Evangelina

With reference to Evangelina,

http://www.anaphoria.com/trans22.PDF

are there any charts relating to this tuning of the kind given for the
previous 7 - limit 22 tone tuning where all the modes are laid out on a
grid?

The "Cassandra" tuning was mentioned in a previous post. Does anyone
have a reference for further details? Thanks in anticipation.

Kind Regards

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> With reference to Evangelina,
>
> http://www.anaphoria.com/trans22.PDF
>
> are there any charts relating to this tuning of the kind given for
the
> previous 7 - limit 22 tone tuning where all the modes are laid out
on a
> grid?

that would be fairly straightforward to produce. note that the tuning
has some alternatives in it -- do you have a list of tetrachords that
could guide us in choosing those alternatives most suitable for your
purposes?

> The "Cassandra" tuning was mentioned in a previous post. Does anyone
> have a reference for further details?

http://www.anaphoria.com/tres.PDF, pp. 7-11 is one example. there are
others, since graham lists 'cassandra 1' and 'cassandra 2' based
linear temperaments as well as his own variant.

paulerlich wrote:

> http://www.anaphoria.com/tres.PDF, pp. 7-11 is one example. there are
> others, since graham lists 'cassandra 1' and 'cassandra 2' based
> linear temperaments as well as his own variant.

They're both from that file. Consecutive pages as I recall. He doesn't
declare them as being distinct, but the two keyboard mappings don't match
up.

Graham

Alison Monteith wrote:

> The "Cassandra" tuning was mentioned in a previous post. Does anyone
> have a reference for further details? Thanks in anticipation.

http://www.anaphoria.com/tres.pdf

Graham

paulerlich wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> > With reference to Evangelina,
> >
> > http://www.anaphoria.com/trans22.PDF
> >
> > are there any charts relating to this tuning of the kind given for
> the
> > previous 7 - limit 22 tone tuning where all the modes are laid out
> on a
> > grid?
>
> that would be fairly straightforward to produce. note that the tuning
> has some alternatives in it -- do you have a list of tetrachords that
> could guide us in choosing those alternatives most suitable for your
> purposes?

Yes, but there are fourteen. I chose them simply because I love the sheer beauty of them and their
the melodic possibilities and because of the similarities and contrasts between them. Oh and
because most have superparticular steps. Here they are, steps between a la "Divisions", in order
Enharmonic, Chromatic, Diatonic: -

28/27, 36/35, 5/4

16/15, 15/14, 7/6

10/9, 36/35, 7/6

22/21, 12/11, 7/6

9/8, 64/63, 7/6

18/17, 17/16, 32/27

17/16, 16/15, 20/17

28/27, 8/7, 9/8

12/11, 11/10, 10,9

35/33, 11/10, 8/7

49/48, 8/7, 8/7

14/13, 13/12, 8/7 (and possibly 13/12, 14,13, 8/7)

19/18, 21/19, 8/7

A tall order you might say, but I have the material for enough tubes. I just wonder about the
harmonic possibilities of such a random bunch of tetrachords.

>
>
> > The "Cassandra" tuning was mentioned in a previous post. Does anyone
> > have a reference for further details?
>
> http://www.anaphoria.com/tres.PDF, pp. 7-11 is one example. there are
> others, since graham lists 'cassandra 1' and 'cassandra 2' based
> linear temperaments as well as his own variant.

Thanks I'll follow these up.

Kind Regards

graham@microtonal.co.uk wrote:

> Alison Monteith wrote:
>
> > The "Cassandra" tuning was mentioned in a previous post. Does anyone
> > have a reference for further details? Thanks in anticipation.
>
> http://www.anaphoria.com/tres.pdf
>
> Graham

Gotcha. Many Thanks.

Regards

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
>
> paulerlich wrote:
>
> > --- In tuning@y..., Alison Monteith <alison.monteith3@w...>
wrote:
> > > With reference to Evangelina,
> > >
> > > http://www.anaphoria.com/trans22.PDF
> > >
> > > are there any charts relating to this tuning of the kind given
for
> > the
> > > previous 7 - limit 22 tone tuning where all the modes are
laid out
> > on a
> > > grid?
> >
> > that would be fairly straightforward to produce. note that the
tuning
> > has some alternatives in it -- do you have a list of tetrachords
that
> > could guide us in choosing those alternatives most suitable
for your
> > purposes?
>
> Yes, but there are fourteen. I chose them simply because I love
the sheer beauty of them and their
> the melodic possibilities and because of the similarities and
contrasts between them. Oh and
> because most have superparticular steps. Here they are,
steps between a la "Divisions", in order
> Enharmonic, Chromatic, Diatonic: -
>
> 28/27, 36/35, 5/4
>
> 16/15, 15/14, 7/6
>
> 10/9, 36/35, 7/6
>
> 22/21, 12/11, 7/6
>
> 9/8, 64/63, 7/6
>
> 18/17, 17/16, 32/27
>
> 17/16, 16/15, 20/17
>
> 28/27, 8/7, 9/8
>
> 12/11, 11/10, 10,9
>
> 35/33, 11/10, 8/7
>
> 49/48, 8/7, 8/7
>
> 14/13, 13/12, 8/7 (and possibly 13/12, 14,13, 8/7)
>
> 19/18, 21/19, 8/7
>
> A tall order you might say, but I have the material for enough
tubes. I just wonder about the
> harmonic possibilities of such a random bunch of tetrachords.

would you allow different tonics for each of these? that might
help bring the number of tones to a manageable quantity.

paulerlich wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> >
> >
> > paulerlich wrote:
> >
> > > --- In tuning@y..., Alison Monteith <alison.monteith3@w...>
> wrote:
> > > > With reference to Evangelina,
> > > >
> > > > http://www.anaphoria.com/trans22.PDF
> > > >
> > > > are there any charts relating to this tuning of the kind given
> for
> > > the
> > > > previous 7 - limit 22 tone tuning where all the modes are
> laid out
> > > on a
> > > > grid?
> > >
> > > that would be fairly straightforward to produce. note that the
> tuning
> > > has some alternatives in it -- do you have a list of tetrachords
> that
> > > could guide us in choosing those alternatives most suitable
> for your
> > > purposes?
> >
> > Yes, but there are fourteen. I chose them simply because I love
> the sheer beauty of them and their
> > the melodic possibilities and because of the similarities and
> contrasts between them. Oh and
> > because most have superparticular steps. Here they are,
> steps between a la "Divisions", in order
> > Enharmonic, Chromatic, Diatonic: -
> >
> > 28/27, 36/35, 5/4
> >
> > 16/15, 15/14, 7/6
> >
> > 10/9, 36/35, 7/6
> >
> > 22/21, 12/11, 7/6
> >
> > 9/8, 64/63, 7/6
> >
> > 18/17, 17/16, 32/27
> >
> > 17/16, 16/15, 20/17
> >
> > 28/27, 8/7, 9/8
> >
> > 12/11, 11/10, 10,9
> >
> > 35/33, 11/10, 8/7
> >
> > 49/48, 8/7, 8/7
> >
> > 14/13, 13/12, 8/7 (and possibly 13/12, 14,13, 8/7)
> >
> > 19/18, 21/19, 8/7
> >
> > A tall order you might say, but I have the material for enough
> tubes. I just wonder about the
> > harmonic possibilities of such a random bunch of tetrachords.
>
> would you allow different tonics for each of these? that might
> help bring the number of tones to a manageable quantity.
>

I would have thought the opposite, but to answer your question, yes, I would allow for different
tonics which would give me me true modal modulation and probably some interesting interval shifts
between tonics.

Regards

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
>
> paulerlich wrote:
>
> > --- In tuning@y..., Alison Monteith <alison.monteith3@w...>
wrote:
> > >
> > >
> > > paulerlich wrote:
> > >
> > > > --- In tuning@y..., Alison Monteith
<alison.monteith3@w...>
> > wrote:
> > > > > With reference to Evangelina,
> > > > >
> > > > > http://www.anaphoria.com/trans22.PDF
> > > > >
> > > > > are there any charts relating to this tuning of the kind
given
> > for
> > > > the
> > > > > previous 7 - limit 22 tone tuning where all the modes
are
> > laid out
> > > > on a
> > > > > grid?
> > > >
> > > > that would be fairly straightforward to produce. note that
the
> > tuning
> > > > has some alternatives in it -- do you have a list of
tetrachords
> > that
> > > > could guide us in choosing those alternatives most
suitable
> > for your
> > > > purposes?
> > >
> > > Yes, but there are fourteen. I chose them simply because I
love
> > the sheer beauty of them and their
> > > the melodic possibilities and because of the similarities
and
> > contrasts between them. Oh and
> > > because most have superparticular steps. Here they are,
> > steps between a la "Divisions", in order
> > > Enharmonic, Chromatic, Diatonic: -
> > >
> > > 28/27, 36/35, 5/4
> > >
> > > 16/15, 15/14, 7/6
> > >
> > > 10/9, 36/35, 7/6
> > >
> > > 22/21, 12/11, 7/6
> > >
> > > 9/8, 64/63, 7/6
> > >
> > > 18/17, 17/16, 32/27
> > >
> > > 17/16, 16/15, 20/17
> > >
> > > 28/27, 8/7, 9/8
> > >
> > > 12/11, 11/10, 10,9
> > >
> > > 35/33, 11/10, 8/7
> > >
> > > 49/48, 8/7, 8/7
> > >
> > > 14/13, 13/12, 8/7 (and possibly 13/12, 14,13, 8/7)
> > >
> > > 19/18, 21/19, 8/7
> > >
> > > A tall order you might say, but I have the material for
enough
> > tubes. I just wonder about the
> > > harmonic possibilities of such a random bunch of
tetrachords.
> >
> > would you allow different tonics for each of these? that might
> > help bring the number of tones to a manageable quantity.
> >
>
> I would have thought the opposite,

well, i'm thinking, for example, that a tuning consisting of
harmonics over a low fundamental would be capable of most or
all of these tetrachords, though they'd have to have different
tonics. see what i'm getting at?

paulerlich wrote:

> well, i'm thinking, for example, that a tuning consisting of
> harmonics over a low fundamental would be capable of most or
> all of these tetrachords, though they'd have to have different
> tonics. see what i'm getting at?

I get your drift - I'm not geared up to work these things out without great mental gymnastics.

Regards

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
>
> paulerlich wrote:
>
> > well, i'm thinking, for example, that a tuning consisting of
> > harmonics over a low fundamental would be capable of most or
> > all of these tetrachords, though they'd have to have different
> > tonics. see what i'm getting at?
>
>I get your drift - I'm not geared up to work these things out
>without great mental gymnastics.

just call me mary lou retton :)

actually, now that i look at your tetrachords, they appear to favor a
subharmonic (utonal) rather than harmonic (otonal) framework. any
reason for this? i.e., why 16/15, 15/14, 7/6 and not 15/14, 16/15,
7/6, etc.? i'm assuming the intervals are consecutive intervals
upwards -- perhaps i'm mistaken, and they're actually consecutive
downward intervals?

paulerlich wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> >
> >
> > paulerlich wrote:
> >
> > > well, i'm thinking, for example, that a tuning consisting of
> > > harmonics over a low fundamental would be capable of most or
> > > all of these tetrachords, though they'd have to have different
> > > tonics. see what i'm getting at?
> >
> >I get your drift - I'm not geared up to work these things out
> >without great mental gymnastics.
>
> just call me mary lou retton :)
>
> actually, now that i look at your tetrachords, they appear to favor a
> subharmonic (utonal) rather than harmonic (otonal) framework. any
> reason for this? i.e., why 16/15, 15/14, 7/6 and not 15/14, 16/15,
> 7/6, etc.? i'm assuming the intervals are consecutive intervals
> upwards -- perhaps i'm mistaken, and they're actually consecutive
> downward intervals?

Mary-Lou (you asked for it),

They are all consecutive intervals upwards. I chose them after auditioning as many as my ears
could take over a few days and settled on those I listed. Must be coincidence or just an
idiosyncracy in my preferences. The particular example you mention is given in "Divisions" as an
Al-Farabi chromatic with a characteristic interval of 7/6. A note is given to the effect that "In
re-arranged form.....is the lower tetrachord of the modern Islamic mode Higaz" which I assume must
be the 15/14, 16/15, 7/6 re-ordering you mention, because, as the note continues, "the Turkish
mode Zirgule is reported to contain this tetrachord with 7/6 medially.

Kind Regards

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

> They are all consecutive intervals upwards. I chose them after
auditioning as many as my ears
> could take over a few days and settled on those I listed. Must be
coincidence or just an
> idiosyncracy in my preferences.

subharmonic it is, then! i give the string lengths:

(..128-126-120)-112-108-105-102-96-90-88-84-77-72-70-68-66-65-64-63-60

this is how your tetrachords would be accomodated:

> > 28/27, 36/35, 5/4

112-108-105-84

> > 16/15, 15/14, 7/6

16-15-14-12 -> 128-120-112-96 = 96-90-84-72

> > 10/9, 36/35, 7/6

40-36-35-30 -> 120-108-105-90

> > 22/21, 12/11, 7/6

88-84-77-66

> > 9/8, 64/63, 7/6

72-64-63-54

> > 18/17, 17/16, 32/27

36-34-32-27 -> 72-68-64-54

> > 17/16, 16/15, 20/17

68-64-60-51 -> 136-128-120-102

> > 28/27, 8/7, 9/8

this one doesn't suggest a subharmonic series - perhaps you can
modify it?

> > 12/11, 11/10, 10/9

12-11-10-9 -> 84-77-70-63 = 72-66-60-54

> > 35/33, 11/10, 8/7

140-132-120-105

> > 49/48, 8/7, 8/7

this one doesn't suggest a subharmonic series - perhaps you can
modify it?

> > 14/13, 13/12, 8/7

28-26-24-21 -> 140-130-120-105

> (and possibly 13/12, 14/13, 8/7)

not subharmonic, i'm afraid

> > 19/18, 21/19, 8/7

ouch. perhaps you'd be willing to accept a close substitute?

anyway, we are able to accomodate 11 of your tetrachords, some in
multiple transpositions, with the subharmonic series above.

in frequency ratios, which are more familiar these days, the scale is

1
15/14
10/9
8/7
20/17
5/4
4/3
15/11
10/7
120/77
5/3
12/7
30/17
20/11
24/13
15/8
40/21
2

or in cents,

0
119.44
182.4
231.17
281.36
386.31
498.04
536.95
617.49
768.12
884.36
933.13
983.31
1035
1061.4
1088.3
1115.5
1200

(the choice of tonic here is arbitrary, of course, as you'll be
modulating quite a bit).

paulerlich wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> > They are all consecutive intervals upwards. I chose them after
> auditioning as many as my ears
> > could take over a few days and settled on those I listed. Must be
> coincidence or just an
> > idiosyncracy in my preferences.
>
> subharmonic it is, then! i give the string lengths:
>
> (..128-126-120)-112-108-105-102-96-90-88-84-77-72-70-68-66-65-64-63-60
>
> this is how your tetrachords would be accomodated:
>
> > > 28/27, 36/35, 5/4
>
> 112-108-105-84
>
> > > 16/15, 15/14, 7/6
>
> 16-15-14-12 -> 128-120-112-96 = 96-90-84-72
>
> > > 10/9, 36/35, 7/6
>
> 40-36-35-30 -> 120-108-105-90
>
> > > 22/21, 12/11, 7/6
>
> 88-84-77-66
>
> > > 9/8, 64/63, 7/6
>
> 72-64-63-54
>
> > > 18/17, 17/16, 32/27
>
> 36-34-32-27 -> 72-68-64-54
>
> > > 17/16, 16/15, 20/17
>
> 68-64-60-51 -> 136-128-120-102
>
> > > 28/27, 8/7, 9/8
>
> this one doesn't suggest a subharmonic series - perhaps you can
> modify it?
>
> > > 12/11, 11/10, 10/9
>
> 12-11-10-9 -> 84-77-70-63 = 72-66-60-54
>
> > > 35/33, 11/10, 8/7
>
> 140-132-120-105
>
> > > 49/48, 8/7, 8/7
>
> this one doesn't suggest a subharmonic series - perhaps you can
> modify it?
>
> > > 14/13, 13/12, 8/7
>
> 28-26-24-21 -> 140-130-120-105
>
> > (and possibly 13/12, 14/13, 8/7)
>
> not subharmonic, i'm afraid
>
> > > 19/18, 21/19, 8/7
>
> ouch. perhaps you'd be willing to accept a close substitute?
>
> anyway, we are able to accomodate 11 of your tetrachords, some in
> multiple transpositions, with the subharmonic series above.
>
> in frequency ratios, which are more familiar these days, the scale is
>
> 1
> 15/14
> 10/9
> 8/7
> 20/17
> 5/4
> 4/3
> 15/11
> 10/7
> 120/77
> 5/3
> 12/7
> 30/17
> 20/11
> 24/13
> 15/8
> 40/21
> 2
>
> or in cents,
>
> 0
> 119.44
> 182.4
> 231.17
> 281.36
> 386.31
> 498.04
> 536.95
> 617.49
> 768.12
> 884.36
> 933.13
> 983.31
> 1035
> 1061.4
> 1088.3
> 1115.5
> 1200
>
> (the choice of tonic here is arbitrary, of course, as you'll be
> modulating quite a bit).

Phew, quite a bit of work there. Great. Many thanks. I'll take some time out to examine it and see
what I can do about the other tetrachords.

Kind Regards