Suggested Learning Resources

1) YFIO

2) Video Lesson: Modular 12 Arithmetic Video, Maths with Jay Channel https://youtu.be/OlLns9fkMtk

3) Online Reading: Modular 12 Arithmetic , Open Music Theory http://openmusictheory.com/mod12.html

4) Interactive Lesson: 

Music Theory QuickThink:

- mod12 arithmetic works similar when converting military time to standard time

- For our purposes, mod12 involves using no negative numbers, and the results of any calculations is a number between 0 and 11

- If the resulting value is larger than 11, subtract 12 to apply the mod12 arithmetic (Example 7+8 = 15 , using mod12 the resulting value is 3.)

- If the resulting value is a negative number, add 12 to apply the mod12 arithmetic (Example 7-8 = -1 , using mod 12 the resulting value is 11.)  An alternative way is to add 12 to the smaller value prior to doing the subtraction. 7-8 becomes 19-8 = 11.

Objective 47.1: Examples in Music: YouTube

https://youtu.be/Jwj7avIYzbo

Objective 47.1: Calculate addition and subtraction using mod12 arithmetic