Re: OT: high-precision tuner app

[musicus]

Hello Andrew,

I'd like to add a few thoughts to this topic:

 

[...]Also, in relation to accuracy, no phone tuner app is more accurate than 0.1 cent[...]

 

Indeed!

Most tuning programs measure the frequency via FFT (Fast Fourier Transformation), which gets only fine results,

if you use a relative long measurement time. This is for music instruments not usable, because barely no instrument can produce

an identical frequency over a time period of a few seconds.
So, either you get a fine resolution or a short measurement time, but not both together.

(frequency resolution = samplingrate / number of values)

 

A much better idea is to filter the signal to the wished frequency and measure the time of its period.

So, if you want to distinguish 440 hz from 441 hz, you need an AD/C with at least 200.000 Samples/second

in order to get reliable results.

(using standard frequency range 0-20 kHz at 1hz resolution and 10-times measurement resolution) (20.000*1*10)

But 1 Hz difference at 440 Hz is about 4 cent!!

So, in order to get 0.01 cent (~0,0025 hz) resolution you need

20 kHz*400*10 = 8 MSp/s

 

In other words: No smartphone (or PC) does have an AD/c with MSp/s, so you need special hardware to measure frequencies at this resolution.

 

 

 

[...]the ear simply cannot hear a hundredth of a cent difference [...]

 

I did an experiment tuning a pair of piano strings at around 440 Hz and could tell a difference up to one beat in 20 seconds.

This means it is possible to distinguish 440,00 Hz from 440,05 Hz

This is finer than 0.1 cent.

 

 

 

Another problem with such fine frequency specifications is inharmonicity.

If you want to tune 2 or more strings together - let's say an octave - you cannot only consider the fundamentals.

A fine difference at the fundamentals can get you very disturbing beats at higher partials, because they are much more affected by inharmonicity.
You need to measure all "overlapping" (-> creating beats) partials (in our case: 1. <-> 2. / 2. <-> 4. / 3. <-> 6. / 4. <-> 8. ...) and consider those dependent of their amplitude.

Then you can calculate the "right" frequency and tune both strings together.

This is the way, good aural piano tuners work and why they get much better results than any tuning app (so far).

 

My point is, you can only set ONE reference frequency (441 or 442 Hz f. e.) and other deviations from "standard" intonation won't work at this fine resolution.
There are some parameters to consider

(deviation of inharmonicity between various instruments / "to which resolution can a musician change the intonation?"...)

before you set values of 1/100 cent. Maybe it is better to specify Beats/second. (tempered quint vs pure quint = 1/2 B/s)

Best regards,

musicus