1/4 CMT vs Blue JI 31EDO vs Blue JI 197eq vs Blue Temperament

For me the most versatile tuning has the greatest number of *good* harmony intervals an octave or less wide within +/-6.776 cents accuracy over 12 keys. Also the notes should go with 1/1 as well. Here are the *good* harmony intervals (according to my own taste)...

9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 11/8, 7/5, 10/7, 3/2, 11/7, 8/5, 5/3, 12/7, 7/4, 9/5, 11/6, 13/7, 2/1.

I worked out how many good intervals (an octave or less wide over 12 keys) occur in the following four scales.

In joint third place is the Quarter Comma Meantone scale Mike gave me and the Blue JI in 31EDO Igs gave me. They both yield 90 good intervals within 6.776 cents (256/255) accuracy.

In second place is Gene's Blue JI in 197 eq which yields 91 good intervals within 6.776 cents accuracy.

The winner, by a margin of 6, is Blue Temperament with 97 good intervals within 6.776 cents accuracy.

So I don't have to eat my hat.

John.

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:
> The winner, by a margin of 6, is Blue Temperament with 97 good intervals within 6.776
> cents accuracy.
>
> So I don't have to eat my hat.

John, again (since I'm assuming you missed my previous post on this subject): I never said your tuning was a meantone or was equivalent to a meantone. It is more on par with a well-temperament. Well-temperaments were quite popular prior to the adoption of 12-TET, and involve a chain of irregularly-tempered fifths that preserve some of the pure harmonies of meantone but lessen the "wolf" intervals by tuning some of the fifths wider than the 1/4-comma fifths. All well-temperaments have some increased level of good intervals over 1/4-comma meantone, and there is a whole spectrum of well-temperaments between 1/4-comma meantone and 12-TET. Your temperament clearly falls in this category, which is a centuries-old category.

Again, I advise you to check out this link:

http://en.wikipedia.org/wiki/Werckmeister_temperament

for a few popular examples from the late 1600's. These are more "extreme" temperaments than yours, but yield more playable keys. There were LOADS of well-temperaments in use throughout that historical period, and it's entirely likely that someone back then considered a temperament like yours. However, your temperament offers only a very slight improvement over meantone, and I suspect the people in that day (and perhaps this day as well) would be unlikely to consider the improvement enough to warrant adoption, since the most popular WT's offered a much larger increase in playable intervals.

And, as I've stated before: they all fell before 12-tET, superior harmonies be damned.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> John, again (since I'm assuming you missed my previous post on this subject): I never said your tuning was a meantone or was equivalent to a meantone. It is more on par with a well-temperament. Well-temperaments were quite popular prior to the adoption of 12-TET, and involve a chain of irregularly-tempered fifths that preserve some of the pure harmonies of meantone but lessen the "wolf" intervals by tuning some of the fifths wider than the 1/4-comma fifths. All well-temperaments have some increased level of good intervals over 1/4-comma meantone, and there is a whole spectrum of well-temperaments between 1/4-comma meantone and 12-TET. Your temperament clearly falls in this category, which is a centuries-old category.

I don't agree with these comparisons. A well-tempered keyboard, or a "good temperament" as Claudio just explained, refers to well precise characteristics that neither Blue JI nor Blue temperament have. They are clearly different.

On Fri, Feb 11, 2011 at 3:39 PM, Jacques Dudon <fotosonix@...> wrote:
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> > John, again (since I'm assuming you missed my previous post on this subject): I never said your tuning was a meantone or was equivalent to a meantone. It is more on par with a well-temperament. Well-temperaments were quite popular prior to the adoption of 12-TET, and involve a chain of irregularly-tempered fifths that preserve some of the pure harmonies of meantone but lessen the "wolf" intervals by tuning some of the fifths wider than the 1/4-comma fifths. All well-temperaments have some increased level of good intervals over 1/4-comma meantone, and there is a whole spectrum of well-temperaments between 1/4-comma meantone and 12-TET. Your temperament clearly falls in this category, which is a centuries-old category.
>
> I don't agree with these comparisons. A well-tempered keyboard, or a "good temperament" as Claudio just explained, refers to well precise characteristics that neither Blue JI nor Blue temperament have. They are clearly different.

I think that Igs meant it more in the sense of it being an
irregularly-tempered 12-note periodicity block.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> (Igs) :
Your temperament clearly falls in this category, which is a centuries-old category.
> >
> > I don't agree with these comparisons. A well-tempered keyboard, or a "good temperament" as Claudio just explained, refers to well precise characteristics that neither Blue JI nor Blue temperament have. They are clearly different.

> I think that Igs meant it more in the sense of it being an
> irregularly-tempered 12-note periodicity block.

So what ? we are not short of irregularly-tempered 12-note periodicity block or whatever that are not "well-tempered keyboards", I simply don't understand this comparison.

On Fri, Feb 11, 2011 at 4:32 PM, Jacques Dudon <fotosonix@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > (Igs) :
>
> Your temperament clearly falls in this category, which is a centuries-old category.
> > >
> > > I don't agree with these comparisons. A well-tempered keyboard, or a "good temperament" as Claudio just explained, refers to well precise characteristics that neither Blue JI nor Blue temperament have. They are clearly different.
>
> > I think that Igs meant it more in the sense of it being an
> > irregularly-tempered 12-note periodicity block.
>
> So what ? we are not short of irregularly-tempered 12-note periodicity block or whatever that are not "well-tempered keyboards", I simply don't understand this comparison.

Perhaps I should have said "unevenly tempered." I think Igs was
getting more at that John's temperament is very close to 12-tet, and
looks a lot like an unevenly tempered 12-tet. I don't think he meant
that it would be something comparable to Werckmeister. Maybe it can be
viewed in a certain sense as a 12-note 11-limit WT.

-Mike