Music Production Math

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1. A sound wave has a frequency of 440 Hz. If you play the note one octave higher, the frequency doubles. What is the new frequency?
2. An interval is a major third if the ratio of the higher frequency to the lower frequency is 5:4. If the lower note is 200 Hz, what is the frequency of the note a major third above it?
3. The frequency of a note can be calculated using f = 440 × 2^(n/12), where n is the number of semitones from A4 (440 Hz). How many semitones above A4 is a note with a frequency of 880 Hz?
4. If you move up a perfect fifth (ratio 3:2) and then down a perfect fourth (ratio 4:3) from 400 Hz, what is the final frequency?
5. If a 4/4 time signature bar contains four quarter notes, how many eighth notes are needed to fill the same duration?
6. A producer is sequencing a drum pattern. If a beat is divided into 4 sixteenth notes, how many sixteenth notes total are in a 3-beat loop?
7. If a triplet subdivision divides a beat into 3 equal parts, how many triplet notes fit into a 4-beat bar?
8. A track has a 2-beat loop. If you place a note on every 0.5 beat (eighth note) and then add an extra note on every 0.25 beat (sixteenth note), how many total notes are in the loop?
9. In music production, sound pressure levels follow a logarithmic scale. If increasing power by 10 times results in a 10 dB increase, what is the total decibel increase when power is increased by 100 times?
10. If a signal is at 0 dBFS and you reduce it by 6 dB, then reduce that result by another 6 dB, what is the final level in dBFS?
11. Two identical sound sources each produce 80 dB. When played together, the level increases by 3 dB. What is the total sound pressure level?
12. A gain stage increases a signal by 20 dB. If the input is 0.1 volts, what is the voltage multiplier? (Hint: 20 dB = 10x voltage increase)
13. A digital audio system uses a sample rate of 44,100 Hz. If you want to calculate how many samples are captured in exactly 2 seconds of audio, what is the total number of samples?
14. Each bit added to bit depth increases the dynamic range by approximately 6 dB. If a system increases from 8-bit to 12-bit, how many decibels of dynamic range are gained?
15. A storage calculation for a mono file is: (Sample Rate × Bit Depth × Duration) / 8. How many bytes are needed for 10 seconds of 44,100 Hz, 16-bit audio?
16. If the Nyquist frequency is half the sample rate, which sample rates allow for the capture of a 20,000 Hz tone without aliasing?
17. A random sequencer triggers a snare drum with a probability of 0.25 on each 16th note. What is the probability that the snare does NOT trigger on a specific 16th note?
18. A drum machine sequencer has a 'chance' knob set to 50%. If the machine cycles through 8 steps, what is the expected number of steps that will trigger a hit?
19. A random sequencer uses an algebraic formula to set velocity: V = (BaseVelocity) × (RandomFactor). If BaseVelocity is 100 and RandomFactor is between 0.6 and 0.9, what is the range of possible velocities?
20. A sequencer triggers a kick drum on beats 1 and 3, and a snare on beats 2 and 4. What is the probability that a random beat selection results in a kick drum?
21. In Algebraic Gain Staging, if a signal enters a plugin at -12 dB and the plugin adds 6 dB of gain, what is the final output level?
22. You have a signal chain with three plugins. Each plugin reduces the gain by 3 dB. If the starting signal is 0 dB, what is the total gain change?
23. A signal is at -20 dB. You need the output to be exactly -5 dB. How much gain (x) must you add?
24. If a gain stage doubles the amplitude (which is +6 dB) and you have 4 of these stages in series, what is the total gain added?

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