Re: [tuning] Digest Number 3100

Hi Paul,

Rightio, I was getting confused there.

Was thinking really about the doubles
of the odd partials (+ fundamental)

1 2 6 10 14 18 etc.

Of course just the even numbers is simply
another harmonic series on 2 instead of on
1 plus you have added a note an octave
below it.

Anyway tried it out and it has a strange
vaguely clarinet type sound but does
get rid of the more obvious beats
using sine waves and is quite smooth
sounding.

Odd is a bit rough but okay, with
a bit of slow beating but not so
obvious as all that.
Prime surprisingly has a bit of slow
beating in it too. All except the
Odd one had the octave in them.
All has lots of beating; many
simultaneous ones.

I'd say of those ones, Odd *2
is the one that is smoothest
if what you want is gentle beats
(some fast but not varying much in volume)
- that is for a single note.

Anyway here is the Odd*2
as sine waves, - it is 1 2 6 10
as the partials

All these are playing the 12eq. major chord.

http://www.robertinventor.com/12_et_oddt2_to_12_seth.mp3

You can hear many simultaneous beats there but they are
gentle (though fast) and it is quite smooth sounding.

Same one, not Setharised:

http://www.robertinventor.com/12_et_oddt2_to_12_un_seth.mp3

Some slow large amplitude beats there in the chord,
when the major third comes in, fairly smooth for the single note.

Setharised, and using all the harmonics, with
many simultaneous large amplitude variation
beats already in the single note at the start
of the clip:

http://www.robertinventor.com/12_et_all_to_13_seth.mp3

This is the same one using Bessel functions (of order 3 in fact)
for the partials - just because it sounds nice, though
with really strong beats already in single notes, but these are
really musical ones so I like it, like bell beats.

http://www.robertinventor.com/12_et_oddt2_to_12_Bessel_Seth.mp3

In fact that would sound nice transposed down a couple of octaves
- here it is again:

http://www.robertinventor.com/12_et_oddt2_to_12_Bessel_Seth_C2.mp3

Here is the buzzy x^3 sin(1/x^3), this time using all
the harmonics up to the 13th, not setharised
(didn't make much difference whether you did it Setharised not):

http://www.robertinventor.com/12_et_all_to_13_xu3_sin_1oxu3_un_seth.mp3

Still a bit beaty there, but as you make it more buzzy they
go away - and it is remarkably unbeaty if you compare it with the
same one using sine waves - here it is again for comparision:
http://www.robertinventor.com/12_et_all_to_13_seth.mp3

I'll do some for 7-et next some time prob. over the weekend,
and some graphics later and put them together to make
a web page, meanwhile back to final testing of the next upload.

If you want to try this idea out in MattLab I'll be interested
to hear what you come up with too.

Thanks,

Robert.

--- In tuning@yahoogroups.com, "Robert Walker" <robertwalker@n...>
wrote:
> Hi Paul,
>
> Rightio, I was getting confused there.
>
> Was thinking really about the doubles
> of the odd partials (+ fundamental)
>
> 1 2 6 10 14 18 etc.

Well, this could potentially have quite prominent beating between the
combinational tones. Difference tones of the form 2*a-b are typically
the loudest ones. Here we have

2*6 - 10 = 2, which could beat with 2
2*10 - 14 = 6, which could beat with 6
2*14 - 18 = 10, which could beat with 10

Just using the primes wouldn't seem a good approach either. What you
want to look into is (generalizing the) "sum-free" sets -- for
example, there are the 'Golomb rulers' which have been discussed
here, and which Manuel has created some scales with.

> but does
> get rid of the more obvious beats

That's good. I think we could do a lot better, though. Also, are you
using a specific inharmonic timbre to test these ideas? A different
inharmonic timbre might change your assessments.

I'll have to read the rest of your message and listen to your sound
examples later.

-p

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

> Anyway here is the Odd*2
> as sine waves, - it is 1 2 6 10
> as the partials
>
> All these are playing the 12eq. major chord.
>
> http://www.robertinventor.com/12_et_oddt2_to_12_seth.mp3
>
> You can hear many simultaneous beats there but they are
> gentle (though fast) and it is quite smooth sounding.

I find it hard to hear any beats in the individual timbres, and the
notes of the chord are struck too far apart for me to hear whether
the chord itself is producing any beating or not.

> Same one, not Setharised:
>
> http://www.robertinventor.com/12_et_oddt2_to_12_un_seth.mp3
>
> Some slow large amplitude beats there in the chord,
> when the major third comes in, fairly smooth for the single note.

Honestly, I can't hear the beats here. Which is no surprise -- a
major third would only beat if the n*5th partial of the lower note
beats against the n*4th partial of the higher note. If you're using
only partial #s 1, 2, 6, and 10, there's no opportunity for this to
happen.

> Setharised, and using all the harmonics, with
> many simultaneous large amplitude variation
> beats already in the single note at the start
> of the clip:
>
> http://www.robertinventor.com/12_et_all_to_13_seth.mp3
>
> This is the same one using Bessel functions (of order 3 in fact)
> for the partials - just because it sounds nice,

Can you elaborate in more detail what you did in this example? I'm
not sure in what sense this is "Setharized", but it's an interesting
sound and I'd like to learn more about it. Also about the connection
with Bessel functions.

> though
> with really strong beats already in single notes, but these are
> really musical ones so I like it, like bell beats.
>
> http://www.robertinventor.com/12_et_oddt2_to_12_Bessel_Seth.mp3

Well, finally here's one where I hear beating when the major third
comes in. Can you explain what this one is, how it's different from
the one above, etc.? You say it's "Seth" (arized?) but somehow I
think there must still be some just 5th partials in these
timbres . . .

>
> In fact that would sound nice transposed down a couple of octaves
> - here it is again:
>
> http://www.robertinventor.com/12_et_oddt2_to_12_Bessel_Seth_C2.mp3

Well here, the timbres don't seem to hold together as single pitches.
When the 2nd "note" comes in, I'm hearing at least an augmented
triad, not a dyad.

> Here is the buzzy x^3 sin(1/x^3), this time using all
> the harmonics up to the 13th, not setharised
> (didn't make much difference whether you did it Setharised not):
>
>
http://www.robertinventor.com/12_et_all_to_13_xu3_sin_1oxu3_un_seth.mp
3

This sounds normal, like a clav or something. These are fully
harmonic timbres, right? Are these "metatimbres" of the sort we were
discussing earlier? When you say, "didn't make much difference
whether you did it Setharised not", did you mean "metatimbres" as the
Setharized case? Can we hear that? I'd be surprised if there was no
audible difference.

> Still a bit beaty there, but as you make it more buzzy they
> go away - and it is remarkably unbeaty if you compare it with the
> same one using sine waves - here it is again for comparision:
> http://www.robertinventor.com/12_et_all_to_13_seth.mp3

Well this timbre sounds inharmonic and the chords "noisy". How is
this "the same one using sine waves"?

> If you want to try this idea out in MattLab I'll be interested
> to hear what you come up with too.

Sure -- I might be particularly interested in pursuing the idea I
mentioned in another thread, which is to come up with two completely
different-looking waveforms -- one continuous, one discontinuous --
which nevertheless sound the same, due to having the same series of
partials with the same amplitudes (only the phases would be
different). In this regard, I asked you for some data on the
waveforms you were using -- looking forward to whatever you might
want to share . . .

>
> Thanks,
>
> Robert.