Beating vs. the Harmonic Series; which is more important (or equal)?

I have been asking myself this question.
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An obvious example of the harmonic series is 100hz, 200hz, 300hz, 400hz...
But is this the cause of the feel of relaxed beating (IE concordance/consonance) in the human brain or an effect of having consistent beating?
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You can see from above that 200hz-100hz = 100hz and 300hz-200hz = 100hz etc. IE the rate between frequencies of the harmonic series show an obvious pattern in beating rate (the constant difference of 100hz between tones).
But, then again, so in a way do mean-tone scales IE apx. 1.5 * 1.5 * 1.5, only the pattern is based on a constant exponential rate of beating (IE 1.5,1.5^2...) instead of based on addition-based rise (IE 100hz + 100hz + 100hz etc.).

So what's more important, consistence in beating as an abstract concept or following the harmonic series (which has "tonal" consistent beating rate as a side effect)...or are they of equal importance?

-Michael

I have been asking myself this question.
*****************************************************
An obvious example of the harmonic series is 100hz, 200hz, 300hz, 400hz...
But is this the cause of the feel of relaxed beating (IE concordance/consonance) in the human brain or an effect of having consistent beating?
*****************************************************************
You can see from above that 200hz-100hz = 100hz and 300hz-200hz = 100hz etc. IE the rate between frequencies of the harmonic series show an obvious pattern in beating rate (the constant difference of 100hz between tones).
But, then again, so in a way do mean-tone scales IE apx. 1.5 * 1.5 * 1.5, only the pattern is based on a constant exponential rate of beating (IE 1.5,1.5^2...) instead of based on addition-based rise (IE 100hz + 100hz + 100hz etc.).

So what's more important, consistence in beating as an abstract concept or following the harmonic series (which has "tonal" consistent beating rate as a side effect)...or are they of equal importance?

-Michael

djtrancendance wrote:
> I have been asking myself this question.
> *****************************************************
> An obvious example of the harmonic series is 100hz, 200hz, 300hz, 400hz...
> But is this the cause of the feel of relaxed beating (IE concordance/consonance) in the human brain or an effect of having consistent beating? > *****************************************************************
> You can see from above that 200hz-100hz = 100hz and 300hz-200hz = 100hz etc. IE the rate between frequencies of the harmonic series show an obvious pattern in beating rate (the constant difference of 100hz between tones). > But, then again, so in a way do mean-tone scales IE apx. 1.5 * 1.5 * 1.5, only the pattern is based on a constant exponential rate of beating (IE 1.5,1.5^2...) instead of based on addition-based rise (IE 100hz + 100hz + 100hz etc.). A "constant exponential rate"?

In general, the beating of meantone chords isn't coherent. There are some special cases where it is -- the standard example being root position triads in metameantone (roughly LucyTuning). Meantones do tend to sound good the closer they approximate the harmonic series.

Phi timbres with phi tuning are another way of getting the beats to align with the timbre, as O'Connell explained. The fact that his has been known for decades without making waves in the musical world suggests it isn't that important.

> So what's more important, consistence in beating as an abstract concept or following the harmonic series (which has "tonal" consistent beating rate as a side effect)...or are they of equal importance?

It's up to you to decide. Try comparing irrational temperaments with "Mt Meru" scales.

Graham