Psychoacoustician needing help understanding complex ratios

Hello everyone!

Reading your posts everyday makes me both feel happy and dizzy.

All those primes (it's OK with Mersenne, though) and ratios are making my head spin...

Could someone get me back in theory and explain me again what 17/8 means?

I've been away from this kind of things for too long. Psychoacoustics and ethnology are really on another plane than ratios.

I remember introducing me as a new member in numbers, but it seems that I get lost into numbers pretty easily!

So, is there someone kind enough to bring me back to the meaning of ratios and primes?

It can be off-group.

Thanks in advance!

-Rowdy JB

17/8 is the multipler that you apply to a fundamental pitch to get a new pitch. Musically speaking, 17/8 is an interval, specifically, a minor ninth. It could also be described as a reference to overtone #17. (Although in technical terms, overtone #17 is 17/1.) For example, given a pitch of 100 Hz, the 17/8 interval points to the next pitch of 100*17/8=212.5 Hz.

The easiest way to identify overtones in this ratio system is that overtones all have denominators which are powers of 2. You'll also often see these ratios expressed with assumed octave equivalence when people talk about scales, meaning that the denominator is multipled or divided by 2 until the ratio itself is at least 1 and less than 2. Thus, 17/8 and 17/16 (the minor second) usually refer to the same pitch in a scale. The exception to this is when a scale covers more or less than an octave.

Andrew

--- In tuning@yahoogroups.com, "collinet" <jbcollinet@...> wrote:
>
> Hello everyone!
>
> Reading your posts everyday makes me both feel happy and dizzy.
>
> All those primes (it's OK with Mersenne, though) and ratios are making my head spin...
>
> Could someone get me back in theory and explain me again what 17/8 means?
>
> I've been away from this kind of things for too long. Psychoacoustics and ethnology are really on another plane than ratios.
>
> I remember introducing me as a new member in numbers, but it seems that I get lost into numbers pretty easily!
>
> So, is there someone kind enough to bring me back to the meaning of ratios and primes?
>
> It can be off-group.
>
> Thanks in advance!
>
> -Rowdy JB
>

Many thanks for your explanation!

Thanks to those who contacted me off-group, too.

Now we'll be able to communicate using the same language ;-)

/JB

--- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@...> wrote:
>
> 17/8 is the multipler that you apply to a fundamental pitch to get a new pitch. Musically speaking, 17/8 is an interval, specifically, a minor ninth. It could also be described as a reference to overtone #17. (Although in technical terms, overtone #17 is 17/1.) For example, given a pitch of 100 Hz, the 17/8 interval points to the next pitch of 100*17/8=212.5 Hz.
>
> The easiest way to identify overtones in this ratio system is that overtones all have denominators which are powers of 2. You'll also often see these ratios expressed with assumed octave equivalence when people talk about scales, meaning that the denominator is multipled or divided by 2 until the ratio itself is at least 1 and less than 2. Thus, 17/8 and 17/16 (the minor second) usually refer to the same pitch in a scale. The exception to this is when a scale covers more or less than an octave.
>
> Andrew
>
>
>
> --- In tuning@yahoogroups.com, "collinet" <jbcollinet@> wrote:
> >
> > Hello everyone!
> >
> > Reading your posts everyday makes me both feel happy and dizzy.
> >
> > All those primes (it's OK with Mersenne, though) and ratios are making my head spin...
> >
> > Could someone get me back in theory and explain me again what 17/8 means?
> >
> > I've been away from this kind of things for too long. Psychoacoustics and ethnology are really on another plane than ratios.
> >
> > I remember introducing me as a new member in numbers, but it seems that I get lost into numbers pretty easily!
> >
> > So, is there someone kind enough to bring me back to the meaning of ratios and primes?
> >
> > It can be off-group.
> >
> > Thanks in advance!
> >
> > -Rowdy JB
> >
>

On Wed, Jul 6, 2011 at 7:28 AM, bigAndrewM <bigandrewm@...> wrote:
>
> 17/8 is the multipler that you apply to a fundamental pitch to get a new pitch. Musically speaking, 17/8 is an interval, specifically, a minor ninth. It could also be described as a reference to overtone #17. (Although in technical terms, overtone #17 is 17/1.) For example, given a pitch of 100 Hz, the 17/8 interval points to the next pitch of 100*17/8=212.5 Hz.
>
> The easiest way to identify overtones in this ratio system is that overtones all have denominators which are powers of 2. You'll also often see these ratios expressed with assumed octave equivalence when people talk about scales, meaning that the denominator is multipled or divided by 2 until the ratio itself is at least 1 and less than 2. Thus, 17/8 and 17/16 (the minor second) usually refer to the same pitch in a scale. The exception to this is when a scale covers more or less than an octave.

You may also hear what Andrew calls "overtones" above referred to on
here as "rooted" intervals.

-Mike