Standard 1: Fundamentals

Our objectives:

  • Accurately write a treble clef and bass clef.
  • Name notes on both treble clef and bass clef, including the use of ledger lines.
  • Determine the subdivisions of note durations and rest durations.
  • Determine the type of meter from a given time signature.


1.1 Pitch

1.11 Notes

In musical notation, a note indicates a pitch and rhythmic value. A note consists of a notehead (either empty or filled in), and optionally can include a stem, beam, dot, or flag.

1.12 Staff

Notes alone can't convey their pitch information without being placed on a staff. A staff consists of five horizontal lines, evenly spaced. The plural of staff is staves.

1.13 Clefs

Notes still can't convey their pitch information if the staff doesn't include a clef. A clef indicates which pitches are assigned to the lines and spaces on a staff. The two most commonly used clefs are the treble and bass clef; others that you'll see relatively frequently are alto and tenor clef.

Here is the pitch C4 (also known as "Middle C") placed on the treble, bass, alto, and tenor clefs.

Take a look at this exercise. How are the letter names of each note arranged on the treble clef? Which letters of the alphabet are used?

Now take a look at this exercise, which uses the bass clef. How are the letter names arranged?

Finally, take a look at this exercise, which removes the "helpers". Can you correctly name the notes?

1.14 Grand staff

The grand staff consists of two staves, one that uses a treble clef, and one that uses a bass clef. The staves are connected by a curly brace. Grand staves are used frequently for notating piano music and other polyphonic instruments.

1.15 Octave Designation

When specifying a particular pitch precisely, we also need to know the register. In fact, if all you have is C-sharp or B-flat, you do not have a pitch, you have a pitch-class. A pitch-class and a register together designate a specific pitch.

We will follow the International Standards Organization (ISO) system for register designations. In that system, middle C (the first ledger line above the bass staff or the first ledger line below the treble staff) is C4. An octave higher than middle C is C5, and an octave lower than middle C is C3.

The tricky bit about this system is that the octave starts on C and ends on B. Therefore, an ascending scale from middle C contains the following pitch designations:

And a descending scale from middle C contains the following pitch designations:

Note that a complete designation contains both the pitch-class name (a letter name plus an optional sharp or flat) and the register (the ISO number indicating the octave in which the pitch is found). Both are required for the full designation of a specific pitch.

Take a look at this exercise. Construct the note requested, and be careful to put the note in the correct octave according to the octave designation.

1.16 Ledger lines

When the music's range exceeds what can be written on the staff, extra lines are drawn so that we can still clearly read the pitch. These extra lines are called ledger lines. In the example below, From Haydn's Piano Sonata in G (Hob. XVI: 39), Ab5 occurs just above the treble staff in the right hand, and G3 and B3 occur just below the treble staff in the left hand.

Now take a look at this exercise. Play around here and test things out. How do these ledger lines affect the letter names?


1.2 Rhythm

1.21 Rhythmic Values

Rhythm refers to the combination of long and short durations in time. Durations are notated with either unfilled or filled noteheads. Unfilled noteheads can appear with or without a stem; filled noteheads always appear with a stem. Flags can be added to the stems of filled noteheads; each flag shortens the duration by half.

Take a look at this online lesson for a summary of how these note values relate to one another.

1.22 Rests

Rests represent silence in musical notation. For each durational symbol there exists a corresponding rest.

Take a look at this online lesson for a summary of how rests and notes work together.

1.23 Dots and ties

Dots and ties allow for basic durations to be lengthened. A dot occurs after a pitch or a rest, and it increases its duration by half. For example, if a quarter note is equivalent in duration to two eighth notes, a dotted quarter note would be equivalent to three eighth notes. Generally, undotted notes divide into two notes; dotted notes divide into three. Thus, undotted notes are typically used to represent the beat level in simple meter, while dotted notes are used to represent the beat in compound meter.

Multiple dots can be added to a duration. Subsequent dots add half the duration of the previous dot. For example, a quarter note with two dots would be equivalent in duration to a quarter, eighth, and sixteenth note.

A tie lengthens a duration by connecting two adjacent identical pitches. Ties are used to either sustain a pitch beyond the length of a single measure, or to make a particular rhythmic grouping in a measure more clear.

In the example below, the duration of the first pitch is longer than a single measure, so it is represented by tying the dotted half note, which lasts the full measure, to the first beat of the subsequent measure.

Take a look at this online lesson for a summary of how dots and ties affect the duration of notes.


1.3 Meter

Meter describes the way multiple pulse layers work together to organize music in time. Standard meters in Western music can be classified with two designation types:

  • Simple or Compound (describes how each pulse is divided)
  • Duple, Triple, or Quadruple (describes how many each measure is divided into pulses)

1.31 Simple vs. Compound

Simple and Compound classifications result from the relationship between the counting pulse and the pulses that are faster than the counting pulse. In other words, it is a question of division: does each pulse generally divide into two equal parts, or three equal parts? Meters that divide the pulse into two equal parts are called simple meters; meters that divide the pulse into three equal parts are called compound meters.

Here is an example of a song in simple meter. Notice that the counting pulse can be evenly divided into groups of two notes (as seen in the first three pulses of the excerpt). The beginning of each pulse is marked by an asterisk.

Here is an example of a song in compound meter. Notice how, in contrast to the above example, the counting pulse is now divided into groups of three notes each, instead of two. The beginning of each pulse is marked by an asterisk.

1.32 Duple, Triple and Quadruple

Duple, Triple, and Quadruple classifications result from the relationship between the counting pulse and the pulses that are slower than the counting pulse. In other words, it is a question of grouping: how many counting pulses (or "beats") are grouped into each bar? If the counting pulse can be organized into groups of two, we have duple meter; groups of three, triple meter; groups of four, quadruple meter.

Here is an example of a song in Duple meter. Notice how the counting pulse are organized into groups of twos. In other words, you can count "ONE two ONE two..." along with the song, where "ONE" is the beginning of each group. Each group of pulses is called a "bar" or "measure".

Here is an example of a song in Triple meter. Notice how the counting pulses are organized into groups of threes. In other words, you can count "ONE two three ONE two three ..." along with the song, where "ONE" is the beginning of each group.

Here is an example of a song in Quadruple meter. Similar to the above song in Triple meter, notice how the counting pulses are now organized into groups of fours. When you play the example, count aloud by saying "ONE two three four" along with the song, where "ONE" is the beginning of each bar or measure. Important: Quadruple meter and Duple meter are very closely related, in that you can almost always hear a bar of music in Quadruple meter as two bars of Duple meter.

Thus, we can combine these two designation types to form six types of standard meter in Western music:

  • simple duple (each measure consists of two pulses, each pulse divides into two equal parts)
  • simple triple (each measure consists of three pulses, each pulse divides into two equal parts)
  • simple quadruple (each measure consists of four pulses, each pulse divides into two equal parts)
  • compound duple (each measure consists of two pulses, each pulse divides into three equal parts)
  • compound triple (each measure consists of three pulses, each pulse divides into three equal parts)
  • compound quadruple (each measure consists of four pulses, each pulse divides into three equal parts)

1.34 Time Signatures: Top Number

These types of meters are notated as a time signature, placed at the beginning of the music, to the right of the clef.

The top number (and the top number only!) describes the type of meter. Following are the top numbers that always correspond to each type of meter:

  • simple duple: 2
  • simple triple: 3
  • simple quadruple: 4
  • compound duple: 6
  • compound triple: 9
  • compound quadruple: 12

A note about definitions:

  • Pulse refers to the regular, recurring sense of stress in music. Think of the way that you would tap your foot to a song; or when you can find your regular heartbeat; that's a pulse.
  • Beat refers to the duration of time from one pulse to the next. Let's say there is a song that goes along at a speed of 60 pulses per minute. In this case, each beat would last exactly 1 second, or 1/60 of a minute.

1.35 Time Signatures: Bottom Number

The bottom number tells us the type of note that is used to represent the duration of one beat. This duration depends on whether the meter is simple or compound.

In simple meters, the bottom number of the time signature corresponds to the type of note corresponding to a single beat. If a simple meter is notated such that each quarter note corresponds to the duration of one beat, the bottom number of the time signature is 4. If a simple meter is notated such that each half note corresponds to a beat, the bottom number of the time signature is 2. If a simple meter is notated such that each eighth note corresponds to a beat, the bottom number of the time signature is 8. And so on.

In compound meters, the bottom number of the time signature corresponds to the type of note corresponding to a single division of the beat.

If a compound meter is notated such that each eighth note corresponds to a single division of the beat, that means that each beat actually consists of three eighth notes, or, a dotted quarter note. Note that because in compound meter, each pulse or beat is divided into three equal parts, the actual beat is always three times as long as the division note that's indicated by the bottom number.

To review, for simple meters:

  • 2: a half note equals one beat.
  • 4: a quarter note equals one beat.
  • 8: an eighth note equals one beat.

For compound meters:

  • 2: a half note equals to one third of a beat. Hence, a dotted whole note equals one beat.
  • 4: a quarter note equals to one third of a beat. Hence, a dotted half note equals one beat.
  • 8: an eighth note equals to one third of a beat. Hence, a dotted quarter note equals one beat.

Take a look at this online lesson to review the difference between meter types.

Standard 1 (videos)