Topic by doug

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Topic: What does the Unison Width number mean? Unison Width & Temperament

Or is it arbitrary? The online help says nothing about it.

The reason I'm asking is that I'd like to experiment with unison width in different temperaments. I'm interested in learning if unison width has a useful relationship with the major third.

For example, if:

-the third of a given temperament is 5 cents sharp of the just third
-and the highest of the three strings (using unison width) is also 5 cents sharp
-will that create more internal resonances between the tonic and third?
-and will it have a particular sound when you play the thirds that haven't been tempered out of range

For example, if these settings matched and you played a C with the damper pedal down, would there be a stronger resonance with the E strings above it. And would the consonance of the major third take on a special timbre that wouldn't be present if these values didn't match?

But I think I need to understand the unison width in cents before I can experiment with it.

Last edited by doug (04-03-2013 16:31)

Reply by custral

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Re: What does the Unison Width number mean? Unison Width & Temperament

On the Home Page, choose Listen To It, then the Workshop tab, which gets to 3 sound simulations of clips of famous performances starting from bare MIDI, each workshop a different sort of music. Each step of a particular workshop gets a downloadable FXP, so you're never in doubt about how you get from the previous step to present.

And in each workshop, Unison Width is used one way or another, and it becomes clear the parameter varies the detuning between the multiple strings of those piano keys which do have multiple strings. I doubt the listening-effort you must apply to workshop similarly by yourself is easy to put out, but 'experiment's the name of the game!

As to where you are coming from or want to go, you seem to have a theory, so work up your own workshop, as it needs to apply, and test it by listening. It may be, for example, the 'better' tuning (for some purpose) is a measure of dis-tuning, which the workshops use as a management-facilty for the purpose of *matching* a sound. I guess lots of ear-training go to getting slick with that, and trying to fathom it out by numbers likely isn't the way. Experiment.

One I can think of at once : interfere with  the workshops by maxing consonance, in the given steps which do different, then contrast your final results with the given finals, (or your present FXPs with the given ones even sharper).

Last edited by custral (06-03-2013 07:46)

Reply by Philippe Guillaume

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  • Philippe Guillaume
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Re: What does the Unison Width number mean? Unison Width & Temperament

doug wrote:

Or is it arbitrary? The online help says nothing about it.

The reason I'm asking is that I'd like to experiment with unison width in different temperaments. I'm interested in learning if unison width has a useful relationship with the major third.

For example, if:

-the third of a given temperament is 5 cents sharp of the just third
-and the highest of the three strings (using unison width) is also 5 cents sharp
-will that create more internal resonances between the tonic and third?
-and will it have a particular sound when you play the thirds that haven't been tempered out of range

For example, if these settings matched and you played a C with the damper pedal down, would there be a stronger resonance with the E strings above it. And would the consonance of the major third take on a special timbre that wouldn't be present if these values didn't match?

But I think I need to understand the unison width in cents before I can experiment with it.

The unison width is a parameter without dimension, which simply multiplies the frequency differences between the strings. For example, if the “factory” frequencies of a given note are [f, f+a, f+b] for unison width = 1, then setting unison width to 2 will provide the frequencies [f, f+2*a, f+2*b].

Thus you are quite close to the situation that a piano tuner is experimenting when he pulls his tuning hammer (except that here 2 strings are simultaneously detuned in case of a 3 strings choir). Listen to the beatings like a piano tuner does and choose the sound you like.

You won’t know directly (nor really need) how many cents are involved, though you can guess it by a simple calculation: a 1 Hz beat on A = 440 Hz means 4 cents, 1 Hz beat on A = 220 Hz means 8 cents, etc. (more generally a 1 Hz beat at frequency f means 1200*log2((f+1)/f) cents which is very close to 1731/f).

As there are some tuners in this forum, maybe one of them would like to prepare an fxp where major thirds are tuned in the way you suggest? That would require the pro version and to use simultaneously detuning (for the pitch) and unison width. Surely an interesting challenge and experiment!

Philippe Guillaume's Website