📚 Year 7 WJEC Music: Quick Reference Guide to Musical Formulae & Theorems | Year 7 WJEC 音乐：公式定理速查手册
This handy guide summarises the essential musical 'formulae' and 'theorems' for Year 7 WJEC Music. Think of these as the building blocks and rules that underpin all the music you play and create — from note values and scales to chords and key signatures. Keep it as a quick reference to reinforce your understanding and support your practical work.
这本便捷手册总结了 Year 7 WJEC 音乐的关键“公式”和“定理”。可以把它们看作支撑你所演奏和创作的所有音乐的基石和规则——从音符时值和音阶到和弦与调号。将它作为速查手册，以巩固你的理解并辅助你的实践练习。
1. Note Value Relationships | 音符时值关系
In music, note durations follow a simple binary formula: each note value is exactly twice the length of the next smaller one. This creates a clear ‘beat hierarchy’. The semibreve (whole note) is the longest value you will use regularly, and it can be subdivided as shown below.
在音乐中，音符时长遵循简单的二分公式：每种音符的长度恰好是下一级较短音符的两倍。这形成了一个清晰的“节拍层级”。全音符是你常用的最长时值，它可以按以下方式细分。
The fundamental relationship can be written as an equation using note symbols: 1 𝅝 = 2 𝅗𝅥 = 4 ♩ = 8 ♪ = 16 𝅘𝅥𝅯 ds, one semibreve equals two minims, four crotchets, eight quavers or sixteen semiquavers.
基本关系可以用音符符号写成等式：1 𝅝 = 2 𝅗𝅥 = 4 ♩ = 8 ♪ = 16 𝅘𝅥𝅯。用文字表述就是：一个全音符等于两个二分音符、四个四分音符、八个八分音符或十六个十六分音符。
| English Name | 中文名称 | Symbol | Relative Duration |
|---|---|---|---|
| Semibreve | 全音符 | 𝅝 | 4 beats |
| Minim | 二分音符 | 𝅗𝅥 | 2 beats |
| Crotchet | 四分音符 | ♩ | 1 beat |
| Quaver | 八分音符 | ♪ | 1/2 beat |
| Semiquaver | 十六分音符 | 𝅘𝅥𝅯 | 1/4 beat |
Dotted notes add half of the original value. The dotted minim (𝅗𝅥.) is therefore worth three crotchet beats. A dotted crotchet (♩.) lasts for one and a half beats, usually followed by a quaver to complete the grouping.
附点音符会增加原时值的一半。因此，附点二分音符 (𝅗𝅥.) 的价值是三拍四分音符。附点四分音符 (♩.) 持续一拍半，通常后接一个八分音符来补全节奏组。
2. Time Signatures & Meter | 拍号与节拍
A time signature is written at the start of a piece and tells you how many beats are in each bar and what type of note counts as one beat. The top number indicates how many, the bottom number shows what kind – 4 stands for a crotchet beat, 2 for a minim beat, and 8 for a quaver beat.
拍号写在乐曲开头，告诉你每小节有几拍以及哪种音符算一拍。上面的数字表示“多少”拍，下面的数字表示“哪种”音符——4 代表四分音符为一拍，2 代表二分音符为一拍，8 代表八分音符为一拍。
The most common time signatures are 4/4 (also written as C, common time), 3/4, and 2/4. The formula for a time signature is: top number ÷ bottom note unit = beats per bar counted in that unit. You must also learn where the strong beats fall: in 4/4 the pattern is strong-weak-medium-weak; in 3/4 it is strong-weak-weak.
最常见的拍号是 4/4（也写作 C，即普通拍号）、3/4 和 2/4。拍号的公式可以理解为：上方的数字 ÷ 下方音符单位 = 以该单位记数的每小节拍数。你还需掌握强拍的位置：4/4 的规律是强-弱-次强-弱；3/4 则是强-弱-弱。
3. Tempo Markings | 速度标记
Tempo tells the performer how fast or slow a piece should be played. These Italian terms act as a speed formula: each word links to a general range of beats per minute (BPM). The most frequently used Year 7 tempo markings are summarised below.
速度告知演奏者乐曲应演奏得多快或多慢。这些意大利术语相当于速度公式：每个词都对应一个大致的每分钟拍数 (BPM) 范围。下面总结了 Year 7 最常用的速度标记。
- Largo – very slow and broad (approx. 40–60 BPM) | 广板 – 非常缓慢宽广（约 40–60 BPM）
- Adagio – slow and stately (approx. 66–76 BPM) | 柔板 – 缓慢而庄重（约 66–76 BPM）
- Andante – at a walking pace (approx. 76–108 BPM) | 行板 – 步行速度（约 76–108 BPM）
- Moderato – moderate speed (approx. 108–120 BPM) | 中板 – 中等速度（约 108–120 BPM）
- Allegro – fast, lively (approx. 120–168 BPM) | 快板 – 快速、活泼（约 120–168 BPM）
- Presto – very fast (approx. 168–200 BPM) | 急板 – 非常快（约 168–200 BPM）
You may also see words like accelerando (gradually getting faster) and ritardando (gradually slowing down), which change the tempo over a passage.
你还会看到诸如 accelerando（渐快）和 ritardando（渐慢）这类词，它们会让速度在一个乐段中逐渐变化。
4. Dynamics Terminology | 力度术语
Dynamics indicate the volume of the music. They work like a scale from very quiet to very loud, and each marking has a clear formula based on Italian abbreviations. The core range is pp, p, mp, mf, f, ff, with gradual changes using crescendo and diminuendo.
力度表示音乐的响度。它们如同一个从很弱到很强的音阶，每个标记都基于意大利语缩写而具有明确的公式。核心范围是 pp、p、mp、mf、f、ff，并使用渐强和渐弱来表示逐渐变化。
pp (pianissimo) – very quiet | 很弱
p (piano) – quiet | 弱
mp (mezzo-piano) – moderately quiet | 中弱
mf (mezzo-forte) – moderately loud | 中强
f (forte) – loud | 强
ff (fortissimo) – very loud | 很强
cresc. (crescendo) – gradually getting louder | 渐强
dim. (diminuendo) or decrescendo – gradually getting softer | 渐弱
Remember that dynamics are relative and depend upon the instrument and ensemble. A 'piano' on a trumpet may sound louder than a 'forte' on a flute.
请记住，力度是相对的，并取决于乐器和乐团编制。小号的“弱”可能听起来比长笛的“强”更响亮。
5. Scale Formulae: Major & Minor | 音阶公式：大调与小调
Scales are built from a fixed sequence of tones (T) and semitones (S). A semitone is the smallest step on a keyboard, while a tone equals two semitones. The major scale formula is T T S T T T S, which in Chinese terms is 全音 全音 半音 全音 全音 全音 半音.
音阶由固定的全音 (T) 和半音 (S) 序列构建而成。半音是键盘上最小的距离，而全音等于两个半音。大调音阶的公式是 T T S T T T S，即全全半全全全半。
Starting on C, this gives: C (T) D (T) E (S) F (T) G (T) A (T) B (S) C. For the natural minor scale, the formula is T S T T S T T (全半全全半全全). Starting on A, the A natural minor scale is A B C D E F G A – this uses the same notes as C major but starts on a different degree.
从 C 开始，得到：C (T) D (T) E (S) F (T) G (T) A (T) B (S) C。自然小调音阶的公式是 T S T T S T T（全半全全半全全）。从 A 开始，A 自然小调音阶为 A B C D E F G A ——它使用与 C 大调相同的音符，但从不同的音级开始。
You can use these tone-semitone patterns to work out any major or natural minor scale on an instrument. Just apply the formula note by note.
你可以运用这些全音半音模式在乐器上推导出任何大调或自然小调音阶。只需逐音套用公式即可。
6. Interval Quick Reference | 音程快速计算
An interval measures the distance between two notes. The interval number is counted by letter names (from the lower note to the higher), and the quality is worked out using the number of semitones. Here is a quick formula table for intervals up to an octave.
音程衡量两个音符之间的距离。音程的度数按照音名字母数出（从较低的音到较高的音），而性质则由半音数决定。下面是一个到八度为止的音程快速公式表。
| Interval | 半音数 | 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 | 5 | C–F |
| Tritone (Aug 4th / Dim 5th) | 6 | C–F♯ / C–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 (next) |
A quick formula: to find a major interval, use the major scale of the lower note; the 2nd, 3rd, 6th and 7th notes of that scale are major intervals. Lower them by one semitone to get minor intervals. For perfect intervals (4th, 5th, octave), check they match the notes of the major scale exactly – they are perfect unless altered.
快速公式：要找出大音程，使用较低音的大调音阶；该音阶的第二、三、六、七级音就是大音程。将它们降低一个半音就能得到小音程。对于纯音程（四度、五度、八度），检查它们是否完全匹配大调音阶中的音符——除非被改变，它们就是纯的。
7. Key Signature Chart | 调号表
A key signature tells you which notes are consistently sharp or flat throughout a piece. The order of sharps follows a fixed pattern: F♯, C♯, G♯, D♯, A♯, E♯, B♯. The order of flats is B♭, E♭, A♭, D♭, G♭, C♭, F♭. To identify the major key from a sharp key signature, find the last sharp and go up one semitone. For flat key signatures (with two or more flats), the second-to-last flat is the major key.
调号告诉你在一首乐曲中哪些音符要持续升高或降低半音。升号的顺序遵循固定模式：F♯、C♯、G♯、D♯、A♯、E♯、B♯。降号的顺序是：B♭、E♭、A♭、D♭、G♭、C♭、F♭。通过升号调号识别大调的方法：找到最后一个升号并向上移动一个半音。对于降号调号（有两个或以上降号），倒数第二个降号就是大调主音。
| Major Key | Sharps / Flats | Notes Affected |
|---|---|---|
| C major | 0 | none |
| G major | 1♯ | F♯ |
| D major | 2♯ | F♯, C♯ |
| A major | 3♯ | F♯, C♯, G♯ |
| F major | 1♭ | B♭ |
| B♭ major | 2♭ | B♭, E♭ |
| E♭ major | 3♭ | B♭, E♭, A♭ |
Memorise these two formulas: Last sharp + semitone = major key; Second-to-last flat = major key (except F major with one flat). The relative minor key shares the same key signature and is found a minor third below the major tonic.
请记住这两条公式：最后一个升号 + 半音 = 大调主音；倒数第二个降号 = 大调主音（只有一个降号的 F 大调除外）。关系小调共享相同的调号，且位于大调主音下方小三度。
8. Chord Construction | 和弦构成
Chords are built by stacking intervals on a root note. The most common are triads – three-note chords consisting of a root, a third and a fifth. The formula for a major triad is: root + 4 semitones (major 3rd) + 3 semitones (minor 3rd), giving a perfect 5th from the root. A minor triad flips the order: root + 3 semitones (minor 3rd) + 4 semitones (major 3rd).
和弦是通过在根音上叠加音程构建的。最常见的是三和弦——由根音、三音和五音构成的三音和弦。大三和弦的公式是：根音 + 4 个半音（大三度）+ 3 个半音（小三度），最终形成与根音相距纯五度的和弦。小三和弦则颠倒顺序：根音 + 3 个半音（小三度）+ 4 个半音（大三度）。
le, C major: C (root) + 4 semitones → E, then E + 3 semitones → G. The complete chord is C–E–G. C minor: C + 3 semitones → E♭, then E♭ + 4 semitones → G, giving C–E♭–G.
例如，C 大调：C（根音）+ 4 个半音 → E，然后 E + 3 个半音 → G。完整的和弦是 C–E–G。C 小调：C + 3 个半音 → E♭，然后 E♭ + 4 个半音 → G，得到 C–E♭–G。
You can also think of chords in Roman numerals based on scale degrees. In a major key, chords I, IV and V are major; ii, iii and vi are minor; and vii° is diminished (root + 3 + 3 semitones).
你还可以根据音级
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