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16
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Circle of fifths · key signatures & relative minors
Circle of fifths · key signatures & relative minors
12 调按纯五度排列 · 调号升降数 · 关系小调 · 等音
The 12 major keys a perfect fifth apart · clockwise +1 sharp, counter-clockwise +1 flat
Interval ratios · just intonation vs equal temperament
Interval ratios · just intonation vs equal temperament
纯律 3:2/5:4 · 音分 1200·log₂ · 对比十二平均律
cents = 1200·log₂(ratio) · comparing just integer ratios with 2^(n/12)
Chord builder · piano keyboard
Chord builder · piano keyboard
根音+性质半音集 · major{0,4,7} 等 · 键盘高亮音名
Pick a root and a quality · built from a set of semitone offsets above the root
七种调式 · 音阶生成器
Diatonic modes · scale builder
七个中古调式=大调旋转 · WWHWWWH 步进 · 键盘音阶
The seven modes as rotations of the major scale's W/H pattern
Chord Progressions
Chord Progressions
I–IV–V–I / ii–V–I · 罗马数字 · 主/下属/属功能
Diatonic triads, Roman numerals, and harmonic function
Cadences
Cadences
正格 V–I · 变格 IV–I · 半终止 · 阻碍 V–vi · 结束/开放
The four cadence types — how a musical phrase closes
Chord Inversions
Chord Inversions
原位/第一/第二转位 · 数字低音 5/3·6/3·6/4 · 低音音
Root position and inversions, with figured bass
Key signatures · sharps, flats & the circle of fifths
Key signatures · sharps, flats & the circle of fifths
升号 F#C#G#… · 降号 BbEbAb… · 大小调 · 五度圈位置
The count of sharps or flats pins down exactly one major key and its relative minor
Scale degrees · names & solfège of the major scale
Scale degrees · names & solfège of the major scale
主/上主/中/下属/属/下中/导音 1–7 · 唱名 do-re-mi
Seven degrees, seven functional names, seven solfège syllables — for any key
Note frequencies · equal temperament & MIDI
Note frequencies · equal temperament & MIDI
f=440·2^((n−69)/12) · A4=440 · 八度倍频 · 半音 2^(1/12)
One formula maps every key on the piano to an exact frequency in hertz
The harmonic series · overtones of a vibrating string
The harmonic series · overtones of a vibrating string
基频 f0 · 谐波 f0,2f0,3f0… · 八度/五度/四度音程
partials at n·f₀ · ratio n:1 · interval between harmonics = n:(n−1)
Interval identification · name any interval by sight
Interval identification · name any interval by sight
半音数 0–12 · 纯/大/小/增/减 · 键盘/谱面识别
semitones + quality · 0 unison … 7 perfect fifth … 12 octave
Transposition · move a melody by a fixed interval
Transposition · move a melody by a fixed interval
按音程/换调整体平移 · 原调 vs 移调对照 · 谱面
add n semitones to every note · the shape stays, the key changes
Rhythm & meter — note values
Rhythm & meter — note values
全=2二分=4四分=… · 时值细分树 · 填满小节
whole = 2 half = 4 quarter = 8 eighth = 16 sixteenth · subdivide a beat, fill a measure
Time signatures — reading the meter
Time signatures — reading the meter
分子=拍数 · 分母=拍单位 · 单/复拍子 · 强弱分组
top = beats per measure · bottom = the note that gets one beat · simple vs compound
Syncopation — accenting the off-beat
Syncopation — accenting the off-beat
重音落弱拍/反拍 · 跨拍连音 · 直白 vs 切分 · 拍格
4/4 in eighths · on-beats 1 2 3 4 vs the 'and' in between · toggle the hits