音程 · 两种计数INTERVALS · TWO COUNTS
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同一个键，
为什么音程名不同？Same piano key.
Why a different interval name?

从C4出发，E4与Fb4在十二平均律钢琴上是同一个键，但C到E经过3个字母，C到F经过4个。From C4, E4 and Fb4 reach the same key on an equal-tempered piano. Yet C to E spans 3 letters; C to F spans 4.

先猜：把E4改写成Fb4，会改变下面哪一种计数？Predict: when E4 is respelled Fb4, which count below changes?

起点固定，只改终点写法Fix the start; change the written endpoint

#表示升高1个半音，b表示降低1个半音；Fb4是F4降低半音。此图只比较列出的上行或同音例子。# raises by 1 semitone; b lowers by 1. Fb4 is F4 lowered a semitone. This model compares only the listed ascending or unison cases.

① 数字母，两端都数① Count letters, including both ends

  1. C
  2. D
  3. E

3度 / third

这里先忽略升降号，保留字母与八度位置。数的是包含几个字母，不是走了几步。Ignore accidentals for this count, retaining letters and octave position. Count included letters, not the gaps between them.

② 数半音，从0出发② Count semitones from 0

这是音高阶梯，不是实体键盘；向上每格增加1个半音。★为终点，●为起点。A pitch ladder, not a physical keyboard. Each step upward adds 1 semitone. ★ marks the endpoint; ● marks the start.

  1. C512
  2. B411
  3. A#4 / Bb410
  4. A49
  5. G#4 / Ab48
  6. G47
  7. F#4 / Gb46
  8. F45
  9. ★ E4 / Fb44
  10. D#4 / Eb43
  11. D42
  12. C#4 / Db41
  13. ● C40

C4 → E4：3度，4个半音，所以是大三度。 / C4 → E4: third, 4 semitones; a major third.

把两个结果合起来，才得到完整名称Combine the counts to name the interval

C4到E4是大三度。C4到Fb4有同样的4个半音，却跨4个字母，所以是减四度。相同琴键在相同条件下发出相同音高；单靠声音听不出它写成E还是Fb。C4 to E4 is a major third. C4 to Fb4 has the same 4 semitones but spans 4 letters, making it a diminished fourth. The same keys under the same conditions give the same pitches; sound alone cannot reveal E versus Fb spelling.

全部例子的文字答案Text answers for every example
终点Endpoint度数Number半音数Semitones名称Quality/name
C410完全一度perfect unison
E434大三度major third
Fb444减四度diminished fourth
F445完全四度perfect fourth
D#423增二度augmented second
Eb433小三度minor third
C5812完全八度perfect octave

本图不发声，不测试听力，也不模拟手指动作。等音关系限于本例的十二平均律；其他调律与演奏语境需要另谈。No sound, hearing test or finger-motion simulation. Enharmonic equivalence here uses equal temperament; other tuning and performance contexts require separate treatment.