Matrices

There are 3 levels of execution in every ScalePlay composition. To accommodate this there are 2 grids or matrices and a huge chord slider. The following may be a bit difficult to grasp at first without the benefit of hearing it, but it will become clear enough very soon. Promise.

 

Phrase Matrix

So we start off with our leftmost matrix which is called the phrase matrix. This matrix is used to construct basic melodic elements and consists of ascending scale tones in the y direction and a time-based x axis. We can see the scale notes named in the y column as there are C, D, E and so forth. Time base in ScalePlay is relative and left up to the user. The bpm given in the tempo indicator makes its output eighth notes, but then one could construct a grid of 9x7 and easily play it into a 4/4 context. Dragging up or down in any column will sound the associated notes and also highlight these pitches in the current instrument (provided that they occur in the instrument’s range).

The interesting thing about the phrase matrix is that it can be made up of a pentatonic scale as shown or the chromatic scale on the other end of the spectrum. So an 8 x 8 grid can cover close to 2 octaves or not even one. That is something to keep in mind when working with ScalePlay.

 

Step Matrix

Next to the phrase matrix, on its right side, is ScalePlay’s step matrix. Now this is an easily confused term in a context of scales, but this naming seems the most natural. The step matrix is used to offset phrases in the phrase matrix by scale degree. That also happens over time. To illustrate let’s go back to the scale in thirds we mentioned earlier. The concept of it was to play all notes of a scale in succession, but instead of moving the to the next note after each note played right away, we first play the notes two steps up:

1, 3, 2, 4, 3, 5, 4, 6, 5, 7

If we were to consider 1, 3 to be a phrase then we could say that it was executed 5 times altogether and on these steps :

1, 2, 3, 4, 5.

1, 3, on step 1 = 1, 3
1, 3, on step 2 = 2, 4
1, 3, on step 3 = 3, 5 …

Now in itself there is nothing much fantastic happening as a result of all that. But imagine that we had a phrase like 1, 4, 2, 6, 3. If we had to calculate that over the same simple step pattern of 1, 2, 3, 4, 5 we might already be in trouble. If we were then to complicate matters further and use 4, 5, 2, 6, 3 as a step pattern instead things would become quite difficult.

So the important take-away here is that we are not shifting anything by a pre-determined interval (i.e. maj 2nd), but by degree of the scale of the moment. As ScalePlay cycles through its set of chords with assigned scales, the same pattern will be interpreted appropriately for each scale.

 

Line

The phrase matrix has one additional option called Line. Lines are set in the Song tab of the app's settings window and are drawn horizontally in the grid. ScalePlay has a line mode that allows to play only notes above or below this line. It makes for an interesting effect as demonstrated in some of the sample compositions.

 

Grid Sizes

Grid sizes are adjusted in the Song tab of the app's settings window. The default is 8x8 (phrase matrix) and 4x4 (step matrix). Phrase grids have a maximum setting of 32x32 and step grids a maximum of 12x32.

 

Observations

Having worked with ScalePlay for a while I have found that it is only a rare circumstance where maxing out these matrices makes any sense. In most cases musically relevant settings may be quite low. The example song Three has a 2x3 phrase matrix and an 11x6 step matrix. First of all that is an interesting choice because it is uneven when applied over a 4/4 meter for example. But it also stays in range for most instruments as with 3 (phrase rows) plus 6 (step rows) it is only a bit wider than an octave when applied on a heptatonic scale (7 notes). The chords in this piece start with C and have G as the highest chord root, so all in all the pattern covers around 2 octaves. And that is nice. 2 as well as 3 octaves are standard ways to practice scale patterns on most instruments.

 

In the Jaco sample song things are inverted when compared with the above. We have a 15x10 phrase matrix and a 2x2 step matrix. Its highest chord root is G again and it also starts on C. So if we do our range calculation again we end up with 10 (phrase rows) + 2 (step rows) + 7 semitones (C to G). We end up with 21 or just around 3 octaves with a heptatonic scale. Playable on most instruments.

One of the major purposes of the architecture we find in ScalePlay is to avoid huge grids. That helps understanding the relation to each other and progression of patterns best. It also ties in with the universal truth in music that notes that are closely together form a memorable shape. Something the listener can repeat. That is why so many children songs like "Mary Had a Little Lamb" and or even the "Ode to Joy" are entirely scale based just going from one note to the next. The wider we cast the intervals between notes the less gravitational pull is felt by the listener and even notes in the same scale obtain a certain atonal aspect if they are distant from each other. Of course that is sometimes what we want.

 

In the Poly sample song we have a 17x32 (phrase matrix) combined with a 9x3 (step matrix). Again we have an uneven rhythmic base configuration here when applied over a 4/4 meter. But the phrase grid itself it cast so widely that it makes no sense at all melodically. What happens instead is that the "gravitational pull" separates our construction into 2 entities - one below the phrase line and one above. And no matter which instrument we assign to this pattern - it maintains a percussive quality. That is much enhanced by the repetition in the bottom part and the wide intervals in the top part. And that is really how music is perceived and works. When a flute and a double bass play consecutive scale tones in their perspective ranges we hear two separate melodies because only notes that are scale adjacent are perceived as lines. The pitch of notes becomes less and less important the further they are apart, because they don't relate to each other any more. That fact is often used in so-called atonal music where two melodies are played in different registers and in different keys. And the listener is not even aware that one of the major concepts in music - that of the key of the piece - was in essence obliterated.

 

Summary

So those are our two matrices - a phrase matrix and a step matrix. And they are assigned a scale. ScalePlay knows over 200 different scale types and it would be a bit boring to play the same scale over and over even with these magnificent patterns we can make. That’s where the big chord slider comes in. It serves as the encompassing harmonic construct in which we play our scales and also serves as a manner of organizing our scale choices. When we hit the play button in ScalePlay it plays one chord after the other. Each chord plays all steps defined for the phrase we drew in our phrase matrix.

Astonishingly enough if we take another look at some of the classical études that so many students play every day we will find that composers have applied the same kind of logic we did above to construct them. Of course with ScalePlay we can construct much more complex patterns if we wanted to :]

Now let's take a look at how drawing works in these matrices.