📚 Year 10 WJEC Music - Formulas & Theorems Quick Reference Guide | WJEC 十年级音乐：公式定理速查手册
This quick reference guide compiles the essential 'formulas' and theoretical rules every Year 10 WJEC music student needs. From interval arithmetic to chord building and rhythmic calculations, these principles form the backbone of your listening, composing, and performing tasks. Keep this handbook close as a revision aid throughout the course.
这本速查手册汇集了每一位 WJEC 十年级音乐学生必备的核心“公式”与理论法则。从音程计算到和弦构成，再到节奏运算，这些原理构成了聆听、作曲与演奏任务的支柱。在课程学习中请随身携带本手册作为复习工具。
1. Semitone Counting and Interval Formulas | 半音计数与音程公式
e semitone count. The formula for a perfect unison is 0 semitones; minor 2nd = 1 semitone; major 2nd = 2; minor 3rd = 3; major 3rd = 4; perfect 4th = 5; augmented 4th/diminished 5th = 6; perfect 5th = 7; minor 6th = 8; major 6th = 9; minor 7th = 10; major 7th = 11; perfect octave = 12.
音程是两个音高之间的距离，以半音为单位测量。要识别音程，首先数字母名，然后根据半音数进行调整。纯一度公式为 0 个半音；小二度 = 1 个半音；大二度 = 2；小三度 = 3；大三度 = 4；纯四度 = 5；增四度/减五度 = 6；纯五度 = 7；小六度 = 8；大六度 = 9；小七度 = 10；大七度 = 11；纯八度 = 12。
| Interval (English/中文) | Semitones (半音数) | Example from C |
|---|---|---|
| Perfect unison / 纯一度 | 0 | C-C |
| Minor 2nd / 小二度 | 1 | C-Db |
| Major 2nd / 大二度 | 2 | C-D |
| Minor 3rd / 小三度 | 3 | C-Eb |
| Major 3rd / 大三度 | 4 | C-E |
| Perfect 4th / 纯四度 | 5 | C-F |
| Tritone / 三全音 | 6 | C-F#/Gb |
| Perfect 5th / 纯五度 | 7 | C-G |
| Minor 6th / 小六度 | 8 | C-Ab |
| Major 6th / 大六度 | 9 | C-A |
| Minor 7th / 小七度 | 10 | C-Bb |
| Major 7th / 大七度 | 11 | C-B |
| Perfect octave / 纯八度 | 12 | C-C' |
2. Major Scale Formula | 大调音阶公式
The major scale follows a fixed pattern of whole tones (W) and semitones (S): W W H W W W H. Starting on any tonic note, apply this sequence to generate the scale degrees. For example, C major: C (W) D (W) E (H) F (W) G (W) A (W) B (H) C.
大调音阶遵循固定的全音（W）和半音（H）模式：全 全 半 全 全 全 半。从任意主音开始，应用这个序列即可生成音级。例如，C 大调：C（全）D（全）E（半）F（全）G（全）A（全）B（半）C。
Tone-Tone-Semitone-Tone-Tone-Tone-Semitone (TTSTTTS)
全-全-半-全-全-全-半
3. Minor Scale Formulas | 小调音阶公式
the 7th degree by a semitone: pattern becomes W H W W H WH H (where WH = augmented 2nd). The melodic minor raises the 6th and 7th degrees ascending (W H W W W W H) and reverts to natural minor descending.
小调音阶主要有三种类型。自然小调用全半全全半全全模式。从 A 开始得出 A B C D E F G A。和声小调升高第 7 级半音：模式变为 全 半 全 全 半 增二度 半。旋律小调上行时升高第 6 和第 7 级（全 半 全 全 全 全 半），下行时还原为自然小调。
| Scale type / 音阶类型 | Formula in tones/semitones / 公式 |
|---|---|
| Natural minor / 自然小调 | W H W W H W W |
| Harmonic minor / 和声小调 | W H W W H WH H |
| Melodic minor (ascending) / 旋律小调（上行） | W H W W W W H |
4. Chord Construction Formulas | 和弦构成公式
nor 3rd (3 semitones) + perfect 5th. A diminished triad = root + minor 3rd + diminished 5th (6 semitones). An augmented triad = root + major 3rd + augmented 5th (8 semitones). These semitone 'formulas' allow you to build any chord from any root.
三和弦通过叠置根音上方的音程构成。大三和弦 = 根音 + 大三度（4 个半音）+ 纯五度（7 个半音）。小三和弦 = 根音 + 小三度（3 个半音）+ 纯五度。减三和弦 = 根音 + 小三度 + 减五度（6 个半音）。增三和弦 = 根音 + 大三度 + 增五度（8 个半音）。这些半音“公式”让你能从任意根音构建任意和弦。
Seventh chords extend the triad with a 7th above the root. A dominant 7th: major triad + minor 7th (10 semitones from root). A major 7th: major triad + major 7th (11 semitones). A minor 7th: minor triad + minor 7th. Half-diminished 7th: diminished triad + minor 7th. Fully diminished 7th: diminished triad + diminished 7th (9 semitones).
七和弦在三和弦基础上增加根音上方的七度音。属七和弦：大三和弦 + 小七度（距根音 10 个半音）。大七和弦：大三和弦 + 大七度（11 个半音）。小七和弦：小三和弦 + 小七度。半减七和弦：减三和弦 + 小七度。全减七和弦：减三和弦 + 减七度（9 个半音）。
5. Primary Chords and Cadence Formulas | 主要和弦与终止式公式
tances from the tonic bass note: I = 0 semitones (root position), IV = 5 semitones up, V = 7 semitones up. Cadences are the punctuation of music: perfect (V-I) sounds final; plagal (IV-I) is the 'Amen'; imperfect (I-V, II-V, IV-V) feels incomplete; interrupted (V-vi) is a surprise.
在任何大调中，主要和弦建立在第 1 级（主和弦，I）、第 4 级（下属和弦，IV）和第 5 级（属和弦，V）上。它们与主音低音的半音距离公式：I = 0 个半音（原位），IV = 向上 5 个半音，V = 向上 7 个半音。终止式是音乐的标点符号：正格终止（V-I）听感终结；变格终止（IV-I）是“阿们”；不完全终止（I-V、II-V、IV-V）感觉未完成；阻碍终止（V-vi）是意外。
6. Time Signatures and Rhythm Formulas | 拍号与节奏公式
nit. Simple time: each beat divides into two equal parts (e.g., 2/4, 3/4, 4/4). Compound time: each beat divides into three equal parts (e.g., 6/8, 9/8, 12/8). Formula: number of beats = top number; beat unit = 1/bottom number (semibreve).
拍号是一个描述节拍结构的数学分数。上方数字表示每小节的拍数，下方数字表示拍的单位。单拍子：每拍分为两个等份（如 2/4、3/4、4/4）。复拍子：每拍分为三个等份（如 6/8、9/8、12/8）。公式：拍数 = 上方数字；拍单位 = 1/下方数字（倍全音符）。
ets; dotted crotchet = 3 quavers. Triplets fit three notes into the time of two: a bracket '3' o a weak beat, often following the formula: tie across a barline or accent on an off-beat.
附点节奏将音符延长其原有时值的一半。附点二分音符 = 3 个四分音符；附点四分音符 = 3 个八分音符。三连音将三个音塞进两个音的时间里：括号“3”压缩时值。一个三连音四分音符的长度等于普通四分音符的（2/3）。切分音将重音转移到弱拍上，通常遵循公式：跨小节线的连结线或在弱拍上加重音。
7. Key Signatures and the Circle of Fifths | 调号与五度圈
Key signatures define the sharps or flats in a piece. The order of sharps: F# C# G# D# A# E# B#. The order of flats: Bb Eb Ab Db Gb Cb Fb. A quick formula: the last sharp is the leading note (7th degree) of the major key, so go up a semitone to find the tonic. For flat keys, the second-to-last flat is the tonic (except F major with one flat).
调号规定了乐曲中的升号或降号。升号顺序：F# C# G# D# A# E# B#。降号顺序：Bb Eb Ab Db Gb Cb Fb。一个快速公式：最后一个升号是该大调的导音（第 7 级），因此向上一个半音找到主音。对于降号调，倒数第二个降号就是主音（只有一个降号的 F 大调除外）。
hare the same key signature and are a minor 3rd below the major tonic. Formula: relative minor = major tonic minus 3 semitones (or plus 9 semitones).
五度圈通过上行五度（顺时针为升号）和下行五度（逆时针为降号）排列各调。关系小调共享相同的调号，位于大调主音下方小三度（或上方大六度）。公式：关系小调 = 大调主音减去 3 个半音（或加 9 个半音）。
8. Dynamics and Tempo Formulas | 力度与速度公式
ezzo-forte) < f (forte) < ff (fortissimo). Crescendo means gradually getting louder; diminuendo/decrescendo means gradually getting softer. Formula: pp = very soft; p = soft; mp = moderately soft; mf = moderately loud; f = loud; ff = very loud.
力度表示音量并遵循分级标度。从最弱到最强典型的标记：pp（很弱）< p（弱）< mp（中弱）< mf（中强）< f（强）< ff（很强）。Crescendo 意为渐强；diminuendo/decrescendo 意为渐弱。公式：pp = 很弱；p = 弱；mp = 中弱；mf = 中强；f = 强；ff = 很强。
-120, Allegro = 120-168, Presto = 168-200. Formula for tempo change: ritardando (rit.) = gradually slower; accelerando (accel.) = gradually faster; a tempo = return to original speed.
速度以每分钟拍数（bpm）计量。节拍器标记给出精确速度：Largo = 40-60 bpm，Adagio = 66-76，Andante = 76-108，Moderato = 108-120，Allegro = 120-168，Presto = 168-200。速度变化公式：ritardando（rit.）= 逐渐变慢；accelerando（accel.）= 逐渐变快；a tempo = 回到原速。
9. Ornamentation Symbols and Performance Formulas | 装饰音符号与演奏公式
Ornaments are decorative notes written in shorthand. A trill (tr) means rapid alternation between the written note and the note above according to the key signature. A mordent (squiggle) is a single rapid alternation: upper mordent goes up and back; lower mordent (with a vertical line) goes down and back. A turn (sideways S) starts on the note above, goes to the main note, below, and back. An acciaccatura (small note with a stroke) is crushed as quickly as possible; an appoggiatura (small note without stroke) takes half the main note's value.
装饰音是用速记法书写的装饰性音符。颤音（tr）意为在谱面音符和其上方根据调号的音符之间快速交替。波音（波浪线）是单次快速交替：上波音向上再返回；下波音（带竖线）向下再返回。回音（横向 S）从上方音开始，到主要音，再到下方音并返回。短倚音（带斜线小音符）尽可能快地压入；长倚音（无斜线小音符）占据主要音符时值的一半。
ts full value or with slight pressure. Accent (>) = attack the note forcefully. Marcato (^) = even more marked. Slur = play smoothly, legato.
演奏法标记影响音符的起奏。断奏（点）= 短促演奏，通常为其书写时值的一半。保持音（横线）= 奏满时值或稍加压力。重音（>）= 强劲起奏。特重音（^）= 更加突出。连线 = 连贯演奏，即连奏。
10. Chord Inversions and Figured Bass Formulas | 和弦转位与数字低音公式
ion: 3rd in bass, figured bass 6 (or 6/3). Second inversion: 5th in bass, figured bass 6/4. For seventh chords: root position = 7; first inversion = 6/5; second inversion = 4/3; third inversion = 4/2 (or just 2). This is a quick way to analyse harmony.
和弦转位发生在根音不是最低音时。原位：低音为根音，数字低音为无标记（或 5/3）。第一转位：低音为三音，数字低音为 6（或 6/3）。第二转位：低音为五音，数字低音为 6/4。对于七和弦：原位 = 7；第一转位 = 6/5；第二转位 = 4/3；第三转位 = 4/2（或仅 2）。这是快速分析和声的方法。
Inversion can be calculated by counting intervals above the bass note. For example, a C major triad in first inversion has E in the bass; the interval to C is a 6th, to G is a 3rd, hence 6/3 (or 6). Second inversion G bass: to C is a 4th, to E is a 6th, hence 6/4.
转位可以通过计算低音上方的音程来确定。例如，C 大三和弦第一转位低音为 E；到 C 的音程为六度，到 G 的音程为三度，因此为 6/3（或 6）。第二转位低音为 G：到 C 是四度，到 E 是六度，因此为 6/4。
11. Clefs and Transposition Formulas | 谱号与移调公式
The treble clef (G clef) fixes G above middle C on the second line. The bass clef (F clef) fixes F below middle C on the fourth line. The alto clef (C clef) fixes middle C on the third line. Transposing from one clef to another requires adjusting pitch according to clef position. For example, a note on the second line of treble clef is G4; the same staff position in bass clef is Bb2 (three lines lower in pitch).
高音谱号（G 谱号）将中央 C 上方的 G 固定在第二线。低音谱号（F 谱号）将中央 C 下方的 F 固定在第四线。中音谱号（C 谱号）将中央 C 固定在第三线。在不同谱号之间移调需要根据谱号位置调整音高。例如，高音谱号第二线上的音是 G4；同一线在低音谱号中是 Bb2（音高低三线）。
Transposing instruments sound at a different pitch from written. Bb instruments (clarinet, trumpet): written C sounds Bb a major 2nd lower. Formula: to transpose concert pitch to Bb instrument, write a major 2nd higher. Eb instruments (alto sax): written C sounds Eb a major 6th lower. Formula: to transpose concert pitch to Eb instrument, write a major 6th higher. F instruments (French horn): written C sounds F a perfect 5th lower; write a perfect 5th higher.
移调乐器的实际音高与记谱音高不同。降B 调乐器（单簧管、小号）：记谱 C 实际发出降B，低大二度。公式：将实际音高移调至降B 调乐器，记谱高大二度。降E 调乐器（中音萨克斯）：记谱 C 实际发出降E，低大六度。公式：记谱高大六度。F 调乐器（圆号）：记谱 C 实际发出 F，低纯五度；记谱高纯五度。
12. Interval Inversion and Compound Intervals | 音程转位与复音程
An interval is inverted by moving the lower note up an octave, or the upper note down an octave. The formula: a 2nd becomes a 7th, 3rd becomes 6th, 4th becomes 5th, 5th becomes 4th, 6th becomes 3rd, 7th becomes 2nd. The quality also changes: major becomes minor, minor becomes major, perfect stays perfect, augmented becomes diminished, diminished becomes augmented. The sum of the intervals always equals 9.
将下方音移高一个八度，或上方音移低一个八度，即可实现音程转位。公式：二度变为七度，三度变为六度，四度变为五度，五度变为四度，六度变为三度，七度变为二度。性质也随之变化：大音程变小，小音程变大，纯音程不变，增音程变减，减音程变增。两个音程数字之和总等于 9。
Compound intervals are larger than an octave. The simplest reduction formula: subtract 7 from the interval number to get its simple equivalent. For example, a compound perfect 5th (a 12th) reduces to a simple perfect 5th. The quality remains the same. This rule helps with analysis and notation.
复音程是大于八度的音程。最简单的还原公式：用音程数字减去 7 即可得到其单音程对应。例如，复纯五度（十二度）还原为单纯五度。性质保持不变。这条规则有助于分析与记谱。
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