What is a "regular" temperament?

I know we've been engaged in terminology wars recently, with me taking
the side that debates over semantics are pointless, but this is
something I actually am curious about. What is the difference between
an "irregular" and a "regular" temperament?

For instance, is something in the 2.3.5.7.9' subgroup an "irregular"
temperament? Or just an "inconsistent" temperament? Or what?

-Mike

Hi, trying again on this.

-Mike

On Fri, Feb 17, 2012 at 1:23 PM, Mike Battaglia <battaglia01@...> wrote:
> I know we've been engaged in terminology wars recently, with me taking
> the side that debates over semantics are pointless, but this is
> something I actually am curious about. What is the difference between
> an "irregular" and a "regular" temperament?
>
> For instance, is something in the 2.3.5.7.9' subgroup an "irregular"
> temperament? Or just an "inconsistent" temperament? Or what?
>
> -Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I know we've been engaged in terminology wars recently, with me taking
> the side that debates over semantics are pointless, but this is
> something I actually am curious about. What is the difference between
> an "irregular" and a "regular" temperament?
>
> For instance, is something in the 2.3.5.7.9' subgroup an "irregular"
> temperament? Or just an "inconsistent" temperament? Or what?
>
> -Mike
>

Well, if we are in the 2.3.9' subgroup, that means we are equating 9' with 9. However, we are not tempering out the difference, otherwise it would result in a ET.

So, I think before we try to define an "irregular" temperament, we first need new terminology to describe ratios which are equated with each other but where their difference is not tempered out. Tempering always implies equating, but the converse is not necessarily true.

Ryan

On Sat, Mar 3, 2012 at 10:52 PM, Ryan Avella <domeofatonement@...>
wrote:
>
> So, I think before we try to define an "irregular" temperament, we first
> need new terminology to describe ratios which are equated with each other
> but where their difference is not tempered out. Tempering always implies
> equating, but the converse is not necessarily true.
>
> Ryan

I think there's already an accepted definition of it, I just don't
know what the heck it is. For example, the 15-note porcupine
temperament we came up with is pretty well handled by the val <15 24
35 42 52|. This val is an "abstract regular temperament." Does that
mean that our well temperament is regular?

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> I think there's already an accepted definition of it, I just don't
> know what the heck it is. For example, the 15-note porcupine
> temperament we came up with is pretty well handled by the val <15 24
> 35 42 52|. This val is an "abstract regular temperament." Does that
> mean that our well temperament is regular?
>
> -Mike
>

Well, lets look at the following scale.

0
396
796
1200

Now, for practical reasons we might ask if 128/125 is tempered out. Here is how we could go about it.

First we would have to call the different generators 5/4, 5'/4, and 5''/4. Then we would say that 5, 5' and 5'' are all equivalent, in the same way that 1/1 and 2/1 are equivalent.

Then we can make a list of commas which are tempered out. The most important comma tempered out by this scale is 128/(5 * 5' * 5'').

Notice however that we said that 5, 5' and 5'' are equivalent. By replacing 5' and 5'' with just a regular 5, we can therefore arguably say that 128/125 is an equivalence ratio as well. So even though 128/125 is not tempered out, it is definitely an equivalence ratio.

Ryan

On Sun, Mar 4, 2012 at 1:33 AM, Ryan Avella <domeofatonement@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > I think there's already an accepted definition of it, I just don't
> > know what the heck it is. For example, the 15-note porcupine
> > temperament we came up with is pretty well handled by the val <15 24
> > 35 42 52|. This val is an "abstract regular temperament." Does that
> > mean that our well temperament is regular?
>
> Well, lets look at the following scale.
>
> 0
> 396
> 796
> 1200
>
> Now, for practical reasons we might ask if 128/125 is tempered out. Here
> is how we could go about it.
>
> First we would have to call the different generators 5/4, 5'/4, and 5''/4.
> Then we would say that 5, 5' and 5'' are all equivalent, in the same way
> that 1/1 and 2/1 are equivalent.
>
> Then we can make a list of commas which are tempered out. The most
> important comma tempered out by this scale is 128/(5 * 5' * 5'').
>
> Notice however that we said that 5, 5' and 5'' are equivalent. By
> replacing 5' and 5'' with just a regular 5, we can therefore arguably say
> that 128/125 is an equivalence ratio as well. So even though 128/125 is not
> tempered out, it is definitely an equivalence ratio.

And what if I just say screw it and map this to the 2.5. val <3 7|? Is
that a "regular mapping" of this "irregular temperament" or something?

-Mike