Cents vs semi-tones on guitar

Question

I was wondering, since we can tune our guitars by cents we can make them sound anywhere close to the note we need. So we can have open A be not 440 but 448 for instance. What restrictions are there not to make it sound bad with other guitars which have A ~440. I assume you can have max 100 cent per note not to go close to a semi-tone?

So for instance if we have A 440 the what is A# Hertz? If we do -50 to +50 around that open A, will it still sound okay with other guitars which are almost 440?

For instance on one guitar A = 442 and on the other A = 467, will they sound okay together? None of my guitar players ever get to exactly 440 on open A.

The idea of this question may be slightly hard to grasp, but basically do the cents matter much? For instance I play on Detuned organ with all notes set to -20 cents and it seems to sound okay with guitar, while we checked that the guitar notes are ~ near the center on the digital tuner.

Answer 1

For instance on one guitar A = 442 and on the other A = 467, will they sound okay together?

There will be a beat frequency of about 25 Hz between them, which would be annoying to most ears. So generally I think the best answer here is "no".

None of my guitar players ever get to exactly 440 on open A.

I'm not sure what you mean by "exactly", but it should be possible to tune an open A string to 110 Hz within 1 Hz (open A is actually two octaves below A 440). Tuning is a learned skill, just like playing, so it may be that your guitarists just have more to learn on the subject of tuning.

...do the cents matter much? For instance I play on Detuned organ with all notes set to -20 cents and it seems to sound okay with guitar, while we checked that the guitar notes are ~ near the center on the digital tuner.

In general, yes they matter a lot, but that doesn't mean that small differences in tuning are always audible or annoying. Being within 5 cents or so is probably fine for most people in most situations, but it really depends a lot. There are many situations where slight mistuning is a desirable sound. Robert Smith of The Cure would deliberately tune his guitars slightly off to get a more chorused and sad sound.

Answer 2

Cents and Hertz are two different scales. Hz increase exponentially between notes, while cents are a linear compression of the same increase.

You can't convert cents to Hz.

There are 100 cents between any A and adjacent A#. But you can’t really make a similar statement in Hz. There will be a different number of Hz between A2 and A#2 and A3 and A#3.

Cents do matter. A great deal. They matter less in different contexts but they are pretty important.

If two notes are played in unison and they are 50 cents apart. Even someone with no musical training would be able to tell that something’s up.

As they get closer and closer they tend to sound fine. I find that most people are ok if unisons are under 10 cents apart if there is vibrato. If no vibrato then under 5 cents different people seem okay with.

When multiple instruments are playing multiple chords precision is much less of an issue. In a band setting if a single string gets about 10 cents off. Another band member might notice but the audience probably won’t.