Thirds and the diatonic collection.

Sequences of major and minor thirds making the diatonic collection
(symmetric)

in 12 EDO

2 5 9 0 4 7 11 2

in 19 EDO

3 8 14 0 6 11 17 3

M

This is obvious. As for Kleisma - I have no idea - but it seemed interesting
to wonder if other 'tonal' collections might exist if other paths from a
pitch to another could be drawn.
>>
>> Yet is is interesting to note that a thirds route is that which
> makes up the
>> diatonic collection (alternating one third with the other).
>>

--- In tuning@y..., Mark Gould <mark.gould@a...> wrote:

> but it seemed interesting
> to wonder if other 'tonal' collections might exist if other paths
from a
> pitch to another could be drawn.

yes -- the diatonic scale can be seen as lying along a path (line),
and so can an impressive proportion of other scales that have been
proposed. i hope gene will explain more about his concept of "scales
along a line" either here or on tuning-math. i've visualized it my
own way, also explained on tuning-math. the vanishing unison vectors
are essential -- this is the syntonic comma in the case of the
diatonic scale.

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_40376.html#40404

wrote:
> --- In tuning@y..., Mark Gould <mark.gould@a...> wrote:
>
> > but it seemed interesting
> > to wonder if other 'tonal' collections might exist if other paths
> from a
> > pitch to another could be drawn.
>
> yes -- the diatonic scale can be seen as lying along a path (line),
> and so can an impressive proportion of other scales that have been
> proposed. i hope gene will explain more about his concept
of "scales
> along a line" either here or on tuning-math. i've visualized it my
> own way, also explained on tuning-math. the vanishing unison
vectors
> are essential -- this is the syntonic comma in the case of the
> diatonic scale.

***This is, of course, shown in all the graphs we've been looking at
lately...

J. Pehrson

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
>
> /tuning/topicId_40376.html#40404
>
>
> wrote:
> > --- In tuning@y..., Mark Gould <mark.gould@a...> wrote:
> >
> > > but it seemed interesting
> > > to wonder if other 'tonal' collections might exist if other
paths
> > from a
> > > pitch to another could be drawn.
> >
> > yes -- the diatonic scale can be seen as lying along a path
(line),
> > and so can an impressive proportion of other scales that have
been
> > proposed. i hope gene will explain more about his concept
> of "scales
> > along a line" either here or on tuning-math. i've visualized it
my
> > own way, also explained on tuning-math. the vanishing unison
> vectors
> > are essential -- this is the syntonic comma in the case of the
> > diatonic scale.
>
>
> ***This is, of course, shown in all the graphs we've been looking
at
> lately...
>
> J. Pehrson

not really . . . i'm talking about scales whose pitches lie along a
line in the lattice (bingo card), not equal temperaments whose errors
lie along a line in a perfect fifth / major third (/ minor third)
plot.

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_40376.html#40425

wrote:
> --- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
> > --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
> >
> > /tuning/topicId_40376.html#40404
> >
> >
> > wrote:
> > > --- In tuning@y..., Mark Gould <mark.gould@a...> wrote:
> > >
> > > > but it seemed interesting
> > > > to wonder if other 'tonal' collections might exist if other
> paths
> > > from a
> > > > pitch to another could be drawn.
> > >
> > > yes -- the diatonic scale can be seen as lying along a path
> (line),
> > > and so can an impressive proportion of other scales that have
> been
> > > proposed. i hope gene will explain more about his concept
> > of "scales
> > > along a line" either here or on tuning-math. i've visualized it
> my
> > > own way, also explained on tuning-math. the vanishing unison
> > vectors
> > > are essential -- this is the syntonic comma in the case of the
> > > diatonic scale.
> >
> >
> > ***This is, of course, shown in all the graphs we've been looking
> at
> > lately...
> >
> > J. Pehrson
>
> not really . . . i'm talking about scales whose pitches lie along a
> line in the lattice (bingo card), not equal temperaments whose
errors
> lie along a line in a perfect fifth / major third (/ minor third)
> plot.

***Hi Paul!

But, aren't all the scales in the "bingo cards" ETs?? I must be
missing something. Please "fill me in" if you have the time.

Thanks!

Joseph

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

> ***Hi Paul!
>
> But, aren't all the scales in the "bingo cards" ETs?? I must be
> missing something. Please "fill me in" if you have the time.
>
> Thanks!
>
> Joseph

i'm talking about scales like the diatonic scale, and the blackjack
scale.

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_40376.html#40446

wrote:
> --- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
>
> > ***Hi Paul!
> >
> > But, aren't all the scales in the "bingo cards" ETs?? I must be
> > missing something. Please "fill me in" if you have the time.
> >
> > Thanks!
> >
> > Joseph
>
> i'm talking about scales like the diatonic scale, and the blackjack
> scale.

***Oh! So, then you're talking about *subsets* of the bingo card
ETs...

JP