Music Theoryafter A. Danhauser
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Appendices, Notes and Modern Appendices

Music Notation Around the World

Once you finish this lesson, you'll move confidently between English letter names, the fixed-do syllables used in France and elsewhere, and German note names. You'll also see how to convert French octave numbers to scientific pitch notation, and how to read a chord symbol.

8 min7 questionsDanhauser Note (b)

Where do, re and mi come from

Let's begin with a little history. The syllables ut, re, mi, fa, sol, la come from the opening syllables of the lines of a hymn to Saint John the Baptist, “Ut queant laxis,” in which each line begins one step higher than the last. This memory aid is credited to Guido of Arezzo (Guido d'Arezzo), an 11th-century monk. Si was added later, from the initials of “Sancte Iohannes.” The Italians replaced ut, which they felt was too dull to sing, with do, and France followed. But ut survives there in the name of the C clefs, “clés d'ut,” and in titles of works, such as “Symphonie en ut mineur,” Symphony in C minor. In 19th-century England, the tonic sol-fa movement changed si to ti, so that every syllable would start with a different letter. That's why English speakers sing “do re mi fa sol la ti.”

Letters and syllables

EnglishFrench (fixed do)German
Cdo (formerly ut)C
DréD
EmiE
FfaF
GsolG
AlaA
BsiH
B-flat (Bb)si bémolB
C-sharp (C#)do dièseCis
E-flat (Eb)mi bémolEs
A-flat (Ab)la bémolAs
In French, dièse means sharp, bémol means flat and bécarre means natural. In German, -is means sharp, -es means flat, and B natural is called H.
Sheet MusicBACH
The B-A-C-H motif.

Octave numbers

In the English-speaking world, octaves follow scientific pitch notation: middle C is C4, the tuning A, at 440 hertz, is A4, and the number goes up at each C. France numbers octaves one step lower, counting from the low C of the old keyboard, so middle C is do3 and the tuning A is la3. To convert a French octave number to scientific notation, just add 1. You may meet two more systems: older and German books use Helmholtz notation, where middle C is written c′, and some keyboards and music software label middle C as “C3.” When in doubt, look for middle C.

WorkshopOnline Piano Keyboard with Note NamesFull screen
Middle C (C4, French do3) and the tuning A (A4, French la3).
Middle C = C4 (French: do3)
C/do
D/ré
E/mi
F/fa
G/sol
A/la
B/si
C/do
D/ré
E/mi
F/fa
G/sol
A/la
B/si
C/do
D/ré
E/mi
F/fa
G/sol
A/la
B/si
C/do

Press a key: you hear the sound and see its name and its place on the staff.

Note values in American, British, and French

AmericanBritishFrenchMatching rest (US, with the French name)
whole notesemibreverondewhole rest (pause)
half noteminimblanchehalf rest (demi-pause)
quarter notecrotchetnoirequarter rest (soupir)
eighth notequavercrocheeighth rest (demi-soupir)
sixteenth notesemiquaverdouble crochesixteenth rest (quart de soupir)
32nd notedemisemiquavertriple croche32nd rest (huitième de soupir)
64th notehemidemisemiquaverquadruple croche64th rest (seizième de soupir)
double whole notebrevenote carrée (brève)double whole rest (bâton de deux pauses)

MIDI and frequencies

Electronic instruments and software identify each key by a MIDI note number. Middle C is number 60, the A at 440 hertz is number 69, and each half step adds 1. In equal temperament, you get the frequency from the formula f = 440 × 2(n - 69)/12, where n is the MIDI number. So middle C vibrates at about 261.6 hertz.

WorkshopTuning PitchFull screen
The same A at different historical and current tuning standards.
415 Hz
Baroque (period instruments)
-101.3 cents
430 Hz
Classical era (estimate)
-39.8 cents
435 Hz
French standard pitch, 1859
-19.8 cents
440 Hz
London conference 1939, ISO 16 standard
reference
442 Hz
Common orchestral pitch
+7.9 cents
443 Hz
Some orchestras (Berlin, Vienna)
+11.8 cents

Beats

Two slightly different A's played together produce a pulsation: the number of beats per second equals the difference in hertz. Musicians and tuners use it to adjust their intonation.

Danhauser speaks of “870 vibrations”: a count of single vibrations (one way), that is 435 complete cycles, 435 Hz.

Chord symbols, chord charts, and tablature

In jazz and pop, harmony is written as chord symbols above the melody, such as C, Am, G7, Fmaj7 or D/F#; you met them in the lessons on chords. Guitarists also read chord diagrams, which are pictures of the fretboard, and tablature, which shows the string and fret to play rather than the pitch. Tablature is handy for fingerings, but it's no substitute for the staff when it comes to rhythm and analysis.

Exercisein the method's spirit

Translate: a) the French “la bémol, mi, fa dièse” into English letter names; b) the German “H, Es, Fis” into English; c) the French octave names “sol2, do4, la3” into scientific pitch notation.

With these few tables, you can now read music written almost anywhere. A few questions to finish, and you're done with this lesson.

Check your understanding

7 questions
1.
In German, H means:
2.
A French book calls the tuning A “la3.” In scientific pitch notation, it is:
3.
A British “quaver” is an American:
4.
Which MIDI note number is the A at 440 hertz?
5.
Middle C, called do3 in France, is written in scientific pitch notation as:
6.
In German, “Es” is:
7.
Who is credited with the syllables ut, re, mi, fa, sol, la?

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