Blackjack question

I'm not getting this one:

C:Eb^:G:Bb^ or

1/3:2/5:1/2:3/5

How does the arithmetic work out on that one??

Thanks!

Joseph

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> I'm not getting this one:
>
> C:Eb^:G:Bb^ or
>
> 1/3:2/5:1/2:3/5
>
> How does the arithmetic work out on that one??
>
> Thanks!
>
> Joseph

this is a good old just minor seventh chord. it can be expressed as
10:12:15:18, and if you divide through by 30, this turns into
1/3:2/5:1/2:3/5. you could then divide through by 6 and express it as
1/18:1/15:1/12:1/10, indicating that the chord is symmetrical under
mirror inversion.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_44306.html#44317

<wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> wrote:
> > I'm not getting this one:
> >
> > C:Eb^:G:Bb^ or
> >
> > 1/3:2/5:1/2:3/5
> >
> > How does the arithmetic work out on that one??
> >
> > Thanks!
> >
> > Joseph
>
> this is a good old just minor seventh chord. it can be expressed as
> 10:12:15:18, and if you divide through by 30, this turns into
> 1/3:2/5:1/2:3/5. you could then divide through by 6 and express it
as
> 1/18:1/15:1/12:1/10, indicating that the chord is symmetrical under
> mirror inversion.

***Whoopie! It's dumb question time, and I'm the first with my hand
up:

But, this is such a simple chord. Wouldn't a minor third be
something like 6:5?? I guess I'm still not getting the numbers...

Thanks!!!!!

JP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
>
> /tuning/topicId_44306.html#44317
>
> <wallyesterpaulrus@y...> wrote:
> > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> > wrote:
> > > I'm not getting this one:
> > >
> > > C:Eb^:G:Bb^ or
> > >
> > > 1/3:2/5:1/2:3/5
> > >
> > > How does the arithmetic work out on that one??
> > >
> > > Thanks!
> > >
> > > Joseph
> >
> > this is a good old just minor seventh chord. it can be expressed
as
> > 10:12:15:18, and if you divide through by 30, this turns into
> > 1/3:2/5:1/2:3/5. you could then divide through by 6 and express
it
> as
> > 1/18:1/15:1/12:1/10, indicating that the chord is symmetrical
under
> > mirror inversion.
>
>
> ***Whoopie! It's dumb question time, and I'm the first with my
hand
> up:
>
> But, this is such a simple chord. Wouldn't a minor third be
> something like 6:5?? I guess I'm still not getting the numbers...
>
> Thanks!!!!!

yes, you could write the chord as 5:6:15/2:9 if you wanted (just the
10:12:15:18 divided through by 2), to highlight the 5:6 at the bottom.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_44306.html#44401

<wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> >
> > /tuning/topicId_44306.html#44317
> >
> > <wallyesterpaulrus@y...> wrote:
> > > --- In tuning@yahoogroups.com, "Joseph Pehrson"
<jpehrson@r...>
> > > wrote:
> > > > I'm not getting this one:
> > > >
> > > > C:Eb^:G:Bb^ or
> > > >
> > > > 1/3:2/5:1/2:3/5
> > > >
> > > > How does the arithmetic work out on that one??
> > > >
> > > > Thanks!
> > > >
> > > > Joseph
> > >
> > > this is a good old just minor seventh chord. it can be
expressed
> as
> > > 10:12:15:18, and if you divide through by 30, this turns into
> > > 1/3:2/5:1/2:3/5. you could then divide through by 6 and
express
> it
> > as
> > > 1/18:1/15:1/12:1/10, indicating that the chord is symmetrical
> under
> > > mirror inversion.
> >
> >
> > ***Whoopie! It's dumb question time, and I'm the first with my
> hand
> > up:
> >
> > But, this is such a simple chord. Wouldn't a minor third be
> > something like 6:5?? I guess I'm still not getting the
numbers...
> >
> > Thanks!!!!!
>
> yes, you could write the chord as 5:6:15/2:9 if you wanted (just
the
> 10:12:15:18 divided through by 2), to highlight the 5:6 at the
bottom.

***There we go. Of course! Thanks, Paul!

JP

Let's say we have a "major seventh" chord in the Blackjack scale:

C#^:G#^:F<:B[

and then decide to *substitute* a Bb^ for the B[

What are we getting, if anything?? What is the relationship? Sure
makes an interesting effect, whatever the case. Beating from inner
voices all over the place, sounds like...

Thanks!

Joseph

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> Let's say we have a "major seventh" chord in the Blackjack scale:
>
> C#^:G#^:F<:B[

"major seventh"? this chord can be written as 0 350 700 933. what kind
of "major seventh" is that?

> and then decide to *substitute* a Bb^ for the B[

0 350 700 900?

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_44306.html#44817

<wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> wrote:
> > Let's say we have a "major seventh" chord in the Blackjack scale:
> >
> > C#^:G#^:F<:B[
>
> "major seventh"? this chord can be written as 0 350 700 933. what
kind of "major seventh" is that?

***Sorry, I should have said "dominant seventh", yes?, although this
kind of terminology doesn't make a lot of sense without "functional
harmony..." This is one of the common Blackjack seventh tetrads,
correct??

How would you get "350" for the F<?? That's the just "major" third
from the starting point, yes??

>
> > and then decide to *substitute* a Bb^ for the B[
>
> 0 350 700 900?

***Why are you starting with C#=0?? Are you always starting with
the root as 0?? In any case, wouldn't that make Bb the 900??

Thanks!

Joseph

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
>
> /tuning/topicId_44306.html#44817
>
>
> <wallyesterpaulrus@y...> wrote:
> > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> > wrote:
> > > Let's say we have a "major seventh" chord in the Blackjack
scale:
> > >
> > > C#^:G#^:F<:B[
> >
> > "major seventh"? this chord can be written as 0 350 700 933. what
> kind of "major seventh" is that?
>
>
> ***Sorry, I should have said "dominant seventh", yes?, although
this
> kind of terminology doesn't make a lot of sense without "functional
> harmony..." This is one of the common Blackjack seventh tetrads,
> correct??

?

> How would you get "350" for the F<?? That's the just "major" third
> from the starting point, yes??

no, C# to F is 400 cents, if you raise C# by 17 cents and lower F by
33 cents, that's 350 cents.

> > > and then decide to *substitute* a Bb^ for the B[
> >
> > 0 350 700 900?
>
> ***Why are you starting with C#=0??

C#^, since you put it as the first note.

> Are you always starting with
> the root as 0??

that's how we've always done it, for example in all the tuning
lab "harmonic entropy" studies.

> In any case, wouldn't that make Bb the 900??

Bb^, yes, 900 is what i wrote.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_44306.html#44833

> > > > C#^:G#^:F<:B[

I'm terribly sorry, Paul. This is *my* mistake, since it was written
late last night.

The chord in question is:

C#v:G#v:F<:B[

one of the Blackjack "dominant seventh" tetrads...

And I'm trying to compare it to the same chord with Bb^ substituting
for B[

Sorry for the confusion...

Joseph

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

/tuning/topicId_44306.html#44841

> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
>
> /tuning/topicId_44306.html#44833
>
> > > > > C#^:G#^:F<:B[
>
> I'm terribly sorry, Paul. This is *my* mistake, since it was
written
> late last night.
>
> The chord in question is:
>
> C#v:G#v:F<:B[
>
> one of the Blackjack "dominant seventh" tetrads...
>
> And I'm trying to compare it to the same chord with Bb^
substituting
> for B[
>
> Sorry for the confusion...
>
> Joseph

***Hi Paul,

Since you're away for a little bit, I'll try to answer this riddle:

I think now that Bb^:B[ constitutes one of this "11th" relationships
that are not shown on the lattice...

Right or wrong??...

buzz...

JP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
>
> /tuning/topicId_44306.html#44833
>
> > > > > C#^:G#^:F<:B[
>
> I'm terribly sorry, Paul. This is *my* mistake, since it was
written
> late last night.
>
> The chord in question is:
>
> C#v:G#v:F<:B[
>
> one of the Blackjack "dominant seventh" tetrads...

ah, ok! 0 383 700 967.

> And I'm trying to compare it to the same chord with Bb^
substituting
> for B[

0 383 700 933.

well, that's a dissonant chord all right . . . if you changed F< to E
(which is not in the blackjack scale) you would have a utonal tetrad,
but as it is you're neither otonal nor utonal . . .

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> ***Hi Paul,
>
> Since you're away for a little bit, I'll try to answer this riddle:
>
> I think now that Bb^:B[ constitutes one of this "11th"
relationships
> that are not shown on the lattice...
>
> Right or wrong??...
>
> buzz...
>
> JP

well, the ratios of 9 and 11 are not shown on the lattice, but Bb^:B[
is not one of them . . . you may need to look at this again:

http://72note.com/1/blackjackintervalmatrix.html

note that ratios of 9 are shown in green and ratios of 11 in cyan, in
accordance with george secor's coloring scheme . . .

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> /tuning/topicId_44306.html#44841
>
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> >
> > /tuning/topicId_44306.html#44833
> >
> > > > > > C#^:G#^:F<:B[
> >
> > I'm terribly sorry, Paul. This is *my* mistake, since it was
> written
> > late last night.
> >
> > The chord in question is:
> >
> > C#v:G#v:F<:B[
> >
> > one of the Blackjack "dominant seventh" tetrads...
> >
> > And I'm trying to compare it to the same chord with Bb^
> substituting
> > for B[
> >
> > Sorry for the confusion...
> >
> > Joseph
>
>
> ***Hi Paul,
>
> Since you're away for a little bit, I'll try to answer this riddle:
>
> I think now that Bb^:B[ constitutes one of this "11th"
relationships
> that are not shown on the lattice...
>
> Right or wrong??...
>
> buzz...
>
> JP

maybe you were thinking of F<:Bb^, which approximates the 11:8 ratio,
and thus falls on a cyan diagonal on

http://72note.com/1/blackjackintervalmatrix.html

this interval occurs in the dissonant chord you were asking
about . . .

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_44306.html#44882

> maybe you were thinking of F<:Bb^, which approximates the 11:8
ratio, and thus falls on a cyan diagonal on
>
> http://72note.com/1/blackjackintervalmatrix.html
>
> this interval occurs in the dissonant chord you were asking
> about . . .

***Thanks Paul. This is what I was looking for. When I alternate
the "normal" B[ in the C#v:G#v:F<:B[ to C#v:G#v:F<:Bb^ I get an 11thy
effect. That's what I thought, but wanted confirmed...

By the way, how does the arithmetic work with that? Do you figure
that F<:Bb^ is an 11:8 by looking at the other connections? How does
one go about that... it's probably not very difficult...

Well... if I go from F< to G, it's 8:7, yes? and if I go from G to
Bb^ it's 5:3??

And if I multiply 8/7 * 5/3 = 40/21 ???

That's not doing much for me... I must be doing something wrong?? :(

Thanks!

Joseph

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
>
> /tuning/topicId_44306.html#44882
>
> > maybe you were thinking of F<:Bb^, which approximates the 11:8
> ratio, and thus falls on a cyan diagonal on
> >
> > http://72note.com/1/blackjackintervalmatrix.html
> >
> > this interval occurs in the dissonant chord you were asking
> > about . . .
>
>
> ***Thanks Paul. This is what I was looking for. When I alternate
> the "normal" B[ in the C#v:G#v:F<:B[ to C#v:G#v:F<:Bb^ I get an
11thy
> effect. That's what I thought, but wanted confirmed...
>
> By the way, how does the arithmetic work with that? Do you figure
> that F<:Bb^ is an 11:8 by looking at the other connections? How
does
> one go about that... it's probably not very difficult...
>
> Well... if I go from F< to G, it's 8:7, yes?

yes.

> and if I go from G to
> Bb^ it's 5:3??

6/5.

> And if I multiply 8/7 * 5/3 = 40/21 ???

8/7 * 6/5 = 48/35.

> That's not doing much for me... I must be doing something wrong??
:(
>
> Thanks!

48/35 is correct -- but remember that all the intervals are tempered.
as it turns out, "48/35" is the same as "11/8" in 72-equal, or in
other words,

48/35 divided by 11/8 = 384/385

vanishes in 72-equal. 384/385 vanishing is what allows you to see the
11:8 relationships between the top and bottom of each hexany, and is
a basic feature of miracle in the 11-limit -- much like 225/224,
1029/1024, and 2401/2400 vanishing are basic features of miracle in
the 7-limit.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_44306.html#44901

> >
> > Well... if I go from F< to G, it's 8:7, yes?
>
> yes.
>
> > and if I go from G to
> > Bb^ it's 5:3??
>
> 6/5.
>

***Paul, I'm not thoroughly understanding how one tells the
difference between a 6/5 and a 5/3 on the lattice. Similarly an 8/7
or a 7/4. I "guessed" right the first time, but then for the second
one my "luck ran out..." :(

>
> 8/7 * 6/5 = 48/35.
>
> 48/35 is correct -- but remember that all the intervals are
tempered. as it turns out, "48/35" is the same as "11/8" in 72-equal,
or in other words,
>
> 48/35 divided by 11/8 = 384/385
>
> vanishes in 72-equal. 384/385 vanishing is what allows you to see
the 11:8 relationships between the top and bottom of each hexany, and
is a basic feature of miracle in the 11-limit -- much like 225/224,
> 1029/1024, and 2401/2400 vanishing are basic features of miracle in
> the 7-limit.

***Oh! So, obviously 384/385 is a comma that "vanishes" or makes
48/35=11/8 in this case. It's great to be able to look at the hexany
for this! I'd never really done this; and it's quite important, I
think!

But the other commas you mention for the 7-limit must *also* be on
this Blackjack lattice, yes? Or are they a part of 72-tET that is
*not* a part of Blackjack??

THANKS!!!

Joseph

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
>
> /tuning/topicId_44306.html#44901
>
> > >
> > > Well... if I go from F< to G, it's 8:7, yes?
> >
> > yes.
> >
> > > and if I go from G to
> > > Bb^ it's 5:3??
> >
> > 6/5.
> >
>
> ***Paul, I'm not thoroughly understanding how one tells the
> difference between a 6/5 and a 5/3 on the lattice. Similarly an 8/7
> or a 7/4. I "guessed" right the first time, but then for the second
> one my "luck ran out..." :(

just remember how the 4:5:6:7 chord is oriented on the lattice, and
you'll always know!

>
> >
> > 8/7 * 6/5 = 48/35.
> >
> > 48/35 is correct -- but remember that all the intervals are
> tempered. as it turns out, "48/35" is the same as "11/8" in
72-equal,
> or in other words,
> >
> > 48/35 divided by 11/8 = 384/385
> >
> > vanishes in 72-equal. 384/385 vanishing is what allows you to see
> the 11:8 relationships between the top and bottom of each hexany,
and
> is a basic feature of miracle in the 11-limit -- much like 225/224,
> > 1029/1024, and 2401/2400 vanishing are basic features of miracle
in
> > the 7-limit.
>
> ***Oh! So, obviously 384/385 is a comma that "vanishes" or makes
> 48/35=11/8 in this case. It's great to be able to look at the
hexany
> for this! I'd never really done this; and it's quite important, I
> think!
>
> But the other commas you mention for the 7-limit must *also* be on
> this Blackjack lattice, yes?

yes, they're the intervals at which the lattice repeats itself. thus
for any given note, the lattice will show the nearest occurences of
this same note separated by this interval.

> Or are they a part of 72-tET that is
> *not* a part of Blackjack??

rest assured, joseph, that the unison is a very common interval in
blackjack :)

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_44306.html#44990

> > ***Paul, I'm not thoroughly understanding how one tells the
> > difference between a 6/5 and a 5/3 on the lattice. Similarly an
8/7 or a 7/4. I "guessed" right the first time, but then for the
second one my "luck ran out..." :(
>
> just remember how the 4:5:6:7 chord is oriented on the lattice, and
> you'll always know!
>

***Pffffft... ! How easy this is. Shudda thunk o' it myself... !

> >
> > But the other commas you mention for the 7-limit must *also* be
on this Blackjack lattice, yes?
>
> yes, they're the intervals at which the lattice repeats itself.
thus for any given note, the lattice will show the nearest occurences
of this same note separated by this interval.
>
> > Or are they a part of 72-tET that is
> > *not* a part of Blackjack??
>
> rest assured, joseph, that the unison is a very common interval in
> blackjack :)

***Ha, ha... gotcha! Another one that's perfectly transparent now
that you've explained it to me!!! :)

JP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
>
> /tuning/topicId_44306.html#44990
>
> > > ***Paul, I'm not thoroughly understanding how one tells the
> > > difference between a 6/5 and a 5/3 on the lattice. Similarly
an
> 8/7 or a 7/4. I "guessed" right the first time, but then for the
> second one my "luck ran out..." :(
> >
> > just remember how the 4:5:6:7 chord is oriented on the lattice,
and
> > you'll always know!
> >
>
> ***Pffffft... ! How easy this is. Shudda thunk o' it myself... !
>
> > >
> > > But the other commas you mention for the 7-limit must *also* be
> on this Blackjack lattice, yes?
> >
> > yes, they're the intervals at which the lattice repeats itself.
> thus for any given note, the lattice will show the nearest
occurences
> of this same note separated by this interval.
> >
> > > Or are they a part of 72-tET that is
> > > *not* a part of Blackjack??
> >
> > rest assured, joseph, that the unison is a very common interval
in
> > blackjack :)
>
> ***Ha, ha... gotcha! Another one that's perfectly transparent now
> that you've explained it to me!!! :)
>
> JP

well, i kinda "copped out" on that one . . . there are certainly
vanishing unison vectors in 72-equal that *don't* have any relevance
for blackjack . . . for example the kleisma -- to get to the kleisma
you need five consecutive ~6:5 minor thirds, something you'll never
find in the blackjack scale (or lattice)! same for the pythagorean
comma, for which you need 12 consecutive ~3:2 perfect fifths -- a
construct not found in blackjack! there are 7-limit examples as
well . . .

but for the 7-limit "commas" in question, 225:224, 1029:1024, and
2401:2400, tempering out any two of them (the third one is not
independent and will vanish as a consequence) is enough to define
miracle temperament (at least within the 7-limit), and therefore the
secor generator, and therefore the blackjack (or canasta, or
studloco . . .) scale. but not 72-equal. in the 7-limit (which is 3-
dimensional, as long as we ignore octave specificity), it takes three
_independent_ vanishing "commas" to define an equal temperament, but
only two to define a linear temperament. just one, and you have a
planar temperament.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_44306.html#45022

>
> well, i kinda "copped out" on that one . . . there are certainly
> vanishing unison vectors in 72-equal that *don't* have any
relevance for blackjack . . . for example the kleisma -- to get to
the kleisma you need five consecutive ~6:5 minor thirds, something
you'll never
> find in the blackjack scale (or lattice)! same for the pythagorean
> comma, for which you need 12 consecutive ~3:2 perfect fifths -- a
> construct not found in blackjack! there are 7-limit examples as
> well . . .
>
> but for the 7-limit "commas" in question, 225:224, 1029:1024, and
> 2401:2400, tempering out any two of them (the third one is not
> independent and will vanish as a consequence) is enough to define
> miracle temperament (at least within the 7-limit), and therefore
the
> secor generator, and therefore the blackjack (or canasta, or
> studloco . . .) scale. but not 72-equal. in the 7-limit (which is 3-
> dimensional, as long as we ignore octave specificity), it takes
three
> _independent_ vanishing "commas" to define an equal temperament,
but
> only two to define a linear temperament. just one, and you have a
> planar temperament.

***Thanks, Paul, for filling this out some more. I appreciate it!
So, by the paragraph above, it seems Blackjack would be classified
a "linear" temperament??

Thanks!

Joseph

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> ***Thanks, Paul, for filling this out some more. I appreciate it!
> So, by the paragraph above, it seems Blackjack would be classified
> a "linear" temperament??

Meantone is a linear temperament, and diatonic is a meantone scale.
In the same way, miracle is a linear temperament and Blackjack is a
miracle scale.

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
>
> /tuning/topicId_44306.html#45022
>
> >
> > well, i kinda "copped out" on that one . . . there are certainly
> > vanishing unison vectors in 72-equal that *don't* have any
> relevance for blackjack . . . for example the kleisma -- to get to
> the kleisma you need five consecutive ~6:5 minor thirds, something
> you'll never
> > find in the blackjack scale (or lattice)! same for the
pythagorean
> > comma, for which you need 12 consecutive ~3:2 perfect fifths -- a
> > construct not found in blackjack! there are 7-limit examples as
> > well . . .
> >
> > but for the 7-limit "commas" in question, 225:224, 1029:1024, and
> > 2401:2400, tempering out any two of them (the third one is not
> > independent and will vanish as a consequence) is enough to define
> > miracle temperament (at least within the 7-limit), and therefore
> the
> > secor generator, and therefore the blackjack (or canasta, or
> > studloco . . .) scale. but not 72-equal. in the 7-limit (which is
3-
> > dimensional, as long as we ignore octave specificity), it takes
> three
> > _independent_ vanishing "commas" to define an equal temperament,
> but
> > only two to define a linear temperament. just one, and you have a
> > planar temperament.
>
> ***Thanks, Paul, for filling this out some more. I appreciate it!

> So, by the paragraph above, it seems Blackjack would be classified
> a "linear" temperament??
>
> Thanks!
>
> Joseph

miracle is the linear temperament here, blackjack is the linear scale
with the same generator and period . . .

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

/tuning/topicId_44306.html#45040

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > ***Thanks, Paul, for filling this out some more. I appreciate
it!
> > So, by the paragraph above, it seems Blackjack would be
classified
> > a "linear" temperament??
>
> Meantone is a linear temperament, and diatonic is a meantone scale.
> In the same way, miracle is a linear temperament and Blackjack is a
> miracle scale.

***Got it. Thanks, Gene!

JP

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_44306.html#45046

>
> miracle is the linear temperament here, blackjack is the linear
scale with the same generator and period . . .

***Thanks, Paul. But why does the Secor generator create a scale
that has only *two* commas tempered out, and why does meantone have
only *two* tempered out??

I guess meantone tempers out the 81:80 which is the Syntonic, yes,
and it tempers out the Pythagorean comma...

So which one *doesn't* it temper out?? And likewise with Miracle??

Thanks!

Joseph

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
>
> /tuning/topicId_44306.html#45046
>
> >
> > miracle is the linear temperament here, blackjack is the linear
> scale with the same generator and period . . .
>
> ***Thanks, Paul. But why does the Secor generator create a scale
> that has only *two* commas tempered out,

in the 7-limit, yes it's two, since any linear tuning in the 7-limit
(which is 3-dimensional) must have 3 - 1 = 2 independent commas
tempered out.

> and why does meantone have
> only *two* tempered out??

meantone in the 5-limit only has *one* comma tempered out. any linear
tuning in the 5-limit (which is 2-dimensional) must have 2 - 1 = 1
comma tempered out.

> I guess meantone tempers out the 81:80 which is the Syntonic, yes,
> and it tempers out the Pythagorean comma...

meantone doesn't temper out the pythagorean comma. the pythagorean
comma in meantone usually changes direction and is typically about 40
cents. if you temper out both the pythagorean comma and the syntonic
comma, you get 12-equal (or, if you do it irregularly, a closed
12-tone well-temperament).

> So which one *doesn't* it temper out??

all the others! the various diesis, diaschisma, schisma, kleisma,
etc.

> And likewise with Miracle??

miracle, in the 7-limit, doesn't temper out any commas that aren't a
combination of some number of 225:224s and some number of 2401:2400s
(you can substitute 1029:1024 for either of these). so it doesn't
temper out the syntonic comma, or any of the important 5-limit
commas, or 64:63, or 126:125, or 245:243, etc, etc.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_44306.html#45080

> in the 7-limit, yes it's two, since any linear tuning in the 7-
limit (which is 3-dimensional) must have 3 - 1 = 2 independent commas
> tempered out.
>
> > and why does meantone have
> > only *two* tempered out??
>
> meantone in the 5-limit only has *one* comma tempered out. any
linear tuning in the 5-limit (which is 2-dimensional) must have 2 - 1
= 1 comma tempered out.
>

***Thanks, Paul. I'm catching on to the pattern... :)

> > I guess meantone tempers out the 81:80 which is the Syntonic,
yes, and it tempers out the Pythagorean comma...
>
> meantone doesn't temper out the pythagorean comma.

***Wow. I shudda known that...

the pythagorean
> comma in meantone usually changes direction and is typically about
40 cents. if you temper out both the pythagorean comma and the
syntonic comma, you get 12-equal (or, if you do it irregularly, a
closed 12-tone well-temperament).
>
> > So which one *doesn't* it temper out??
>
> all the others! the various diesis, diaschisma, schisma, kleisma,
> etc.
>
> > And likewise with Miracle??
>
> miracle, in the 7-limit, doesn't temper out any commas that aren't
a
> combination of some number of 225:224s and some number of
2401:2400s (you can substitute 1029:1024 for either of these). so it
doesn't temper out the syntonic comma, or any of the important 5-
limit commas, or 64:63, or 126:125, or 245:243, etc, etc.

***Thanks, Paul. I'll keep working on this using the _Forms of
Tonality_. I find this fascinating, and would love to gradually get
a better "grip" on this whole "comma tempering" idea...

JP