The different aspects of a melody
Some objects present a different aspect depending on the angle from which they are viewed. An upside-down ice cream cone looks like a triangle seen from the side, but like a circle seen from the top. The same melody may also be presented in various aspects, both in the World of Pitch (in its Mode, major or minor, diatonic or chromatic) and in the World of Time (in its Rhythm, binary, ternary, quinternary ...), which we will see here.

Transformations At Small Levels

Binary and Ternary Meters

Example
A well-known example of change of meter is the Mexican song La Cucaracha, originally conceived in 3/4 time, but which the rest of the world knows in 4/4 time with jazzy syncopations.

We will first examine the different possibilities
          of binary and ternary subdivision of the small levels
     and discover the different rhythmical aspects of the same melody.

Footsies
Don’t forget the Footsies for all the following musical examples,
because understanding them is one thing,
but feeling them is the most important thing.

Choice of note values
For the sake of consistency (in totally binary rhythm),
     each Beat (and Off-Beat) of Level 0 will always consist of the .
As we subdivide,
     each Beat (and Off-Beat) of Level -1 will consist of the ,
     each Beat (and Off-Beat) of Level -2 will consist of the ,
     each Beat (and Off-Beat) of Level -3 will consist of the ,
     each Beat (and Off-Beat) of Level -4 will consist of the .
The bar-lines will always be placed at Level -1, with bars in 4/4 (or 2/2) time.
     The bar-lines of Level 0 will be indicated solid, the others, at Level -1, dashed.

Let’s run through our list of 7 melodies.

1. Twinkle, Twinkle, Little Star

(a) The shortest notes of this song will be represented as s
     and bars would normally be expressed in 2/2 time.


(b) With only two notes in a bar (at Level -1) it is not possible to produce ternary subdivision
     which requires another level of subdivision (Level -2, with four s per bar).
However it is possible to produce ternary subdivision (grouping) using Level 0,
     both with Level -1, and with Level +1,
          which we will see in the following section (Transformations at Level 0).

2. Polly, Put The Kettle On

(a) The shortest notes of this song will be represented as s
     and bars would normally be expressed in 4/4 time.


(b) Discovering its aspect in 3/4 time would mean removing beat 2 from each bar.
     The logical way to do this without losing any material
          is to reduce by half all the values of beats 1 and 2
               (the first 2 notes of each 4/4 bar becoming s instead of s
                    the at the beginning of Bar 7 becomes a ).
Each bar in 3/4 time would be at what we call Level -2-1
     (a ternary fusion of Level -2 and Level -1).
Try this for yourself- the song will take on a Mazurka flavor.

Footsies
At the smallest level (ternary Level -2-1), the feet start R(ight), L(eft), T(ouch).
At the next level (binary Level 0), the feet start L as in the original binary aspect.

(c) Discovering its aspect in 6/8 time is not possible at the small levels
     because we would need subdivision at Level -3 to have the required s.

3. Red River Valley

(a) The shortest notes of this song will be represented as s
     and bars would normally be expressed in 4/4 time.


There are several possibilities here.

(b) Since a complete bar is made up of two identical parts of
     it is very tempting to start by discovering its aspect in 6/8 time
          by reducing by half all the values of beats 1 and 3 (the first and third s).
     giving the song a Waltz flavor
          with a meter quite similar to that of Mexican Hat Dance.

Footsies
At the smallest level (ternary Level -3-2), the feet start L-T-R.
At the next level (binary Level -1), the feet start R-L, with 2 notes pickup,
     as in the original binary aspect.

(c) However, nothing prevents us from discovering its aspect in 3/4 time
     by reducing by half all the values of beats 1 and 2 (the first and second s)
          (as we did for Polly Put The Kettle On).
     We are back to the Mazurka flavor.

Footsies
At the smallest level (binary Level -3), the feet start R-L, as in the original aspect.
At the next level (ternary Level -2-1), the feet start T-R-L.
At the next level (binary Level 0), the feet start L-R, with 2 notes pickup, as in the original aspect.

(d) It is now possible to find a fourth aspect
     by maintaining exactly the same note values of the 3/4 aspect (c),
     but by performing the melody in 6/8 time, with a binary Level -1 and a ternary Level -2-3,
          producing what are known as “hemioles” (3 in the time of 2).
     Without changing the note-values, the Mazurka flavor has been replaced by a more Spanish flavor.

Footsies
At the smallest level (ternary Level -3-2), the feet start L-T-R.
At the next level (binary Level -1), the feet start R-L, with 2 notes pick-up, as in the original aspect.
Don’t forget to sing the (c) 3/4 version again with a ternary footsie (T-R-L) at Level -2-1
     to really feel the difference.

This gives us 4 different aspects of the same song.
We will also find 4 different aspects in 5. Oh Where Is My Little Dog Gone ?

4. Rock-A-Bye, Baby

(a) The shortest notes of this song will be represented as s
     and bars would normally be expressed in 3/4 time.

Footsies
At the smallest level (ternary Level -2-1), the feet start R-L-T,
     as we already know.

There is only one possibility of transformation here.

(b) Bringing it to the fundamental, independent binary levels (Level -2 and Level -1)
     will imply doubling the note values of beat 1 of each bar of 3/4,
          the will become a , the will become a . and the . will become a .
     It will give the song a March flavor (in 4/4 time, probably 2/2).

Footsies
Try beating the 2 smallest binary levels (Level -2 and Level -1) at the same time
     with the feet starting R-T-L-T, which we already saw.
Don’t forget to sing the (a) 3/4 version again with a ternary footsie (R-L-T) at Level -2-1
     to really feel the difference, and notice that the left foot T has been removed.

(c) Since there are no s in Level -3 ,
     the 6/8 aspect is not applicable in the small levels.

5. Oh Where Is My Little Dog Gone?

(a) The shortest notes of this song will be represented as s
     and bars would normally be expressed in 6/8 time.

Footsies
At the smallest level (ternary Level -3-2), the feet start T-R-L.
At the next level (binary Level -1), the feet start R-L with 1 note pickup.
     as we already know.

Like song 3. Red River Valley, there are several possibilities here.

(b) The first is to bring it from its original 6/8 meter to the fundamental 4/4 meter
     by doubling the note values of the first and fourth s of each bar.
          We evidently have the March flavor.

Footsies
Try beating the 2 smallest binary levels (Level -3 and Level -2) at the same time
          with the feet starting T-R-T-L, which we already saw.
     Don’t forget to sing the (a) 3/4 version again with a ternary footsie (T-R-L) at Level -3-2
          to really feel the difference, and notice that the left foot T has been removed.
At the next level (Level -1), the feet start R-L with 1 note pickup, as in (a).

(c) Then we can discover its aspect in 3/4 time
     by reducing by half all the values of beats 1 and 2 (the first and second s)
          We have the Mazurka flavor.

Footsies
At the smallest level (binary Level -3), the feet start L-R.
     (There are not enough s notes to warrant Level -4)
At the next level (ternary Level -2-1), the feet start , R-L-T with 1 note pickup.
At the next level (binary Level 0), the feet start L-R with 1 note pickup
     as in the original aspect.

(d) Now we can maintain exactly the same note values of the 3/4 aspect,
     but perform the melody in 6/8 time, with a binary footsie (R-L) at Level -1,
          with the Spanish hemioles.

Footsies
At the smallest level (ternary Level -3-2), the feet start T-R-L.
At the next level (binary Level -1), the feet start R-L with 1 note pickup.
Don’t forget to sing the (c) 3/4 version again with a ternary footsie (R-L-T) at Level -2-1
     to really feel the difference. (Don’t forget the 1-note pickup)

This melody was also used as an example in the 4 Strong Modes.
With 4 aspects of modes and 4 aspects of meter,
we could have 16 aspects by crossing the modes and the meters.

6. Happy Birthday

(a) The shortest notes of this song will be represented as s
     and bars would normally be expressed in 3/4 time.

Footsies
At the smallest level (binary Level -3), the feet start R-L.
At the next level (ternary Level -2-1), the feet start T-R-L.
At the next level (binary Level 0), the feet start L-R with 2 notes pickup
     as we already know.

There is only one possibility of transformation here.

(b) Bringing it from its original 3/4 meter to the fundamental 4/4 meter
     by doubling the note values of beat 1 of each bar of 3/4.
          We evidently have the March flavor.

Footsies
At the smallest level (binary Level -3), the feet start R-L as in the original aspect.
Try beating the 2 next binary levels (Level -2 and Level -1) at the same time
     with the feet starting T-R-T-L.

(c) We cannot produce the 6/8 meter aspect in the small levels
     because we do not have a sufficient number of s.

7. Down In The Valley

(a) The shortest notes of this song will be represented as s
     and bars would normally be expressed in 9/16 time.

Footsies
At the smallest level (ternary Level -4-3), the feet start R-L-T.
At the next level (ternary Level -2-1), the feet start T-R-L.
     as we already know.

There is only one possibility here.

(b) Bringing it from its original 9/16 meter to the fundamental 4/4 meter by transforming
     - each group of 3 s on the third beat of each bar into 1 and 2 s,
     - each . on the first beat of each bar into a ,
     - each . on the second beat of each bar into a .
          We evidently have the March flavor.

Footsies
All the levels being binary, the footsies are quite simple here.

(c) We cannot produce the 6/8 meter aspect
     because we do not have a sufficient number of s.

Those on a Guided tour should click on in the Navigation Bar below.

Those browsing might wish to see the exercises for this section
and/or see what happens to ternary rythms at larger levels (-1 0, 0+1, +1+2)

Quinternary Meters

The 5/8 bar (2+3) is considerably more sophisticated than the 3/4 or 6/8 bars
     because 3 levels are fused together into Level -3-2-1
          rather than 2 levels as in the previous cases -
               Level -2-1for the 3/4 bars, and
               Level -3-2for the 6/8 bars,
     and very little music is written directly in this meter.
However, it is quite simple to transform music from 6/8 to 5/8
     by removing the second from each 6/8 bar.
          Here again, we would have the choice of removing whatever we find on this second
               or "squeezing" the material of the first 2 s down to half-size.
Let's see a few examples -

3. Red River Valley (5/8)

If we take the 6/8 version of Red River Valley
     and remove the second from each 6/8 bar

we get the Red River Limp 2 clip
     with relatively little loss if we remove the contents of the second
          so as not to interrupt the flow of s with the appearance of s.

5. Where, Oh Where, Is My Little Dog Gone ? (5/8)

If we take the original 6/8 version of Where, Oh Where, Is My Little Dog Gone ?
     and remove the second of each bar

we get a 5/8 version of the song
     with relatively little loss if we remove the contents of the second .

Those on a Guided tour should click on in the Navigation Bar below.

Those browsing might wish to see the exercises for this section
or see, for more on 5/8 time,
the Footsies, the Graphics, and the Melo-rthytm Boxes.
Back to Home