Re: [tuning] Digest Number 3099

Hi Paul,

> P.S. You don't really need to add a quadratic term or even a linear
> term to get the areas above and below zero to be the same, a constant
> would suffice. If you don't add a linear term, you might end up with
> a discontinuous waveform but plenty of waveforms are discontinuous,
> for example sawtooth, square, and pulse waves.

Yes I know. I might add the option to switch the linears or quadratics off
or choose what type of compensation you want to use (maybe
even to make the slope continuous at the endpoints too for
the quarter and complete wave ones). Or inded could add
in square waves, saw tooth curves, and pulses as functions that the user
can use, e.g. H(a,b) = 1 between a and b and 0 outside it or
S(a,b) slopes from 0 to 1 betwen a and b. P(a,b) goes
from 0 to 1 at midpoint of a,b then back again to 0
- or some such, will have to think about it.

The reason for doing it like this is
just that the discontinuous ones tend to be a bit harsh on the ear and
probably most users will want something a bit more melodious
than say a pure saw or square wave. I include those but
with an option to round them - as they are normally done in
fact if you have a saw or square waveform in synths I believe.

Discontinuities in the slope of the curve are much more acceptable, e.g.
a triangle wave sounds really rather nice even using
straight lines.

Robert

--- In tuning@yahoogroups.com, "Robert Walker" <robertwalker@n...>
wrote:

> The reason for doing it like this is
> just that the discontinuous ones tend to be a bit harsh on the ear

I think the harshness may have to do with the higher partials having
amplitude that's inversely proportional to partial number, while
higher-partial amplitudes inversely proportional to *squared* partial
number are a lot less harsh on the ear. Can you verify this (or help
me verify it) for the discontinuous waveforms you had in mind? It
might be interesting to construct some continuous waveforms which
however maintain the same amplitude spectrum, and see how the sounds
compare.

on 5/21/04 4:09 PM, Robert Walker <robertwalker@ntlworld.com> wrote:

> Hi Paul,
>
>> P.S. You don't really need to add a quadratic term or even a linear
>> term to get the areas above and below zero to be the same, a constant
>> would suffice. If you don't add a linear term, you might end up with
>> a discontinuous waveform but plenty of waveforms are discontinuous,
>> for example sawtooth, square, and pulse waves.
>
> Yes I know. I might add the option to switch the linears or quadratics off
> or choose what type of compensation you want to use (maybe
> even to make the slope continuous at the endpoints too for
> the quarter and complete wave ones). Or inded could add
> in square waves, saw tooth curves, and pulses as functions that the user
> can use, e.g. H(a,b) = 1 between a and b and 0 outside it or
> S(a,b) slopes from 0 to 1 betwen a and b. P(a,b) goes
> from 0 to 1 at midpoint of a,b then back again to 0
> - or some such, will have to think about it.
>
> The reason for doing it like this is
> just that the discontinuous ones tend to be a bit harsh on the ear and
> probably most users will want something a bit more melodious
> than say a pure saw or square wave. I include those but
> with an option to round them - as they are normally done in
> fact if you have a saw or square waveform in synths I believe.

I agree it is a good thing to do, maybe for a slightly different reason.
The large probability of a discontinuous edge would it seems to me reduce
the degree of control the user would experience. There would be too much
chance of getting things that sound too much the same.

> Discontinuities in the slope of the curve are much more acceptable, e.g.
> a triangle wave sounds really rather nice even using
> straight lines.

But it strike me that making the options be whether you want:
(1) continuous
(2) 1st derivative continuous
(2) 2nd derivative continuous

might be a useful way of expressing it, although clearly these concepts are
more advanced than what the user needs to know about. I'd recommend
continuous as a default, as you have already done. As far as how you
achieve the continuity, linear and quadratic offsets make a lot of sense
off-hand.

It also occurs to me it might be useful to specify what fraction of the
waveform period th entered waveform should corresond to, with the option of
"padding" the rest either with:

* a mirror of the original (probably just like what you do when a "half
wave" is entered)

* a spline segment

* a segment of a sine wave going from its maximum to minimum value, or more
or less of the cycle, as needed to achieve (optionally) a continuous 1st
derivative (when that is even possible).

etc.

I just jumped into this discussion nievely. I have never used FTS but have
read a couple messages (so far) from this thread.

-Kurt

on 5/21/04 4:59 PM, Kurt Bigler <kkb@breathsense.com> wrote:

> It also occurs to me it might be useful to specify what fraction of the
> waveform period th entered waveform should corresond to, with the option of
> "padding" the rest either with:
>
> * a mirror of the original (probably just like what you do when a "half wave"
> is entered)

I meant to say here:

* a mirror of the original (probably just like what you do when a "half
wave" is entered except that the user gets to specify the "duty cycle"
rather than having it be always 50/50).

-Kurt