Year 9 SQA 音乐课程中的核心公式、模式与理论‘定理’，涵盖调号、音阶、音程、和弦、节奏与移调，采用中英双语简明格式，方便快速复习。
1. The Circle of Fifths and Key Signatures | 五度圈与调号
The order of sharps in key signatures follows the sequence: F♯ C♯ G♯ D♯ A♯ E♯ B♯ (Father Charles Goes Down And Ends Battle). For major keys, the tonic is a semitone above the last sharp.
升号调中升号出现的顺序为：F♯ C♯ G♯ D♯ A♯ E♯ B♯（Father Charles Goes Down And Ends Battle）。对于大调，主音是最后一个升号上方小二度（半音）。
The order of flats is the reverse: B♭ E♭ A♭ D♭ G♭ C♭ F♭ (Battle Ends And Down Goes Charles's Father). For flat major keys (except F major), the tonic is the second-to-last flat. F major has one flat and is memorised separately.
降号调的顺序相反：B♭ E♭ A♭ D♭ G♭ C♭ F♭（Battle Ends And Down Goes Charles's Father）。对于降号大调（F大调除外），主音是倒数第二个降号。F大调只有一个降号，需单独记忆。
To find the relative minor of any major key, go down three semitones from the major tonic. The relative minor shares the same key signature.
找出任何大调的关系小调：从大调主音向下三个半音。关系小调使用相同的调号。
The circle of fifths shows the relationship among keys: moving clockwise adds one sharp (or removes one flat); moving anticlockwise adds one flat (or removes one sharp).
五度圈展示各调性之间的关系：顺时针移动增加一个升号（或去掉一个降号）；逆时针移动增加一个降号（或去掉一个升号）。
2. Major Scale Formula | 大调音阶公式
The major scale follows the step pattern: Tone, Tone, Semitone, Tone, Tone, Tone, Semitone (T-T-S-T-T-T-S). In semitones from the tonic: 0, 2, 4, 5, 7, 9, 11, 12.
大调音阶的音程模式为：全音、全音、半音、全音、全音、全音、半音（全-全-半-全-全-全-半）。以主音为0半音，各音级半音数为：0, 2, 4, 5, 7, 9, 11, 12。
Scale degree names (tonic, supertonic, mediant, subdominant, dominant, submediant, leading note) remain the same for all major keys. The leading note is always a semitone below the tonic.
音级名称（主音、上主音、中音、下属音、属音、下中音、导音）在所有大调中保持一致。导音总是比主音低一个半音。
The formula for constructing any major scale: start on the tonic, then apply the tone-semitone pattern. Use accidentals to maintain the pattern without changing the letter names.
构成任何大调音阶的公式：从主音开始，然后运用全音-半音模式。使用临时升降号来维持该模式，但不改变音名。
3. Minor Scale Formulas | 小调音阶公式
The natural minor scale uses the pattern: Tone, Semitone, Tone, Tone, Semitone, Tone, Tone (T-S-T-T-S-T-T). Semitone sequence: 0, 2, 3, 5, 7, 8, 10, 12. It shares the key signature of its relative major.
自然小调音阶的模式为：全音、半音、全音、全音、半音、全音、全音（全-半-全-全-半-全-全）。半音序列：0, 2, 3, 5, 7, 8, 10, 12。它与它的关系大调使用相同的调号。
The harmonic minor scale raises the 7th degree of the natural minor by a semitone. Its pattern: T-S-T-T-S-3 semitones-S. Semitone sequence: 0, 2, 3, 5, 7, 8, 11, 12.
和声小调音阶将自然小调的第七级音升高半音。其模式为：全-半-全-全-半-增二度-半。半音序列：0, 2, 3, 5, 7, 8, 11, 12。
The melodic minor scale ascends with raised 6th and 7th degrees (T-S-T-T-T-T-S; semitones: 0,2,3,5,7,9,11,12) and descends as the natural minor (T-T-S-T-T-S-T).
旋律小调音阶上行时升高第六与第七级音（全-半-全-全-全-全-半；半音：0,2,3,5,7,9,11,12），下行时还原为自然小调（全-全-半-全-全-半-全）。
4. Interval Semitone Count | 音程半音数
Intervals can be calculated by counting semitones between two notes. The table below lists the most common intervals up to an octave.
音程可以通过计算两个音之间的半音数来确定。下表列出了八度以内最常见的音程。
| Interval | Semitones | Example (from C) |
|---|---|---|
| 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 | 5 | C – F |
| Augmented 4th / Diminished 5th | 6 | C – F♯ / G♭ |
| Perfect 5th | 7 | C – G |
| Minor 6th | 8 | C – A♭ |
| Major 6th | 9 | C – A |
| Minor 7th | 10 | C – B♭ |
| Major 7th | 11 | C – B |
| Perfect octave | 12 | C – C' |
当计算更复杂音程时，首先确定音名数量（如C到E为三度），然后根据半音数判断是大、小、纯还是增减。增减音程比纯或大小音程多半音。
When calculating compound intervals, first determine the numeric size from letter names (e.g. C to E is a 3rd), then judge major/minor/perfect quality from the semitone count. Augmented intervals are one semitone larger than major/perfect; diminished intervals are one semitone smaller.
5. Triad Construction Formulas | 三和弦构成公式
A triad is a three-note chord built by stacking two thirds. The quality depends on the types of thirds used.
三和弦是由两个三度音程叠置而成的三音和弦。和弦的性质取决于所用三度的类型。
= major 3rd (4 semitones) + minor 3rd (3 semitones). Semitone pattern from root: 0, 4, 7.
大三和弦 = 大三度（4半音）+ 小三度（3半音）。自根音起的半音序列：0, 4, 7。
Minor triad = minor 3rd (3 semitones) + major 3rd (4 semitones). Pattern: 0, 3, 7.
小三和弦 = 小三度（3半音）+ 大三度（4半音）。序列：0, 3, 7。
Diminished triad = minor 3rd + minor 3rd (3+3 semitones). Pattern: 0, 3, 6.
减三和弦 = 小三度 + 小三度（3+3半音）。序列：0, 3, 6。
Augmented triad = major 3rd + major 3rd (4+4 semitones). Pattern: 0, 4, 8.
增三和弦 = 大三度 + 大三度（4+4半音）。序列：0, 4, 8。
Use these formulas to build any triad on any root. For example, C major: C (0), E (4), G (7); A minor: A (0), C (3), E (7).
使用这些公式可在任意根音上构建三和弦。例如，C大三和弦：C(0), E(4), G(7)；A小三和弦：A(0), C(3), E(7)。
6. Seventh Chord Formulas | 七和弦构成公式
A seventh chord adds a seventh above the root to a triad. The most common types are defined by stacking specific thirds.
七和弦在三和弦基础上叠加一个根音上方的七度音。最常见的类型由特定三度叠置定义。
Dominant 7th = major triad + minor 7th (10 semitones). Pattern: 0, 4, 7, 10.
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