How tuner and computer tunes the instrument ?

[Henrietta Stoffels]

Hello Guys,

I want to understand what is the meaning of a string tuned in 440 hz in the logic of computer or tuner ?
I only know short term fourier transform peaks. Which peak is responsible to computer to say my string in tune. May be there are lots of harmonics at the window and strongest peak is responsible for the tuning ?
Or may be the first peak is responsible for tuning ?

Could you please help me ?

Thanks

 

[Will_White]

Hello Guys,

I want to understand what is the meaning of a string tuned in 440 hz in the logic of computer or tuner ?
I only know short term fourier transform peaks. Which peak is responsible to computer to say my string in tune. May be there are lots of harmonics at the window and strongest peak is responsible for the tuning ?
Or may be the first peak is responsible for tuning ?

Could you please help me ?

Thanks

I don't know for sure but it's probably the second harmonic(twelfth fret) on a bass it's still the same note it's just an octave up so the tuner picks it up better.

 

[Dojix]

If you have an audio interface and a DAW, you can look at it on a spectrum analyser. As I see it, there's a big peak at the exact frequency the note is, and then ratios on all the corresponding harmonics. By that, I mean that if you were to play a normal E, it'd be at 41.204 Hz (assuming A440 tuning). It does also depend on what the tuner is designed for, because a guitar tuner will freak out with the E and A strings if it doesn't have the setup to cope with strings bleeding.

 

[fdeck]

The two lowest order harmonics are an octave apart, so it doesn't matter whether the tuner picks up an A at 440 or 880, it's still an A. I suspect that tuners are simply designed to assume that one or both of those harmonics are strong enough in the signal to prevent mistakenly picking a higher harmonic such as a fifth above the octave. Under this assumption, the tuner can do one of two things:

1. Measure the frequency of zero crossings going in one direction, for instance from negative to positive. This kinda has to be how cheap tuners work, since they're older than the technology for computing an Fourier Transform in a small battery powered circuit.

2. Compute a Fourier transform and pick the lowest harmonic above a given threshold.

In both cases, the tuner might have some additional means to avoid picking up 60 and 120 Hz (or 50 and 100 outside the US) such as filtering those frequencies out.

This is all a guess on my part, but an educated guess. My day job is for a company that makes Fourier Transform analysis equipment, among other things.

 

[Dojix]

I just realised that the tuner never has to pick up what octave the note is, which makes this a lot easier. I'm guessing every note in the 12 twelve tones has a specific set of harmonics and it reads based on shapes.

 

[fdeck]

1. The signal from the bass (or microphone) is a voltage that varies with time, typically swinging above and below zero Volts. When the signal swings from positive to negative, or vice versa, it's called a "zero crossing." A circuit that detects a zero crossing in a specific direction is easy to design.

2. You can construct a "time base" that generates a signal at a high frequency, based on something like the vibrations of a ceramic crystal. The crystal is made to have a particular frequency, and is quite accurate and stable. This is how electric or digital watches keep time.

The circuit counts the cycles of the time base in between two zero crossings of the audio signal. Now it knows the time period of the audio signal. The reciprocal of the time period is frequency. It can "look up" the note associated with a given range of frequencies in a table of numbers, and then compute the deviation of your input signal.