Sharps, flats and the twelve
#music/accidentals · Note 3 of 9 · part of Guitar
Seven letters, twelve pitches. The five extra ones are where most of the confusion in music theory lives, and all of it comes from one historical accident.
A semitone is one fret
♯ (sharp) raises a note by one semitone — one fret toward the body. ♭ (flat) lowers it by one — one fret toward the nut. ♮ (natural) cancels either.
Twelve semitones make an octave. On a string:
C C♯ D D♯ E F F♯ G G♯ A A♯ B C
0 1 2 3 4 5 6 7 8 9 10 11 12
Read it downward and the same pitches take flat names: D♭, E♭, G♭, A♭, B♭.
Why there is no E♯ or B♯
Look at the row above. Between E–F and between B–C there is no gap. They are already a semitone apart. Everywhere else the letters are two semitones — a whole tone — apart.
This is not arbitrary and it is not a mistake. The letter names were assigned to a seven-note diatonic scale, and that scale's shape is
W W H W W W H
— the two half steps land at degrees 3→4 and 7→8. Name those degrees C D E F G A B and the half steps fall on E–F and B–C by construction.
So a piano has no black key there, and a guitar has no spare fret. Everything downstream — why key signatures exist, why some scales need five sharps — follows from those two gaps.
In keys like F♯ major you will see E♯ written, meaning the pitch F. It is written that way so each letter appears exactly once in the scale. It sounds like F and is fingered like F.
Enharmonics: two names, one fret
F♯ and G♭ are the same fret. So are C♯/D♭, D♯/E♭, G♯/A♭, A♯/B♭.
On a guitar they are identical pitches, because the instrument is fretted in equal temperament — every semitone is exactly the same ratio. On a violin, or in a vocal ensemble, a player may bend F♯ slightly higher than G♭, because the two have different harmonic functions. Guitars cannot, and mostly nobody minds.
Which name to use is decided by the key, not by preference:
- D major has F♯ and C♯ — because a scale uses each letter once. Calling it G♭ would give you two Gs and no F.
- D♭ major has G♭ for exactly the same reason, running the other way.
In sargam, the same twelve
From Sargam and the scale:
| Semitones | Sargam | Western (Sa = C) |
|---|---|---|
| 0 | Sa | C |
| 1 | komal Re | D♭ |
| 2 | Re | D |
| 3 | komal Ga | E♭ |
| 4 | Ga | E |
| 5 | Ma | F |
| 6 | tivra Ma | F♯ |
| 7 | Pa | G |
| 8 | komal Dha | A♭ |
| 9 | Dha | A |
| 10 | komal Ni | B♭ |
| 11 | Ni | B |
Sargam solves the naming problem differently and, arguably, more neatly:
- Sa and Pa never move. They are achal — the tonic and the fifth, the two most stable intervals, are simply fixed.
- Re, Ga, Dha, Ni have komal (flattened) forms. Four of them.
- Ma alone has a tivra (sharpened) form. One.
4 komal + 1 tivra + 7 shuddha = twelve names for twelve pitches, with no enharmonic ambiguity at all. There is no "komal Re or tivra Sa" argument to have, because Sa cannot be sharpened. Western notation needs double sharps to keep its letters straight; sargam never does.
Sharps on the fretboard
The practical version. Open strings and where their sharps sit:
| String | Open | ♯ at fret |
|---|---|---|
| 6th | E | F♯ at 2 |
| 5th | A | A♯ at 1 |
| 4th | D | D♯ at 1 |
| 3rd | G | G♯ at 1 |
| 2nd | B | C♯ at 2 |
| 1st | E | F♯ at 2 |
Note the 6th and 2nd: from E and B there is no sharp at fret 1, because fret 1 is F and C. The gaps again.
Key signatures, in one line
Sharps always appear in the order F C G D A E B; flats in exactly the reverse, B E A D G C F. One key signature per position on the circle of fifths — see Reading music.
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