Yahoo Tuning Groups Ultimate Backup tuning Sagittal79

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Dear George and Dave, I prepared a font especially for usage with
79/80 MOS
> 159-tET, and await your approval. It may be downloaded here:
>
> http://www.ozanyarman.com/misc/Sagittal79.pdf
>
> http://www.ozanyarman.com/misc/79mos159tET.ttf

Hi Oz,

I only just came across this message. Sorry.

My first reaction was: Why not just use the standard font and use
software to map it to the keyboard however you want? Also, we'd
normally use the approximate-look-alike latin characters v k \ e / y ^
rather than a physical layout on the keyboard, and we don't see the
need to combine multiple symbols into a single character in the font.

But I know you wouldn't have gone to so much trouble unless you had a
real need.

We'd prefer not have a proliferation of modified Sagittal fonts, but
we'd rather have you using some modified version than not use it at all.

We note that combining down sagittals with double flats or up
sagittals with double sharps results in combinations that are
extremely unlikely to ever be needed and they do not have a pure
sagittal equivalent. So we'd prefer you didn't have them in the font.
But again, if you have a real need, go ahead.

Thank you for acknowledging the original source. Could you also please
include the URL of the sagittal website.
http://dkeenan.com/sagittal

Thanks Oz.

-- Dave Keenan

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

----- Original Message -----
From: "Dave Keenan" <d.keenan@bigpond.net.au>
To: <tuning@yahoogroups.com>
Sent: 02 Mayï¿½s 2007 ï¿½arï¿½amba 1:33
Subject: [tuning] Re: Sagittal79

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > Dear George and Dave, I prepared a font especially for usage with
> 79/80 MOS
> > 159-tET, and await your approval. It may be downloaded here:
> >
> > http://www.ozanyarman.com/misc/Sagittal79.pdf
> >
> > http://www.ozanyarman.com/misc/79mos159tET.ttf
>
> Hi Oz,
>
> I only just came across this message. Sorry.
>

Quite alright.

> My first reaction was: Why not just use the standard font and use
> software to map it to the keyboard however you want?

What software did you have in mind? I have no option at the moment but
suffer the QWERTY keyboard mapping of Windows with the option to switch to
Turkish layout.

Also, we'd
> normally use the approximate-look-alike latin characters v k \ e / y ^
> rather than a physical layout on the keyboard, and we don't see the
> need to combine multiple symbols into a single character in the font.
>

Look-alike characters may be good for visual representation, but when
searching quickly for the right symbol, are not so attractive. In the layout
for 79mos159tet.TTF, I have reserved:

1. The upper-most keys till BACKSPACE the apotome-to-natural-to-apotome &
doubleapotome-to-apotome-to-doubleapotome range for pure Sagittal symbols (6
is natural),

2. QWERTYU to mixed Sagittal sharps (R is sharp),

2. The 7 keys right below to mixed Sagittal flats (F is flat),

3. And the 7 keys below them to mixed Sagittal doublesharps (V is
doublesharp)

4. Left-hand-side non-letter keys to Sagittal double-flats (' is
doubleflat),

5. Which, when SHIFT is pressed, will yield naturals (" is natural).

Of course, I am open to suggestions for a better layout.

> But I know you wouldn't have gone to so much trouble unless you had a
> real need.
>

Finale does not accept two-letters for custom accidentals.

?? I haven't widened it, I borrowed all glyphs from Sagittal Font version 2.

> We'd prefer not have a proliferation of modified Sagittal fonts, but
> we'd rather have you using some modified version than not use it at all.
>

You certainly appreciate the fact that both |\ and |) are represented by the
same 2 degrees of 79/80 MOS 159-tET? While I understand the need to
emphasize the 7-limit with a unique symbol not related to the 5-comma, I
still do not think your preference is elegant. Arguably,
lateral-confusability is still an issue with my selection, but I think
dividing the quarter-tone shaft into two serves my purposes all too well.

> We note that combining down sagittals with double flats or up
> sagittals with double sharps results in combinations that are
> extremely unlikely to ever be needed and they do not have a pure
> sagittal equivalent. So we'd prefer you didn't have them in the font.
> But again, if you have a real need, go ahead.

I am aware that some of them do not have a pure Sagittal equivalent, and
again, I am very certain that a few, as you say, are extremely unlikely to
be used. Nevertheless, there are cases when one might wish to utilize them.
Consider a A#_B|\_C\|/x_D# Gypsy Hijaz tetrachord in 80 MOS 159-tET:

-14 -5 9 19 : 9 14 10 : 135 213 151

You have, in the pure version, a sharp+qt, but not a doublesharp-qt symbol.
For that very reason, your pure version cannot notate this tetrachord
diatonically.

Another example involves a mixed doublesharp, Db_E|/bb_\|/F_Gb:

7 15 33 40 : 8 18 7 : 122 271 105

Again, in the pure version, there is no possibility of notating this
tetrachord diatonically.

By introducing commatic flavours on the 2nd and 3rd degrees of the
above-given tetrachords, I may eventually need all the glyphs in my arsenal.
Don't you agree?

>
> Thank you for acknowledging the original source. Could you also please
> include the URL of the sagittal website.
> http://dkeenan.com/sagittal
>

I will see to that.

> Thanks Oz.
>
> -- Dave Keenan
>
>

Oz.

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> What software did you have in mind? I have no option at the moment but
> suffer the QWERTY keyboard mapping of Windows with the option to
switch to
> Turkish layout.

I was thinking of Hudson Lacerda's MicroABC and Jacob Barton's scripts
for use with Sibelius. Unfortunatley Jacob's a busy fellow and hasn't
had time to finish updating them for the new font yet.

> Look-alike characters may be good for visual representation, but when
> searching quickly for the right symbol, are not so attractive. In
the layout
> for 79mos159tet.TTF, I have reserved:
>...
> Of course, I am open to suggestions for a better layout.

Oh no, I understood the layout. It is quite logical for the size of
the subset you are using.

> Finale does not accept two-letters for custom accidentals.

I remember looking at it a long time ago for use with sagittal. I seem
to remember you have to use the feature called "Custom key
signatures", buried deep. Is that what you're trying to use?

No two letter accidentals is a serious limitation. Anyone else out
there know a way around this in Finale?

> ?? I haven't widened it, I borrowed all glyphs from Sagittal Font
version 2.

That's good. I must have done a better job than I remembered. :-)

> You certainly appreciate the fact that both |\ and |) are
represented by the
> same 2 degrees of 79/80 MOS 159-tET? While I understand the need to
> emphasize the 7-limit with a unique symbol not related to the 5-comma, I
> still do not think your preference is elegant. Arguably,
> lateral-confusability is still an issue with my selection, but I think
> dividing the quarter-tone shaft into two serves my purposes all too
well.
>

That's entirely your call. The main thing is that you are using
symbols in a way that corresponds with their standard comma meanings,
given your choice of notational fifth for the nominals. I assume that
the nominals are in a chain of best fifths from 159-EDO and so /| |\
and /|\ represent 3, 4 and 7 degrees of 159-EDO respectively.

> I am aware that some of them do not have a pure Sagittal equivalent, and
> again, I am very certain that a few, as you say, are extremely
unlikely to
> be used. Nevertheless, there are cases when one might wish to
utilize them.
> Consider a A#_B|\_C\|/x_D# Gypsy Hijaz tetrachord in 80 MOS 159-tET:
...
> By introducing commatic flavours on the 2nd and 3rd degrees of the
> above-given tetrachords, I may eventually need all the glyphs in my
arsenal.
> Don't you agree?

I'm sorry, I couldn't follow it (I know you corrected this several
times). But it doesn't matter. I'll take your word for it. I'm just
happy that you can make use of Sagittal.

I suggest using colon : rather than underscore _ to separate pitches
in chords in ASCII sagittal notation. Underscore _ is shorthand for \\!
Colon : was reserved as a separator for this purpose. We thought that
since it is always used in numerical chord specifications like 4:5:6
in might as well be used in alphabetical ones as well.

Also the convention is that the symbol representing the largest
alteration should be placed nearest to the nominal. But at least there
is no ambiguity either way.
e.g. A#:B|\:Cx\|/:D#
Spaces can improve readability too.
e.g. A# : B|\ : Cx\|/ : D#

-- Dave Keenan

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

----- Original Message -----
From: "Dave Keenan" <d.keenan@bigpond.net.au>
To: <tuning@yahoogroups.com>
Sent: 06 Mayï¿½s 2007 Pazar 10:32
Subject: [tuning] Re: Sagittal79

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> > What software did you have in mind? I have no option at the moment but
> > suffer the QWERTY keyboard mapping of Windows with the option to
> switch to
> > Turkish layout.
>
> I was thinking of Hudson Lacerda's MicroABC and Jacob Barton's scripts
> for use with Sibelius. Unfortunatley Jacob's a busy fellow and hasn't
> had time to finish updating them for the new font yet.
>

That is all very well, but I haven't been able to use MicroABC, or have the
patience to wait for Jacob's updates.

> > Look-alike characters may be good for visual representation, but when
> > searching quickly for the right symbol, are not so attractive. In
> the layout
> > for 79mos159tet.TTF, I have reserved:
> >...
> > Of course, I am open to suggestions for a better layout.
>
> Oh no, I understood the layout. It is quite logical for the size of
> the subset you are using.
>

Thank you for this acknowledgement.

> > Finale does not accept two-letters for custom accidentals.
>
> I remember looking at it a long time ago for use with sagittal. I seem
> to remember you have to use the feature called "Custom key
> signatures", buried deep. Is that what you're trying to use?
>

That is so.

> No two letter accidentals is a serious limitation. Anyone else out
> there know a way around this in Finale?
>

There is no possibility of inserting two accidentals next to each other on a
single note in Finale.

> > ?? I haven't widened it, I borrowed all glyphs from Sagittal Font
> version 2.
>
> That's good. I must have done a better job than I remembered. :-)
>

Indeed.

> > You certainly appreciate the fact that both |\ and |) are
> represented by the
> > same 2 degrees of 79/80 MOS 159-tET? While I understand the need to
> > emphasize the 7-limit with a unique symbol not related to the 5-comma, I
> > still do not think your preference is elegant. Arguably,
> > lateral-confusability is still an issue with my selection, but I think
> > dividing the quarter-tone shaft into two serves my purposes all too
> well.
> >
>
> That's entirely your call. The main thing is that you are using
> symbols in a way that corresponds with their standard comma meanings,
> given your choice of notational fifth for the nominals. I assume that
> the nominals are in a chain of best fifths from 159-EDO and so /| |\
> and /|\ represent 3, 4 and 7 degrees of 159-EDO respectively.
>

Actually, they correspond respectively to 1,2, and 3 degrees of 79 MOS
159-tET. Remember, that I treat the 79-tone tuning as a standalone system.

> > I am aware that some of them do not have a pure Sagittal equivalent, and
> > again, I am very certain that a few, as you say, are extremely
> unlikely to
> > be used. Nevertheless, there are cases when one might wish to
> utilize them.
> > Consider a A#_B|\_C\|/x_D# Gypsy Hijaz tetrachord in 80 MOS 159-tET:
> ...
> > By introducing commatic flavours on the 2nd and 3rd degrees of the
> > above-given tetrachords, I may eventually need all the glyphs in my
> arsenal.
> > Don't you agree?
>
> I'm sorry, I couldn't follow it (I know you corrected this several
> times). But it doesn't matter. I'll take your word for it. I'm just
> happy that you can make use of Sagittal.
>

My point was, that there are the rarest of times when you need, in a
diatonical procedure, a doublesharp minus a quartertone, or a doubleflat
plus a quarter-tone, which are impossible to notate with pure Sagittal.

> I suggest using colon : rather than underscore _ to separate pitches
> in chords in ASCII sagittal notation. Underscore _ is shorthand for \\!
> Colon : was reserved as a separator for this purpose. We thought that
> since it is always used in numerical chord specifications like 4:5:6
> in might as well be used in alphabetical ones as well.
>

Agreed.

> Also the convention is that the symbol representing the largest
> alteration should be placed nearest to the nominal. But at least there
> is no ambiguity either way.
> e.g. A#:B|\:Cx\|/:D#
> Spaces can improve readability too.
> e.g. A# : B|\ : Cx\|/ : D#
>

Here it is once more then...

----------------------------------------------------

A# : B|\ : Cx\|/ : D#

-14 -5 9 19 : 9 14 10 : 135 213 151 (80mos159tet)

-------------------------------------------------------------

Db : Ebb/|\ : F\| : Gb

7 17 32 40 : 10 15 8 : 152 227 119 (80mos159tet)

--------------------------------------------------------------

> -- Dave Keenan
>

Oz.

🔗Dave Keenan <d.keenan@bigpond.net.au>

Hi Oz,

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> That is all very well, but I haven't been able to use MicroABC, or
have the
> patience to wait for Jacob's updates.

As I said, I knew you wouldn't have done it unless you had a real
need, so go ahead, with my blessing.

> There is no possibility of inserting two accidentals next to each
other on a
> single note in Finale.

Then yours is a good workaround.

> Actually, they correspond respectively to 1,2, and 3 degrees of 79 MOS
> 159-tET. Remember, that I treat the 79-tone tuning as a standalone
system.
>

I'm sorry I was not reading the list during the time that you
explained this system. How many degrees of 159-edo is the generator of
these MOS?

> My point was, that there are the rarest of times when you need, in a
> diatonical procedure, a doublesharp minus a quartertone, or a doubleflat
> plus a quarter-tone, which are impossible to notate with pure Sagittal.
>

I have no objection to those. It _is_ possible to notate them in pure
sagittal. It is only alterations _greater_ than a double apotome that
cannot be notated. My objections were to the symbols that consist of a
double-sharp _plus_ a sagittal or a doubleflat _minus_ a sagittal.

> Here it is once more then...
>
> ----------------------------------------------------
>
> A# : B|\ : Cx\|/ : D#
>
> -14 -5 9 19 : 9 14 10 : 135 213 151 (80mos159tet)
>
> -------------------------------------------------------------
>
> Db : Ebb/|\ : F\| : Gb
>
> 7 17 32 40 : 10 15 8 : 152 227 119 (80mos159tet)
>
> --------------------------------------------------------------

Those are both notatable in pure sagittal and so I have no objection
to the mixed combinations used.

I'm sorry I do not understand the significance of the numbers.

-- Dave Keenan

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

----- Original Message -----
From: "Dave Keenan" <d.keenan@bigpond.net.au>
To: <tuning@yahoogroups.com>
Sent: 09 Mayï¿½s 2007 ï¿½arï¿½amba 13:57
Subject: [tuning] Re: Sagittal79

> Hi Oz,
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> > That is all very well, but I haven't been able to use MicroABC, or
> have the
> > patience to wait for Jacob's updates.
>
> As I said, I knew you wouldn't have done it unless you had a real
> need, so go ahead, with my blessing.
>
> > There is no possibility of inserting two accidentals next to each
> other on a
> > single note in Finale.
>
> Then yours is a good workaround.
>
> > Actually, they correspond respectively to 1,2, and 3 degrees of 79 MOS
> > 159-tET. Remember, that I treat the 79-tone tuning as a standalone
> system.
> >
>
> I'm sorry I was not reading the list during the time that you
> explained this system. How many degrees of 159-edo is the generator of
> these MOS?
>

No single degree of 159 can generate these MOS in their entirety. But an
alteration of 92nd & 93rd fifths will yield 79 MOS 159-tET, and 93rd & 94th,
80 MOS 159-tET.

> > My point was, that there are the rarest of times when you need, in a
> > diatonical procedure, a doublesharp minus a quartertone, or a doubleflat
> > plus a quarter-tone, which are impossible to notate with pure Sagittal.
> >
>
> I have no objection to those. It _is_ possible to notate them in pure
> sagittal. It is only alterations _greater_ than a double apotome that
> cannot be notated. My objections were to the symbols that consist of a
> double-sharp _plus_ a sagittal or a doubleflat _minus_ a sagittal.
>

I see. Here is, once again, a seldom-occuring, yet valid instance of
doubleflat _minus_ a sagittal:

Cb : Db : Ebb|/ : Fb : Gb

-6 7 12 27 40 : 13 5 15 13 : 196 76 227 195 (80mos159tet)

Conversely, an acceptable counterpart featuring double-sharp _plus_ a
sagittal once more:

E# : Fx/| : G# : A# :B#

32 46 53 66 79 : 14 7 13 13 : 211 97 196 196 (80mos159tet)

> > Here it is once more then...
> >
> > ----------------------------------------------------
> >
> > A# : B|\ : Cx\|/ : D#
> >
> > -14 -5 9 19 : 9 14 10 : 135 213 151 (80mos159tet)
> >
> > -------------------------------------------------------------
> >
> > Db : Ebb/|\ : F\| : Gb
> >
> > 7 17 32 40 : 10 15 8 : 152 227 119 (80mos159tet)
> >
> > --------------------------------------------------------------
>
> Those are both notatable in pure sagittal and so I have no objection
> to the mixed combinations used.
>

You mean to say, that you can notate Cx\|/ or Ebb/|\ as pure without
reverting to enharmonic respelling? Show me how.

> I'm sorry I do not understand the significance of the numbers.
>

The first array of numbers are degrees of 80 MOS 159-tET, second array are
consecutive steps, third array are cents.

> -- Dave Keenan
>
>

Oz.

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> No single degree of 159 can generate these MOS in their entirety.

> But an
> alteration of 92nd & 93rd fifths will yield 79 MOS 159-tET, and 93rd
& 94th,
> 80 MOS 159-tET.

Then they are not, strictly speaking, MOS.

I suspect the only generator that would have both 79 and 80 as MOS of
159-edo would be 2 steps of 159-edo.

> I see. Here is, once again, a seldom-occuring, yet valid instance of
> doubleflat _minus_ a sagittal:
>
> Cb : Db : Ebb|/ : Fb : Gb
>
> -6 7 12 27 40 : 13 5 15 13 : 196 76 227 195 (80mos159tet)
>
>
> Conversely, an acceptable counterpart featuring double-sharp _plus_ a
> sagittal once more:
>
> E# : Fx/| : G# : A# :B#
>
> 32 46 53 66 79 : 14 7 13 13 : 211 97 196 196 (80mos159tet)

Yes.

> You mean to say, that you can notate Cx\|/ or Ebb/|\ as pure without
> reverting to enharmonic respelling? Show me how.

Cx\!/ = C#(|) = C(|||)

Ebb/|\ = Eb(!) = E(!!!)

> > I'm sorry I do not understand the significance of the numbers.
> >
>
>
> The first array of numbers are degrees of 80 MOS 159-tET, second
array are
> consecutive steps, third array are cents.

Thanks for explaining.

-- Dave K

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

----- Original Message -----
From: "Dave Keenan" <d.keenan@bigpond.net.au>
To: <tuning@yahoogroups.com>
Sent: 09 Mayï¿½s 2007 ï¿½arï¿½amba 18:16
Subject: [tuning] Re: Sagittal79

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> > No single degree of 159 can generate these MOS in their entirety.
>
> > But an
> > alteration of 92nd & 93rd fifths will yield 79 MOS 159-tET, and 93rd
> & 94th,
> > 80 MOS 159-tET.
>
> Then they are not, strictly speaking, MOS.
>

They are, because there are only two comma sizes.

> I suspect the only generator that would have both 79 and 80 as MOS of
> 159-edo would be 2 steps of 159-edo.
>

All except a single degree.

79 MOS 159-tET follows the pattern or mode 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2. In 80 MOS 159-tET, the 3
step gap at the centre is replaced by 2+1 steps...

Odd numbers cannot be generated no matter which step you choose.

> > I see. Here is, once again, a seldom-occuring, yet valid instance of
> > doubleflat _minus_ a sagittal:
> >
> > Cb : Db : Ebb|/ : Fb : Gb
> >
> > -6 7 12 27 40 : 13 5 15 13 : 196 76 227 195 (80mos159tet)
> >
> >
> > Conversely, an acceptable counterpart featuring double-sharp _plus_ a
> > sagittal once more:
> >
> > E# : Fx/| : G# : A# :B#
> >
> > 32 46 53 66 79 : 14 7 13 13 : 211 97 196 196 (80mos159tet)
>
> Yes.
>
> > You mean to say, that you can notate Cx\|/ or Ebb/|\ as pure without
> > reverting to enharmonic respelling? Show me how.
>
> Cx\!/ = C#(|) = C(|||)
>
> Ebb/|\ = Eb(!) = E(!!!)
>

Ah, but you have respelled them enharmonically. Instead of Cx minus qt, you
used C# plus qt. Again, instead of Ebb plus qt, you used Eb minus qt. You do
not have a pure diatonical equivalent for Cx\|/ or Ebb/|\, whereas I can
notate them as C#/|\ or Eb\|/ also.

> > > I'm sorry I do not understand the significance of the numbers.
> > >
> >
> >
> > The first array of numbers are degrees of 80 MOS 159-tET, second
> array are
> > consecutive steps, third array are cents.
>
> Thanks for explaining.
>
> -- Dave K
>
>

Oz.

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > > No single degree of 159 can generate these MOS in their entirety.
> >
> > > But an
> > > alteration of 92nd & 93rd fifths will yield 79 MOS 159-tET, and 93rd
> > & 94th,
> > > 80 MOS 159-tET.
> >
> > Then they are not, strictly speaking, MOS.
>
> They are, because there are only two comma sizes.

That is not the only requirement. The two sizes must also be
distributed with maximum evenness, and this only occurs when the
sequence can be generated by iterating a single interval modulo the
octave.

> > I suspect the only generator that would have both 79 and 80 as MOS of
> > 159-edo would be 2 steps of 159-edo.
>
> All except a single degree.
>
> 79 MOS 159-tET follows the pattern or mode 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2
> 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2
2 2 2 2
> 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2. In 80 MOS 159-tET,
the 3
> step gap at the centre is replaced by 2+1 steps...

In fact these _are_ MOS generated by a 2 step interval. The octave is
considered cyclically and you can start wherever you like. In these
cases the odd interval remains between the beginning and end of the
chain of generators.

> Odd numbers cannot be generated no matter which step you choose.

I'm not sure what you mean by this. Clearly any interval that includes
the odd-sized step of the MOS will contain an odd number of steps of
159-tET.

> > > You mean to say, that you can notate Cx\|/ or Ebb/|\ as pure without
> > > reverting to enharmonic respelling? Show me how.
> >
> > Cx\!/ = C#(|) = C(|||)
> >
> > Ebb/|\ = Eb(!) = E(!!!)
>
> Ah, but you have respelled them enharmonically. Instead of Cx minus
qt, you
> used C# plus qt. Again, instead of Ebb plus qt, you used Eb minus
qt. You do
> not have a pure diatonical equivalent for Cx\|/ or Ebb/|\, whereas I can
> notate them as C#/|\ or Eb\|/ also.

There is a (perhaps subtle) distinction here. Not all respellings are
enharmonic as you would understand. Otherwise your usage of
"enharmonic respelling" would be redundant.

You must at least admit that respelling without changing the nominal
does not offend diatonic spelling (i.e. you still have a unique
nominal for every note).

My understanding is that an enharmonic respelling is a respelling that
is only valid for a particular temperament. That is, it does not alter
the pitch in the temperament in question but it _will_ refer to a
different pitch if the temperament is changed.

The respelling of C#\!/ as C(|), and therefore also Cx\!/ as C#(|), is
valid in all temperaments and in just intonation. That is because the
meaning of the symbol (|) is _defined_ by the equation /|\ + (|) = #
independent of any particular tuning. So in my way of thinking, this
is not an enharmonic respelling.

However, if I had respelled C#\!/ as C/|\ then this would be an
enharmonic spelling because although it is valid in many temperaments
it is not valid in all. For example they are the same pitch in 72-tET
but not 53-tET.

-- Dave K

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

----- Original Message -----
From: "Dave Keenan" <d.keenan@bigpond.net.au>
To: <tuning@yahoogroups.com>
Sent: 10 Mayï¿½s 2007 Perï¿½embe 13:34
Subject: [tuning] Re: Sagittal79

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > > > No single degree of 159 can generate these MOS in their entirety.
> > >
> > > > But an
> > > > alteration of 92nd & 93rd fifths will yield 79 MOS 159-tET, and 93rd
> > > & 94th,
> > > > 80 MOS 159-tET.
> > >
> > > Then they are not, strictly speaking, MOS.
> >
> > They are, because there are only two comma sizes.
>
> That is not the only requirement. The two sizes must also be
> distributed with maximum evenness, and this only occurs when the
> sequence can be generated by iterating a single interval modulo the
> octave.
>
> > > I suspect the only generator that would have both 79 and 80 as MOS of
> > > 159-edo would be 2 steps of 159-edo.
> >
> > All except a single degree.
> >
> > 79 MOS 159-tET follows the pattern or mode 2 2 2 2 2 2 2 2 2 2 2 2 2
> 2 2 2 2
> > 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2
> 2 2 2 2
> > 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2. In 80 MOS 159-tET,
> the 3
> > step gap at the centre is replaced by 2+1 steps...
>
> In fact these _are_ MOS generated by a 2 step interval. The octave is
> considered cyclically and you can start wherever you like. In these
> cases the odd interval remains between the beginning and end of the
> chain of generators.
>

Ah, of course. My mistake. Both 79 and 80 are MOS 2deg 159-tET. Clumsy of me
to forget to octave as the interval of repetition.

You can generate either from G to g with 2 degrees of 159-tET, where G is
393 Hz.

> > Odd numbers cannot be generated no matter which step you choose.
>
> I'm not sure what you mean by this. Clearly any interval that includes
> the odd-sized step of the MOS will contain an odd number of steps of
> 159-tET.
>

That was obviously a garble. Please forget I said that.

> > > > You mean to say, that you can notate Cx\|/ or Ebb/|\ as pure without
> > > > reverting to enharmonic respelling? Show me how.
> > >
> > > Cx\!/ = C#(|) = C(|||)
> > >
> > > Ebb/|\ = Eb(!) = E(!!!)
> >
> > Ah, but you have respelled them enharmonically. Instead of Cx minus
> qt, you
> > used C# plus qt. Again, instead of Ebb plus qt, you used Eb minus
> qt. You do
> > not have a pure diatonical equivalent for Cx\|/ or Ebb/|\, whereas I can
> > notate them as C#/|\ or Eb\|/ also.
>
> There is a (perhaps subtle) distinction here. Not all respellings are
> enharmonic as you would understand. Otherwise your usage of
> "enharmonic respelling" would be redundant.
>
> You must at least admit that respelling without changing the nominal
> does not offend diatonic spelling (i.e. you still have a unique
> nominal for every note).
>

Ah, you are right. I was poorly trying to stress the doublesharpness or
doubleflatness of said tones, to no avail.

> My understanding is that an enharmonic respelling is a respelling that
> is only valid for a particular temperament. That is, it does not alter
> the pitch in the temperament in question but it _will_ refer to a
> different pitch if the temperament is changed.
>
> The respelling of C#\!/ as C(|), and therefore also Cx\!/ as C#(|), is
> valid in all temperaments and in just intonation. That is because the
> meaning of the symbol (|) is _defined_ by the equation /|\ + (|) = #
> independent of any particular tuning. So in my way of thinking, this
> is not an enharmonic respelling.
>

I am still thinking in terms of 79/80 MOS 2deg 159-tET.

> However, if I had respelled C#\!/ as C/|\ then this would be an
> enharmonic spelling because although it is valid in many temperaments
> it is not valid in all. For example they are the same pitch in 72-tET
> but not 53-tET.
>

Thank you for the clarifications.

> -- Dave K
>
>

Oz.