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I.7Part I, The Signs of Notation
How the Clefs Relate
This lesson teaches you to find the same pitch in all seven clefs, and to tell conjunct motion from disjunct motion.
9 min9 questionsDanhauser § 23 to 26, note (d)
To give each sound an exact place in the range of pitches, musicians chose a reference sound: a landmark that fixes how all the other sounds relate to one another. This sound is the A written in the 2nd space of the treble clef. It's called concert A, or the tuning A.
Concert A, written in treble clef.
This same A can be written with the other clefs. Each clef puts it in a different place on the staff, but the sound is exactly the same.
The French violin clef: a G clef on the 1st line, no longer used.The soprano clef: a C clef on the 1st line.The mezzo-soprano clef: a C clef on the 2nd line.The alto clef: a C clef on the 3rd line.The tenor clef: a C clef on the 4th line.The baritone clef: an F clef on the 3rd line.The bass clef: an F clef on the 4th line.
Choose a pitch: the tool writes it in all seven clefs at once. Notes in the same column sound the same and have the same name.
A4
Same sound, same name, different place: the clef decides where the note is written. Clefs run from low (bass) to high (treble).
bass
Too far from the staff
baritone
above the staff
tenor
above the staff
alto
above the staff
mezzo-soprano
4th space
soprano
3rd space
treble
2nd space
French violin (historical)
1st space
The table of clefs
Danhauser gives a table in which the same series of notes is written in every clef. It teaches us three things:
notes in the same column produce the same sound and have the same name;
in each clef, the note on the clef's line carries the clef's name;
concert A appears in every clef, each time at a different place on the staff.
Middle C, or C4, in bass clef: it sits on the 1st ledger line above the staff.The same C in alto clef sits on the 3rd line. Every C clef marks this same middle C on its own line.In treble clef, the same C sits on the 1st ledger line below the staff.
Clef
Note on the 1st line
Note on the clef's line
Where A4 is found
Bass (F, 4th line)
G2
F3
above the 3rd ledger line
Baritone (F, 3rd line)
B2
F3
above the 2nd ledger line
Tenor (C, 4th line)
D3
C4
above the 1st ledger line
Alto (C, 3rd line)
F3
C4
above the 5th line
Mezzo-soprano (C, 2nd line)
A3
C4
4th space
Soprano (C, 1st line)
C4
C4
3rd space
Treble (G, 2nd line)
E4
G4
2nd space
French violin (G, 1st line)
G4
G4
1st space
The clefs arranged from low to high, in scientific pitch notation, where middle C is C4.
Compare historical and present-day pitch 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.
Melodic motion
Let's finish with melody. Any succession of different notes forms a melodic motion, and there are two kinds:
When two immediately neighboring notes follow each other, they form conjunct motion, also called stepwise motion: C to D, E to F or A to G, for example.
When two non-neighboring notes follow each other, they form disjunct motion, a leap: C to E, G to D or A to C, for example.
First conjunct motion, then disjunct motion.
Exercisein the method's spirit
Write these notes, given in alto clef, in treble clef, keeping the same sound and the same name.
Solution
C4, E4, G4, A3, F3, D4. In treble clef, C4, A3 and F3 need ledger lines below the staff.
Exercisein the method's spirit
Write these notes, given in bass clef, in treble clef at the same actual pitch.
Solution
A3, C4, B3 and G3. In treble clef, they all need ledger lines below the staff.
Exercisein the method's spirit
Say whether each melodic motion is conjunct or disjunct.
Solution
From C to D, conjunct; from D to F, disjunct; from F to E, conjunct; from E to G, disjunct; from G to C, disjunct; from C to B, conjunct; and from B to G, disjunct.
In the next lesson, we'll leave the clefs aside for a moment and look at human voices.
Check your understanding
9 questions
1.
Which sound serves as the reference for fixing the pitch of all the others?
2.
In which clef is concert A written in the 3rd space?
3.
Two notes in the same column of the table of clefs:
4.
Which clef puts the lowest register on the staff?
5.
The C written on the 3rd line in alto clef and the C written on the 4th line in tenor clef:
6.
The French standard pitch of 1859 was 870 simple vibrations. That corresponds to:
7.
What frequency does the ISO 16 standard set for the reference A?
8.
What kind of melodic motion do these two notes form?
9.
What kind of motion do B and C form?
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