Let me share my idea regards interpolation. Various interpolation methods are used in FLStudio when resampling sounds.

It's well known that interpolations are not exact solution of finding functons running along measurement points.
Wouldn't be better to solve 3 grade polynomial and calculate the value of it, for points between measurements?
Solving the polynomial factors to drive it through sampling points would be desriable. 

Could be that, I am splitting the hair into four, but there were always warious remarks about sound quality of FLSudio, so maybe adding this feature
on top of existing ones would teach that there's no much to argue. Or maybe there's lot of difference and solving the polynomial is the holy grail of lost quality crusaders.

Difference in sound wouldn't be huge, maybe apart from the fact, that solving polynomial wouldn't return values from outside measured ones.
interpolation likes to return results fractions of decibels louder than original sample, because of approaching interpolated points from bottom or top.
And that could be the point were it is worth checking it out on solved polynomial, which do not tend to go like this.

so:

it is four samples that are our source for resampling. thise quadrant rolls to the left everytime new sample pops from the right.

0.9 -0.1 -0.85 0.05
 s1   s2    s3   s4
  0    1     2    3
 t1   t2    t3   t4

there are moments in time - t1, t2, t3 and t4 - ranging from 0 to 3 - the sample number
there are readouts in time - s1, s2, s3 and s4 - having values in example - 0.9 -0.1 -0.85 0.05 - some measured or playbacked points of sample

we aproximate the chart with polynomial:

ax^3+bx^2+cx+d=y

x's are our t's and y's are s.

here's the set of equations of polynomial written for each of four samples

at1^3+bt1^2+ct1+d=s1
at2^3+bt2^2+ct2+d=s2
at3^3+bt3^2+ct3+d=s3
at4^3+bt4^2+ct4+d=s4

such a set can be solved by matrix determinant method. here are necessary matrices:

w:
t1^3 t1^2 t1 1
t2^3 t2^2 t2 1
t3^3 t3^2 t3 1
t4^3 t4^2 t4 1

wa:
s1 t1^2 t1 1
s2 t2^2 t2 1
s3 t3^2 t3 1
s4 t4^2 t4 1

wb:
t1^3 s1 t1 1
t2^3 s2 t2 1
t3^3 s3 t3 1
t4^3 s4 t4 1

wc:
t1^3 t1^2 s1 1
t2^3 t2^2 s2 1
t3^3 t3^2 s3 1
t4^3 t4^2 s4 1

wd:
t1^3 t1^2 t1 s1
t2^3 t2^2 t2 s2
t3^3 t3^2 t3 s3
t4^3 t4^2 t4 s4

after inserting the values and calculating the powers, each of determinants (w, wa, wb, wc and wd) is solved according to formula:

w
a1 b1 c1 d1
a2 b2 c2 d2
a3 b3 c3 d3
a4 b4 c4 d4

w=a1*(b2*c3*d4+c2*d3*b4+d2*b3*c4-(b4*c3*d2+c4*d3*b2+d4*b3*c2))-a2*(b1*c3*d4+c1*d3*b4+d1*b3*c4-(b4*c3*d1+c4*d3*b1+d4*b3*c1))+
a3*(b1*c2*d4+c1*d2*b4+d1*b2*c4-(b4*c2*d1+c4*d2*b1+d4*b2*c1))-a4*(b1*c2*d3+c1*d2*b3+d1*b2*c3-(b3*c2*d1+c3*d2*b1+d3*b2*c1))

what remains is to solve all determinants and get a=wa/w, b=wb/w, c=wc/w and d=wd/w of polynomial ax^3+bx^2+cx+d=y

then we can find preciselly points inbetween moments t1 and t4 by inserting values between 0 and 3 to the polynomial equation (including fractions of points) to get values of polynomial
that would be more true, than receiving it by interpolation.
