Music theory can be a complex subject, but one concept that is essential to understand is the matrix. A matrix is a tool used in music theory to organize information about musical intervals and chords.

In order to fill out a matrix, you must first understand the basics of musical intervals and chords. An interval is the distance between two notes, while a chord is a group of three or more notes played together.

To begin filling out a matrix, you will need to create columns and rows. The columns will represent the notes of the scale, while the rows will represent the intervals between those notes. For example, if you are working with the C major scale, your columns would be labeled C, D, E, F, G, A, and B.

Next, you will need to label your rows based on the interval between each note. The most common intervals used in music theory are unison (the same note), second (one note apart), third (two notes apart), fourth (three notes apart), fifth (four notes apart), sixth (five notes apart), seventh (six notes apart), and octave (eight notes apart).

Once you have labeled your rows and columns, it’s time to start filling in the matrix. Begin by placing a “1” in each box where the row interval matches the actual interval between the two notes.

For example, in our C major scale matrix, we would place a “1” in the box where C and C meet for unison because they are both the same note. We would also place a “1” in the box where C and D meet for second because they are one note apart.

Next, you will need to fill in all of the other boxes based on their corresponding intervals. To do this, you can use simple addition or subtraction to determine how many half-steps there are between each note. For example, to find the interval between C and E, you would count up four half-steps (C to C#, C# to D, D to D#, and D# to E), so you would place a “3” in the box where C and E meet for third.

Finally, you can use your completed matrix to determine the chords that can be built from each note in the scale. To do this, simply look at the rows of each note and find all of the boxes with a “1” in them.

These are the intervals that make up a major chord. For example, in our C major scale matrix, we would see that the notes C, F, and G all have boxes with “1”s in them for unison, fourth, and fifth intervals. This means that these notes can be used to build major chords.

In conclusion, filling out a matrix is an important skill for any musician learning music theory. By understanding intervals and using simple addition or subtraction, you can create a tool that will help you understand chord structures and progressions. So grab your pen and paper or open up your favorite music notation software and start filling out your own musical matrix today!