Let's also look at an actual waltz, just to establish the feeling in our ears. This is a recording of the so-called "Minute Waltz" by Chopin. I include here just the opening melody, after the four-bar introduction. But go ahead and listen to the entire piece (it actually takes closer to two minutes to play expressively).

6/8 time

6/8 time is a combination of a triple feeling with a duple pulse -- thus it is considered a compound meter. If you look at the second measure, you'll notice the two groupings of three eighth notes. This is the essence of 6/8 time. So too are the measures that contain a quarter followed by an eighth. This long-short, long-short rhythm is also indicative of 6/8 time and is reflected in many dances that use this time signature. This chant is a perfect expression of the essence of this meter. After a number of repetitions, you'll notice the women begin to sing in very "open" harmonies. The sound of these open harmonies is something we will explore soon.

Sometimes, however, 6/8 time can be given an assymetrical rhythm, usually associated with folk or non-Western traditions. A famous variant of 6/8 time is to alternate between feelings of 6/8 and 3/4, since both meters contain the same number of eighth notes (6). Leonard Bernstein made this famous in the song America from the great Broadway musical West Side Story (which was heavily influenced by salsa rhythms and modal scales). Here, setting the phrase "I like to be in America", the "I like to be in A-" is set to six eighth notes in 6/8 time, but the "-mer-i-ca" is set to three steady quarter notes, as if it were 3/4 time. The meter doesn't change, the sheet music reads 6/8 throughout, but the shift to the 3/4 feeling is wonderfully infectious:

Here's the main chorus of the song:

5/4 time

This time signature, while once considered rare and exotic, like an orchid amongs daisies, has become more commonplace these days. It is best known by the jazz standard "Take Five", which is in 5/4. The essence of 5/4 is the combination of 3/4 and 2/4 into one measure. Conceptually, we count it as 1-2-3 / 4-5. In this charming Libana chant, (composed by one of their members, not a traditional tune), you can see the grouping of three quarters followed by two quarters ("Under the // full moon"). This tune is made more interesting by the syncopated feeling in the first part of bars 2, 3 and 4. Rather than three simple quarter notes, you get a pattern of quarter-eighth-quarter, with the last quarter getting the dot to extend it out the full length of the three quarter note pattern. This is followed in each instance by straight rhythms on the 4th and 5th beats of the bar, either two quarters or two eights plus a quarter. Listen to this tune until you get a strong sense of the feeling of 5/4. Hurray for assymmetrical rhythms!

Here's the main melody (the "head") of Paul Desmond's Take Five, to give you another sense of this great assymmetric rhythm:

9/8 and 12/8 time

9/8 time is very similar to 6/8, in that you have a triple division of the beat, but the actual number of beats in the measure feels like a division of three (also a "compound time"). Thus, 6/8 feels like 2/4 with each beat receiving a pulse of three eighth notes (you could think of it as 2/dotted quarter time). Similarly, 9/8 time feels like 3/4, only each beat is subdivided by three. The basic feeling is either three groups of three eighth notes, or the lilting long-short rhythm:

12/8 time is just another extension of the same idea. We think of it as being four beats to the measure, but every beat receives three eighth notes, as opposed to the 2 eighth notes that would be expected in 4/4 time. One example of this meter is the opening of the Pastoral interlude in Handel's Messiah, which depicts the shepherds in the fields. This is a commonplace rhythm, when played at a stately tempo, for pastoral scenes. The main melody runs something like:

I should also mention that sometimes 9/8 time can be grouped assymmetrically. This is common in middle eastern music. Dave Brubeck created a famous example of this on the late 50's jazz album Time Out (the same album that has Take Five.) Here, instead of grouping 9/8 as 3+3+3, he groups it as 2+2+2+3. The basic right hand rhythm on the piano looks like this:

The tune is called Blue Ronda ala Turk, after the Turkish influence on the rhythm. (It's also a play on Mozart's Rondo ala Turk from the A major piano sonata). You'll notice that every fourth bar switches back to the standard grouping of 3+3+3. The opening section of the piece is a continuing variation on this four-bar rhythm. Check it out:

7/8 and 7/4 time

The last metrical scheme to discuss is measures group in either 7 eighth notes or 7 quarter notes. I can't think of a standard that is in 7/8 time, but you could imagine such a melody, grouped normally in a pattern of 4+ 3 or 3+4. Let's make one up that has two measures grouped 4+3, followed by two measures groupd 3+4.

One famous rock song has an opening bass line and verse in 7/4: Pink Floyd's "Money." It opens with the sounds of cash registers and clinking coins, moving into this great bass riff:

Here's the opening:

Rhythmic patterns of 7 are also rather common in Indian raga music, where the rhythm continually cycles back to the beginning every 7 beats. Here is an excerpt from an Indian raga. Can you hear the cycle of 7? It begins exactly at the moment when the voice comes in strongly, starting on the syllable "Jai", and then cycle of seven beats carry on for the duration of the track (the full performance is 9 minutes long.) You might also be able to hear the tabla drum play strong accents every seven beats. The singer sings a recurring 7-beat tune, in between which he is improvising within the notes of the raga. We'll be learning a lot more about Indian music in the coming weeks.

Triplets and Duplets

Of course, the existence of duple and triple meters does not preclude the use of the triple feeling in duple time or the duple feeling in triple time. This is done by grouping notes into triplets or duplets, depending on the context. Here's an invented phrase in 4/4 time that uses triplets, switching into a phrase in 6/8 that uses duplets. The main idea here is that the beat does not change, all that switches is whether the beat gets divided by 2 or by 3. This switching between duples and triples is of course an important compositional device for rhythmic contrast and interest.

Cross rhythms (three against two)

Finally, it is not at all uncommon for different instruments in an ensemble to be playing two different metrical feelings at the same time. Most often, this is a triplet against a duplet. A very clear example of this is Debussy's Arabesque No. 1, where the left hand keeps a steady eighth note pulse while the right hand plays triplets over it.

Mixed Meters

Lastly, much great music, especially classical music composed in the 20th Century, alternates sometimes wildly between various meters. The Russian composer Igor Stravinsky made this technique quite famous, and genrally pioneered its use. In this style you will often see time signatures such as 3/8 or 7/16 or 5/8 or other quick divisions in fast moving tempi that continually give an assymmetrical feeling to the music. Part of Stravinsky's inspiration for this approach to rhythm came from cubist painting, with its (i.e. Picasso's) tendency to paint familiar forms, such as faces, in assymetrical views. We will look at one of these pieces during class.

Next: 1E Pentatonic Scales