The process of counting time requires two basic operations:
- addition of time: the passing of time as the shifting from unit to unit following a constant increment (pulse to pulse, beat to beat, measure to measure, etc.)
- division of time: to place an event on a given sub-division of a unit (measure, beat, pulse).
Tempo Marks
Before the invention of the metronome in the early 1800's composers described the overall rate of events in a given piece, what musicians call tempo (Italian: time), with word association, linking musical time to human emotional and kinestetic experiences. Such references included, for example, describing the rate of articulations as similar to a walking pace (Andante) or, asking for a joyful musical character, or cheerful emotional state with a fast tempo (Allegro or Molto Allegro).
After the metronome's invention, words continued to be used to describe tempo, but now often combined with metronome marks. In some instances, expressive marks are used in lieu of tempo markings, and in other cases, tempo is described by the BPM mark alone.
After the metronome's invention, words continued to be used to describe tempo, but now often combined with metronome marks. In some instances, expressive marks are used in lieu of tempo markings, and in other cases, tempo is described by the BPM mark alone.
Pulse
A minimal temporal unit of musical time, a pulse is perceived as the shortest most common duration underlying the time-grid for a given sequence of events.
Although hierarchically beat descends from meter, and pulse from the ongoing beat-unit, pulse remains a contextual parameter, changing with the rhythmic profile of the stream of events.
Therefore, the perceived duration of a pulse has an equal or smaller (but not larger) value than the perceived beat-unit itself.
Although hierarchically beat descends from meter, and pulse from the ongoing beat-unit, pulse remains a contextual parameter, changing with the rhythmic profile of the stream of events.
Therefore, the perceived duration of a pulse has an equal or smaller (but not larger) value than the perceived beat-unit itself.
Polyrhythms
The minimal requirement for polyrhythmia is the concurrent presence of at least two perceived different rates of beat sub-division which can not be not multiple of each-other.
Metronome Marks
A metronome is a chronometric (i.e., a time measuring) device designed to perform two main functions: to signal the passing of each unit of time with a clicking sound, and to mathematically scale time.
Contrary to the functioning of a regular clock which invariably outputs 60 seconds per minute, the metronome's mechanism assumes that rate of units, not as a constant, but rather as a user assigned variable. By choosing a different rate than the referential 60 seconds per minute, the user is in effect scaling time.
Contrary to the functioning of a regular clock which invariably outputs 60 seconds per minute, the metronome's mechanism assumes that rate of units, not as a constant, but rather as a user assigned variable. By choosing a different rate than the referential 60 seconds per minute, the user is in effect scaling time.
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| Beethoven conducting. |
It took just a few years after its commercial release for the metronome to become a referential instrument among musicians. By 1817, Beethoven was using a metronome model by Johann Mälzel (1772–1838) and, for the first time, documented metronome marks as means to define tempo in his works.
Mälzel's metronome featured a clockwork mechanism inside a pyramid-shaped wooden box. Outside the box, a metal weight on a calibrated pendulum rod. While the pendulum swinged back and forth at a constant rate (the lower the weight, the faster the pendulum swings, and vice versa), the inside mechanism produced a clicking sound, ear-marking each oscillation. Adjusting the rate of clicks per second was done by simply sliding the weight up or down the pendulum. The pendulum rod came preset with a finite number of metronome marks, leaving the desired rate as a choice of one from a logarithmic scale of pre-defined tempo rates. On mechanical metronomes, tempo marks range between a rate of 40 to 208 units per minute. With the advent of digital instruments, any positive integer or floating point number can be used to scale time.
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| Mälzel's Metronome |
Defining a metronome mark requires a minimum of two parameters: a time-unit (typically represented by a note-value), and a number for the respective rate of time-units per minute (a.k.a., Beats Per Minute - BPM). Other standard representations of metronome marks include using the equal sign " = " between the two parameters above, and less frequently, to have metronome marks proceeded by the initials MM, for Mälzel's Metronome.
Tuplets
A tuplet (also irrational rhythm) specifies a change in the number of expected subdivisions for a given pulse as set forth by the type of meter (simple or compound). For example, in a 2/4, a simple binary meter, time is subdivided in multiples of two, and so, the quarter note (the beat unit in 2/4 ) is expected to subdivide in two eighth notes. A tuplet of three eighth notes (triplet) changes the number of subdivisions, allowing to specifically represent the moment when the reference beat sub-division becomes three eighth notes instead of two expected in a simple meter (figure 7a); in a 3/8 meter (simple ternary), the eighth note (beat unit) is expected to subdivide in two 16th notes and four 32th notes.
A tuplet of five 32th notes (quintuplet) indicates that the number of subdivisions has been changed from four to five 32th notes (figure 7b); in a 6/16 meter (compound binary), the dotted eighth note (beat unit) is expected to subdivide in three 16th notes, each 16th note in four 64th notes. A tuplet of five 64th notes (quintuplet) subdivides the time of a 16th note in five 64th notes rather than the regular subdivision by four (figure 7c). Tuplets can also call for a number of subdivisions that is smaller than what is expected. In figure 7d, the beat unit of a 9/8 (dotted quarter note) subdivides in three eighth notes. The duplet of eighth notes is to be played in the time of the three eighth notes that originally divided the beat unit.
A tuplet of five 32th notes (quintuplet) indicates that the number of subdivisions has been changed from four to five 32th notes (figure 7b); in a 6/16 meter (compound binary), the dotted eighth note (beat unit) is expected to subdivide in three 16th notes, each 16th note in four 64th notes. A tuplet of five 64th notes (quintuplet) subdivides the time of a 16th note in five 64th notes rather than the regular subdivision by four (figure 7c). Tuplets can also call for a number of subdivisions that is smaller than what is expected. In figure 7d, the beat unit of a 9/8 (dotted quarter note) subdivides in three eighth notes. The duplet of eighth notes is to be played in the time of the three eighth notes that originally divided the beat unit.
Irregular Meters
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| Irregular Meters in Music |
Irregular Meters
Irregular meters (also called asymmetrical meters) establish a regular metric pattern from an asymmetrical sequence of two or more time signatures. A 5/8 time signature, for example, is usually understood as the sum of two simple meters 3/8 + 2/8 or 2/8 + 3/8. Beat hierarchy in irregular meters, just like in regular meters, is either simple (diving in two equal parts) or compound (diving in three equal parts). The time signature of 15/16, however, corresponds to the compound meter relative of 5/8. Compound meters include only those time signatures whose numerator is a multiple of three (figure 6).
Used frequently by different folk traditions across the globe, the use of asymmetrical meters is often associated as a stylistic trait of Balkan music, in Southeast Europe. In classical music asymmetrical meters are used sporadically before the twentieth century. The second movement of Tchaikovsky's Sixth Symphony (1891-93) is commonly referenced as one of the first examples of orchestral music written entirely in an asymmetrical meter (5/4).
Irregular meter can be seen represented in different ways. Hungarian composer Bela Bartok (1841-1945), for instance, wrote Six Dances in Bulgarian Rhythm using time signatures, exposing the respective addends, such as, 4+2+3/8, 2+2+3/8, 3+2+3/8 (also called a 4/4 unevenly grouped), 2+2+2+3/8.
Meters and Beat Hierarchy
Meter determines the number of beats per measure and the type of beat subdivision. There are two types of beat hierarchy: simple and compound.
Simple meters have a binary hierarchy, that is, the unit of time is sub-divided in multiples of two -subdivision of the beat in two equal parts.
Compound meters follow a termany subdivision -subdivision of the beat in three equal parts.
Any time signature whose numerator is a multiple of three (i.e., 6, 9, 12, etc.) symbolizes a compound meter, otherwise, it represents a simple meter. In simple time, a binary is represented with time signatures whose numerator is 2, the ternary with 3 and the quaternary with 4.
The process to find the corresponding compound version of a simple meter is done by multiplying the numerator of the given time signature times three (the number of beat subdivisions) and the denominator times two. The compound meter that corresponds to, for example, a 2/4 meter is found by:
multiplying the given numerator by three, that is, 2 * 3 = 6
multiplying the denominator by two, that is, 4 * 2 = 8 .
The simple meter that corresponds to a 6/8 is found by the inverse operation in which the numerator is divided by three and the denominator is divided by 2. Figures 5a, 5b, and 5c illustrate the correspondence between, respectively, binary, ternary and quaternary meters, presented side by side in their simple and compound beat subdivisions.
Figure 5a, for example, shows, on the left side, a binary simple meter identified by a 2/4 time signature and, on the right side, a 6/8 time signature corresponding to the respective compound version. The bottom staff in figure 5a illustrates how the beat unit is subdivided differently in two or three parts for, respectively, simple and compound meters.
Simple meters have a binary hierarchy, that is, the unit of time is sub-divided in multiples of two -subdivision of the beat in two equal parts.
Compound meters follow a termany subdivision -subdivision of the beat in three equal parts.
Any time signature whose numerator is a multiple of three (i.e., 6, 9, 12, etc.) symbolizes a compound meter, otherwise, it represents a simple meter. In simple time, a binary is represented with time signatures whose numerator is 2, the ternary with 3 and the quaternary with 4.
The process to find the corresponding compound version of a simple meter is done by multiplying the numerator of the given time signature times three (the number of beat subdivisions) and the denominator times two. The compound meter that corresponds to, for example, a 2/4 meter is found by:
multiplying the given numerator by three, that is, 2 * 3 = 6
multiplying the denominator by two, that is, 4 * 2 = 8 .
The simple meter that corresponds to a 6/8 is found by the inverse operation in which the numerator is divided by three and the denominator is divided by 2. Figures 5a, 5b, and 5c illustrate the correspondence between, respectively, binary, ternary and quaternary meters, presented side by side in their simple and compound beat subdivisions.
Figure 5a, for example, shows, on the left side, a binary simple meter identified by a 2/4 time signature and, on the right side, a 6/8 time signature corresponding to the respective compound version. The bottom staff in figure 5a illustrates how the beat unit is subdivided differently in two or three parts for, respectively, simple and compound meters.
Time Signatures
The symbol of a time signature indicates the meter of a piece. In modern notation, it is typically represented by two numbers vertically aligned. The bottom number (denominator) stands for the unit of measurement, that is, the note value representing the beat-unit; the top number (numerator) indicates the metrical unit as the number of units per measure. To sum up, a time signature expresses the number of beats in a measure versus the type of beat-unit.
In a time signature, the number as denominator represents one specific note-value as the beat-unit. And the numbers that can be used are limited to 1, 2, 4, 8, 16, 32, 64. Why these and not any others? Because they represent the proportional relations between all note values. Since the whole note is the largest and therefore the referential value it gets to be represented by 1. The value of one whole note equals to two half notes, hence 2 representing the half-note, four quarter notes are equal to the duration of one whole-note, then the quarter-note is represented by 4, and so on.
Examples of Time Signatures - What does 4 4 time mean?
A time signature 4 / 4 means that:
A time signature 3 / 4 means that:
A time signature 3 / 2 means that:
A time signature 8 / 8 means that:
Time Signature Change
A time signature is graphically positioned in the beginning of a movement at the right of the clef and key signature. During the course of a composition, to indicate a change in meter, the new meter appears at the right side that closes the previous measure.
Alla Breve
Some specific time signatures may be written differently with icons without the use of numerical ratios, as C instead of 4/4, and C in the place of 2/2 (also called alla breve, also known as cut-time or half-time).
In a time signature, the number as denominator represents one specific note-value as the beat-unit. And the numbers that can be used are limited to 1, 2, 4, 8, 16, 32, 64. Why these and not any others? Because they represent the proportional relations between all note values. Since the whole note is the largest and therefore the referential value it gets to be represented by 1. The value of one whole note equals to two half notes, hence 2 representing the half-note, four quarter notes are equal to the duration of one whole-note, then the quarter-note is represented by 4, and so on.
Examples of Time Signatures - What does 4 4 time mean?
A time signature 4 / 4 means that:
- the beat-unit equals to a quarter note (denominator)
- each measure has a time-length equal to four quarter notes (numerator).
A time signature 3 / 4 means that:
- the beat-unit equals to a quarter note (denominator)
- each measure has a length equal to the combined duration of three quarter notes (numerator).
A time signature 3 / 2 means that:
- the beat-unit equals to a half-note (denominator)
- each measure has a time-length equal to three half-notes (numerator).
A time signature 8 / 8 means that:
- the beat-unit equals to an eighth note (denominator)
- each measure has a total time-length equal to eight eighth-notes (numerator).
Time Signature Change
A time signature is graphically positioned in the beginning of a movement at the right of the clef and key signature. During the course of a composition, to indicate a change in meter, the new meter appears at the right side that closes the previous measure.
Alla Breve
Some specific time signatures may be written differently with icons without the use of numerical ratios, as C instead of 4/4, and C in the place of 2/2 (also called alla breve, also known as cut-time or half-time).
Augmentation Dot: Altering Note-Values
Note-values can acquire additional value with the use of the augmentation dot and a tie.
The augmentation dot expands a note value to which is applied (i.e., the dotted note) by adding it half of its own value. A dotted whole note, for example, equals the value of one whole note plus one half note (figure 4a); a dotted half note equals the value of one half note plus one quarter note (figure 4b); a dotted quarter note equals the value of one quarter note plus an eighth note (figure 4c), and so on.
The augmentation dot is placed immediately to the right of the respective note head. When the note head appears written on a staff line, the augmentation should be placed on the right in the space above the respective staff line.
A tie joins two consecutive note values sharing the same tone into one (figure 4d). The symbol of a tie is placed in between the two note-heads that unites. The use of ties is restricted no note-values and are never employed between rests. To join more than two consecutive note values more ties must be used accordingly, one in between each two consecutive note values (figure 4e).
In certain cases, the use of a tie equals and can interchange with the augmentation dot (figure 4f).
Augmentation dots and ties can be used simultaneously.
The augmentation dot expands a note value to which is applied (i.e., the dotted note) by adding it half of its own value. A dotted whole note, for example, equals the value of one whole note plus one half note (figure 4a); a dotted half note equals the value of one half note plus one quarter note (figure 4b); a dotted quarter note equals the value of one quarter note plus an eighth note (figure 4c), and so on.
The augmentation dot is placed immediately to the right of the respective note head. When the note head appears written on a staff line, the augmentation should be placed on the right in the space above the respective staff line.
A tie joins two consecutive note values sharing the same tone into one (figure 4d). The symbol of a tie is placed in between the two note-heads that unites. The use of ties is restricted no note-values and are never employed between rests. To join more than two consecutive note values more ties must be used accordingly, one in between each two consecutive note values (figure 4e).
In certain cases, the use of a tie equals and can interchange with the augmentation dot (figure 4f).
Augmentation dots and ties can be used simultaneously.
Notation of Rests
For clarity, the representation of rests follows the following conventions.
whole note rest: on a five-line staff, the whole note rest should be just beneath the fourth line (figure 3a); when writing on a one-line staff (as used for some percussion instruments), it should appear below that line.
half note rest: on a five-line staff, the whole note rest should be just above the third line (figure 3a); when writing on a one-line staff, it should appear above that line.
the quarter note rest centered on the staff, confining the representing shape between the first and the fourth spaces (figure 3c).
the eighth note rest between the second and fourth lines, with the “hook” of the symbol on the third space (figure 3d).
the 16th note rest between the first and fourth lines, with the top “hook” on the third space, and the remaining “hook” in the space immediately below (figure 3e).
the 32th note rest between the first and fifth lines, with the symbol's top “hook” on the fourth space, and each of the remaining “hooks” on each of the spaces immediately below (figure 3f).
the 64th note rest between one space bellow the first line and the fifth lines, with the top “hook” of the icon on the fourth space, and each of the remaining “hooks” on each of the spaces immediately below (figure 3g).
whole note rest: on a five-line staff, the whole note rest should be just beneath the fourth line (figure 3a); when writing on a one-line staff (as used for some percussion instruments), it should appear below that line.
half note rest: on a five-line staff, the whole note rest should be just above the third line (figure 3a); when writing on a one-line staff, it should appear above that line.
the quarter note rest centered on the staff, confining the representing shape between the first and the fourth spaces (figure 3c).
the eighth note rest between the second and fourth lines, with the “hook” of the symbol on the third space (figure 3d).
the 16th note rest between the first and fourth lines, with the top “hook” on the third space, and the remaining “hook” in the space immediately below (figure 3e).
the 32th note rest between the first and fifth lines, with the symbol's top “hook” on the fourth space, and each of the remaining “hooks” on each of the spaces immediately below (figure 3f).
the 64th note rest between one space bellow the first line and the fifth lines, with the top “hook” of the icon on the fourth space, and each of the remaining “hooks” on each of the spaces immediately below (figure 3g).
Note Values: Equivalence
The equivalence between the different note values is arranged proportionally. A constant duple relationship applies to all note values, where each note value corresponds to half the value of the next larger and twice the value of the next smaller (figure 2).
Observing this principle, the quarter note, for example, has twice the value of one eighth note (the next smaller) and half the value of one half note (next larger); the eighth note, has twice the value of one 16th note (the next smaller) and half of one quarter note (next larger); and so on.
Figure 2 shows the equivalence between all note values in relation to the whole note, the largest note value: one whole note equals to two half notes, four quarter-notes, eight eighth notes, sixteen 16th notes, thirty-two 32th notes, and sixty-four 64th notes.
Observing this principle, the quarter note, for example, has twice the value of one eighth note (the next smaller) and half the value of one half note (next larger); the eighth note, has twice the value of one 16th note (the next smaller) and half of one quarter note (next larger); and so on.
Figure 2 shows the equivalence between all note values in relation to the whole note, the largest note value: one whole note equals to two half notes, four quarter-notes, eight eighth notes, sixteen 16th notes, thirty-two 32th notes, and sixty-four 64th notes.
Note Values
A note value represents the duration of a sound or a rest (silence). Each note value has two corresponding symbols, one that implies the production of sound (fig. 1, left column), and one for rest (fig. 1, right column).
From largest to smallest, the most commonly used note values are:
From largest to smallest, the most commonly used note values are:
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