Narrow Intervals

Michael,

it seems I was wrong about 6/5 being the narrowest 'good' interval. When I tested narrower intervals on my keyboard in the past I always heard an annoying 'trill' and so I ruled them out. I was using the wrong 'voice'. Today I played a 9/8 interval but this time using a Church Organ 'voice' on my keyboard and it not only sounded tolerable, but very sweet with no annoying trill. So 9/8 is in. I'm not to hot about 10/9 though so at the moment, for me, 9/8 is the narrowest legal interval.

I've gone a bit stricter on the tolerance for deviation from a "perfect" interval: 256/255 or 6.789 cents. As I said before, the next step is to temper my NPT scale to get the maximum number of good dyads.

My calculator should still work, just add 'x' to the result. 'x' will give the 9/8 a positive result and the 10/9 a negative result. In other words the hierarchy of intervals is still the same.

John.

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:
>
>Today I played a 9/8 interval but this time using a Church Organ 'voice' on my keyboard and it not only sounded tolerable, but very sweet with no annoying trill. So 9/8 is in. I'm not to hot about 10/9 though so at the moment, for me, 9/8 is the narrowest legal interval.

> I've gone a bit stricter on the tolerance for deviation from a "perfect" interval: 256/255 or 6.789 cents.

It's progress, but why do you need your calculator?

To avoid 'bad' intervals.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "john777music" <jfos777@> wrote:
> >
> >Today I played a 9/8 interval but this time using a Church Organ 'voice' on my keyboard and it not only sounded tolerable, but very sweet with no annoying trill. So 9/8 is in. I'm not to hot about 10/9 though so at the moment, for me, 9/8 is the narrowest legal interval.
>
> > I've gone a bit stricter on the tolerance for deviation from a "perfect" interval: 256/255 or 6.789 cents.
>
>
> It's progress, but why do you need your calculator?
>

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:
>
> To avoid 'bad' intervals.

I thought you'd changed your method to one of listening to the intervals.

Gene,

I can't trust my ears hence the need for the calculator. Testing the 15/8 interval in the past, sometimes I thought it was good and other times bad. I couldn't be sure.

John.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "john777music" <jfos777@> wrote:
> >
> > To avoid 'bad' intervals.
>
> I thought you'd changed your method to one of listening to the intervals.
>

Something about this seems backwards.

-Mike

On Sun, Apr 25, 2010 at 5:20 PM, john777music <jfos777@...> wrote:
>
>
>
> Gene,
>
> I can't trust my ears hence the need for the calculator. Testing the 15/8 interval in the past, sometimes I thought it was good and other times bad. I couldn't be sure.
>
> John.
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, "john777music" <jfos777@> wrote:
> > >
> > > To avoid 'bad' intervals.
> >
> > I thought you'd changed your method to one of listening to the intervals.
> >
>
>

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:
>
> Gene,
>
> I can't trust my ears hence the need for the calculator.

If your calculator is based on your ears, and you can't trust your ears, how can you possibly trust your calculator?

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Something about this seems backwards.

That's being kind.

>"I'm not to hot about 10/9 though so at the moment, for me, 9/8 is the narrowest legal interval."
Ah, now that sounds a whole lot more reasonable to me. At least this way you would cover most of the intervals used in chords for "common practice music".
Admittedly, the use of ratios such as 11/10 and 12/11 are partly my own "thing"...as in I well realize that they are not part of common practice music which, ironically, makes them all that more intriguing to me to find ways to "extend" common practice music to include them. Then again, as I, Chris, and several others have debated and agreed upon, even 15/14 (which has far more "trill" than something like 12/11) is used in "common practice" chords like inverted 7th but (at least so far as I've seen) it's not used nearly as much as intervals like 9/8.

>"I've gone a bit stricter on the tolerance for deviation from a
"perfect" interval: 256/255 or 6.789 cents. As I said before, the next
step is to temper my NPT scale to get the maximum number of good dyads."
That goes from virtually in-detectable to the untrained ear to virtually in-detectable to the trained ear. To me the real challenge looks like how to make such a tempered system without running into standard 12-tone JI as your answer (since, to the best of my knowledge, 12-tone JI meets those conditions). Not that it's impossible but it's a very hard thing to do...so many experts before you have had exactly the same goal so you have some pretty stiff competition. As a side note, if you're looking toward maximizing the consonance of historical intervals (and only such intervals), it might be useful to look at and compare your work to things like 1/4 comma mean-tone, which do a very good job at said above tasks. I'm not saying it's impossible to compete with such tunings but that it's a realistic way to benchmark your system.

--- In tuning@yahoogroups.com, "jonszanto" <jszanto@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > Something about this seems backwards.
>
> That's being kind.

If you get rid of the goofy correction term, and simply sort rational numbers q in lowest terms according to the size of 1/numer(q)+1/denom(q), the practical result doesn't seem to be too greatly different from Tenney height, though I like Tenney (which for example rates 7/6 better than 9/5) better. Here is what the 11-limit tonality diamond looks like when sorted:

2, 3/2, 4/3, 5/3, 5/4, 7/4, 6/5, 7/5, 8/5, 9/5, 7/6, 8/7, 11/6, 9/7, 10/7, 9/8, 11/7, 12/7, 11/8, 10/9, 11/9, 11/10, 14/9, 12/11, 16/9, 14/11, 16/11, 18/11, 20/11

Gene,

the calculator is based on intervals that are "obviously" consonant.

John.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "john777music" <jfos777@> wrote:
> >
> > Gene,
> >
> > I can't trust my ears hence the need for the calculator.
>
> If your calculator is based on your ears, and you can't trust your ears, how can you possibly trust your calculator?
>