We have paid great attention to the pull of harmonic and tonal centers and have beat voice leading over the head with a stick but another element crucial to our discussions of contemporary music theory is the metric structure of music.

Metric Structure = The combined implementation of Meter & Tempo & Rhythm

Meter

1. Meter = a measure of stressed and unstressed pulses or "beats" with a fixed amount of time (a measure) and a given tempo.

a. The written expression of meter is a time signature
b. Meter has no rhythm of its own.
c. Most often expressed as the underlying pulse of a time signature
d. Time signature indicates how many pulses (top) and what kind of beat is the pulse (bottom)
e. The most basic rhythms contiain pulses that conincide with the metric points dictated by the time signature.

2. Compound Meter = a time signature or meter in which each measure is divided into multiple parts, calling for the measures to be played with principal and subordinate metric accents (the latter called subaccents)

a A compound time signature is written to better describe an irregular pulse
b. Below the first two measures of Brick Impromptu Chapter 8 were conceived not as two bars but 1 bar with 13 eigth notes



c. The metrical accents of the above example are best described as follows

c. A slight shift in the metrical accent creates a different compound meter with the same number of beats

In class assignment create various compound meters from 10/8.

 

3. Asymmetrical Meter = A meter which carries a regular pattern of uneven pulses that deviates from a possible regular pulse

a. Asymmetrical Meters often show the standard, even pulse meter with a compound meter in parenthesis.
b. A very standard common time (4/4) shows every pulse with a staccato left hand.

c. In an asymmetrical meter we get The same common time signature shown with an irregular pattern of pulses. (it is common to show the division of the pulse with a compound time signature in parenthesis)

In class assignment create various asymmetrical meters from 6/4.

 

 

4. Polymeter = The simultaneous use of two Meters

a. "tactus-preserving polymeter." = multiple simultaneous meters all occur within the same pulse (measure divisions vary)



b. "measure preserving polymeter"= multiple simultaneous meters all occur within the same measured time frame (pulse varies)

 

In class assignment Attempt to perform both examples above ;-)

 

5. Irrational Meter = time signatures which have a denominator which is not a power of two (1, 2, 4, 8, 16, 32, etc.)

a. used to express the division of a whole note into equal parts (just as ordinary signatures do)

b. Can be confusing to players not familiar with contemporary techniques.
c. Metric Modulation is better.

6. Metric Modulation = a change (modulation) from one temporal value (time signature/tempo/meter) to another, wherein a note value from the first is made equivalent to a note value in the second

a. Essentially exactly the same as an irrational meter just stated in a more common manner that shows:
b. There exists an exact relationship between two different temporal values that is created by a common note value called a metric pivot
c. A common pulse must exist between these two temporal values
d. The name and function of the pulse changes.


e. To determine the new tempo use the formula: (or goto http://www.thenewstyle.org/calculator/calculator.html)

New Tempi --------------- Old Tempi	=	# of Pivots in Old measure ----------------------------------- # of Pivots in New measure

1. From previous example: The new tempi = 135

New Tempi --------------- 90	=	6 ----------------------------------- 4

f. Most common. however is not a change in tempo, but rather an indication of the metric equivalence.

 

 

Homework: Assignment 1: Due next class 1. Write a short passage (between single and double period) for Pizz string ensemble and Clarint in Phrygian mode with a key center of C. Somewhere in the middle of the passage create a metric modulation. Realize your composition with Garritan and submit your score and mp3 Note: Finale has a very difficult time understanding metric modulation. Determine the new tempo equivalence of the metric modulation and, using the midi tool, create the new tempo in the modulated measures. hmu415@gmail.com

7. Hypermeasure = a metric unit in which, generally, each regular measure is one beat (actually hyperbeat) of a larger meter.

8. Hyperbeat = a single measure (actually hyperbeat) of a larger hypermeasure.

Rhythm

One of the preeminant contemporary composers who explored new rhythmic possabilities was Oliver Messiaen . Much of our discussion of contemporary rhythmic techniques can be attributed to Messiaen and there is a very good primer that considers his thoughts on rythm here: http://www.oliviermessiaen.net/musical-language/rhythmic-language

1. Rhythmic Displacement = A shift of a rhythm or rhythmic phrase by a consistant rhythmic value

2. Rhythmic Cannon = a contrapuntal device that employs a rhythmic phrase with one or more imitations of the rhythmic phrase played after a given rhythmic displacement.


3. Rhythmic Retrograde = Like a melodic retrograde, this is simply a rhythm or rhythmic phrase played backwards.

4. Rhythmic Inversion = A given notes durational value is inverted around the underlying rhythmic value of the pulse. For example in 4/4 with a quarter note pulse, the rhythmic inversion of an Eigth note (1/2 the value of the pulse) is a half note (twice the value of the pulse). The rhythmic inversion of a 16th note (1/4 the value of the pulse) is a whole note (4 times the pulse) (Please note that this is a technique I derived without previous reference. Proceed with caution when discussing the concept as some will not be immediately aware of such a notion.


5. Additive Rhythm = Like a Rhythmic Displacement except the shift is created by adding a durational value to a pre-existing note in the rhythmic phrase.


6. Rhythmic Augmentation = a multiplying of a rhythmic value by some constant.


7. Rhythmic Diminution = a division of a rhythmic value by some constant.

8. Isorhythm = one or more voices of changing notes adheres to a single rhythmic pattern. (does not require a repeat of pitch)

9. Isomelos = rhythm is free but contains a repeated melodic pattern.

10. Polyrhythm = two or more rhythmic phrases of unequal length occuring simultaneously (may repeat)

 

In class assignment Analyze Dog Fight World War 2 MP3

Homework: Assignment 2: Due next class 1. Write a short rhythmic passage for triangle and snare drum. From that passage create the following derivations: Rhythmic Retrograde,Rhythmic Inversion, Additive Rhythm, Rhythmic Augmentation, Rhythmic Diminution. Realize your composition with Garritan and submit your score and mp3 Homework: Assignment 3: Due next class 2a Write a short melody for Tuba that demonstrates an Isorhythm. 2b. Write a short melody for English Horn that demonstrats an Isomelos 3. Create a string accompanyment to 2a or 2b above that is polyrhythmic against the melody. Realize your composition with Garritan and submit your score and mp3 hmu415@gmail.com