Atmospheric Ozan depletion -- a partial remedy

Hello, all.

In recent days, the Tuning list has confronted the unpleasant
phenomenon of atmospheric Ozan depletion. While some decades ago it
was feared that the Supersonic Transport (SST) might result in the
depletion of Earth's ozone layer, our Ozan layer is no less vital to
the well-being of the Tuning list, protecting us from unmitigated
doses of "ultraviolet radiation" that might reduce our thriving
ecosystem to a 24-EDO or 72-EDO monoculture.

The cause for our present problem, happily, is itself a great good:
the super-sonic quality transport of Ethno2, inspiring a forthcoming
demo from our worthy Ozan but also raising the issue of Ozan depletion
if this same Ozan is asked to explain the limitations of equal
temperaments even in the throes of preparing this demo.

Therefore, to help us weather this temporary Ozan depletion problem, I
now step forward to explain a few things about 72-EDO and Yarman-79,
albeit definitely in an "unauthorized" version, and with notes on my
own strange tastes in maqam music and tunings for which he is yet more
absolutely not responsible, if that were possible! Ozan's writings, of
course, are the ideal "authorized" source, and I would be delighted if
this article raises more interest in them <http://www.ozanyarman.com/>.

Also, taking a break from my own process of exploring and
understanding Dastgah-e Segah, I send warmest greetings to Jacques,
and congratulations on the creative force which Ethno2 is proving.

Additionally, I'd like to thank you, Cameron, for the best pretext I've
seen yet in favor of my regular temperament that gets 9/7 "wrong" by a
tad more than 5 cents, albeit in the more interesting direction:
actually I'm getting 22/17 wrong by only 6.25 cents! As for my clever
"Peppermint" idea, if I would only stick with Keenan Pepper's high
concept and make it a regular 24-note chain, I'd be only 0.395 cents
off (so quoth Scala).

Now back to the Ozanosphere which is the main focus. Why use Yarman-79,
basically an ingeniously tweaked MOS of 159-EDO, rather than 72-EDO,
or 43-EDO for Persian music, or for that matter my favorite nonequal
scheme of the moment (which doubtless can be virtually cloned by some
EDO with enough steps to do so)?

Again, this is an _unauthorized_ version by a weird alien musician who
shares with Ozan mainly the curious view that medieval and later Near
Eastern theorists are worth reading, and that the practices of quotidian
performers (an adjective Ozan has taught me to love!) are worth
studying and indeed measuring scientifically where possible and
appropriate.

First of all, to put things directly, Yarman-79 includes both pure
fifths and a pathway for meantone through the "Baroque" fifths and
fourths respectively about 1/3 Holdrian comma narrow and wide. He can
thus have the steps or perdeler rast and segah about 380 cents apart,
and connect them via a chain of four perfect fifths each impure by no
more than 1/3 comma.

Just try this in 72-EDO! As Paul Erlich summed things up about a
decade ago, it isn't a meantone, and Ozan wants some meantone
capabilities. While 383.33 cents might be an acceptable distance
between rast and segah for Ozan's purposes, there's no way to connect
these two steps at this distance with a chain of four fifths where one
isn't impure by 16.67 cents -- over twice the 1/3 Holdrian comma of
Yarman-79.

I consider that pretty straightfoward, and I even quoted Paul Erlich,
not to my knowledge a Near Eastern theorist!

How about a 53-note circulating Pythagorean tuning, or 53-EDO, both of
which might claim Near Eastern precedents (although I'm not sure I've
seen Pythagorean schemes beyond 24 notes, a Pythagorean-53 would be my
own preference if going in this direction)?

Here the Ozanian literary canon -- and also his kanun -- supply two
answers. The first is that 53-EDO, like 72-EDO, is not a meantone, and
neither includes meantone capabilities. However, Yarman-79 has both
many of the intervals of 53-EDO, plus that meantone option!

Also, with 53-EDO, we are limited to two sizes of middle or Zalzalian
or neutral intervals -- call them what we will. With a Pythagorean 53,
we get four sizes, since there will be some variations by the
3.615-cent comma of Mercator, but still not the diversity of
Yarman-79.

For an alien focusing on curious concepts of mostly Arab and Persian
tuning, life can be a bit simpler: I often get by with middle seconds
of 132 or 154 cents, and middle thirds of 341 and 363 cents, even
observing that maybe 363 cents, a near-just 37/30 as it happens
although structurally more like a tempered 121/98, "isn't so far" from
the classic Turkish 26/21. In fact, at least one Syrian 24-note
scheme, that of Tawfiq al-Sabbagh, likewise has two sizes of middle or
Zalzalian intervals -- but again, a lot less diversity than Yarman-79!

Why not just tune 159-EDO, or an expertly tweaked variation to get
some just fifths and fourths, as in Yarman-79? Here Ozan is seeking
above all to choose a system that can actually be implemented on a
practical qanun, as we know that Yarman-79 can.

Getting back to musical values as opposed to practical implementation
limits with instruments of interest, Ozan is quite rightly a sticker
for the right shade or flavor of intonation in a given maqam as
interpreted in the Ottoman tradition! I know as someone at times at
the receiving end of that discernment.

For example, I may think of 154-132-209 cents as a fine tetrachord for
Maqam Huseyni: but Ozan will helpfully inform me that 165 cents for
that lower middle step would be much more like it, as studies of
Turkish performers have shown! While I may think of my quotidian
tuning as fine for Arab music, or even invoke the steps of Ibn Sina's
Mustaqim (9:8-13:12-128:117) as the basis for my very approximate
permutation, Ozan and his colleagues can for their part cite actual
Turkish practice! Of course, since I'm going for a "generic" Huseyni
rather than the specific tradition that Ozan knows and embraces, there's
no conflict in these views, and we would likely find various shades of
tuning in different parts of the Near East.

Actually I have found an attractive (for me) tuning that would do much
more justice for an Osmanli Huseyni (i.e. an Ottoman Huseyni, if I'm
correct) at 161-127-208 cents, which actually satisfies one of George
Secor's criteria (at least if read literally, which here is to say
generously) for a "near-just" temperament -- Peppermint doesn't quite
meet the test, but does support 159-129-208, a better Turkish Huseyni
than 154-132-209.

In the new temperament I'm looking at, actually a spinoff of a recent
thread about EDO's, the middle steps would be 127-138-151-161 cents,
more variety than 132-154 cents but not the total kind of variety that
Ozan needs. Indeed, he needn't spend one second showing why this
scheme is no substitute for Yarman-79 when he could be more usefully
preparing his Ethno2 demo or listening to some classic sharki as a
welcome diversion!

For one, any 24-note tuning I use for maqam music is likely either
_not_ to be a meantone (or putting it another way, much more
17-EDO-like than meantone-like), or to be something like Zest-24 with
171-cent steps not so ideal for a maqam style (yes, Ozan does mention
32:29 in his writings, but not as an ideal middle second!).

For Ozan's views and explanations, his own writings are the best
source, not to speak of his own music on his 79-tone kanun or
otherwise.

That's a partial response until our Ozan gets undepleted.

With many thanks,

Margo Schulter
mschulter@...

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:
>
> Hello, all.
>
> In recent days, the Tuning list has confronted the unpleasant
> phenomenon of atmospheric Ozan depletion.

LOL! :) Thanks, Margo. -Carl

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:

> First of all, to put things directly, Yarman-79 includes both pure
> fifths and a pathway for meantone through the "Baroque" fifths and
> fourths respectively about 1/3 Holdrian comma narrow and wide. He can
> thus have the steps or perdeler rast and segah about 380 cents apart,
> and connect them via a chain of four perfect fifths each impure by no
> more than 1/3 comma.
>
> Just try this in 72-EDO!

As I've pointed out, you can do that in 72 notes of ennealimmal if you are willing to accept 3/8 comma flat. But this misses the point; when I said I understood in part what Ozan was up to, I meant one part was I understood he wanted to do this. When I said I didn't see the special relevance to maqam music, I meant I don't know why being able to do this is important for maqam music.

:)

Oz.

✩ ✩ ✩
www.ozanyarman.com

On Jun 12, 2010, at 6:34 AM, Margo Schulter wrote:

> Hello, all.
>
> In recent days, the Tuning list has confronted the unpleasant
> phenomenon of atmospheric Ozan depletion. While some decades ago it
> was feared that the Supersonic Transport (SST) might result in the
> depletion of Earth's ozone layer, our Ozan layer is no less vital to
> the well-being of the Tuning list, protecting us from unmitigated
> doses of "ultraviolet radiation" that might reduce our thriving
> ecosystem to a 24-EDO or 72-EDO monoculture.
>
> The cause for our present problem, happily, is itself a great good:
> the super-sonic quality transport of Ethno2, inspiring a forthcoming
> demo from our worthy Ozan but also raising the issue of Ozan depletion
> if this same Ozan is asked to explain the limitations of equal
> temperaments even in the throes of preparing this demo.
>
> Therefore, to help us weather this temporary Ozan depletion problem, I
> now step forward to explain a few things about 72-EDO and Yarman-79,
> albeit definitely in an "unauthorized" version, and with notes on my
> own strange tastes in maqam music and tunings for which he is yet more
> absolutely not responsible, if that were possible! Ozan's writings, of
> course, are the ideal "authorized" source, and I would be delighted if
> this article raises more interest in them <http://www.ozanyarman.com/
> >.
>
> Also, taking a break from my own process of exploring and
> understanding Dastgah-e Segah, I send warmest greetings to Jacques,
> and congratulations on the creative force which Ethno2 is proving.
>
> Additionally, I'd like to thank you, Cameron, for the best pretext
> I've
> seen yet in favor of my regular temperament that gets 9/7 "wrong" by a
> tad more than 5 cents, albeit in the more interesting direction:
> actually I'm getting 22/17 wrong by only 6.25 cents! As for my clever
> "Peppermint" idea, if I would only stick with Keenan Pepper's high
> concept and make it a regular 24-note chain, I'd be only 0.395 cents
> off (so quoth Scala).
>
> Now back to the Ozanosphere which is the main focus. Why use
> Yarman-79,
> basically an ingeniously tweaked MOS of 159-EDO, rather than 72-EDO,
> or 43-EDO for Persian music, or for that matter my favorite nonequal
> scheme of the moment (which doubtless can be virtually cloned by some
> EDO with enough steps to do so)?
>
> Again, this is an _unauthorized_ version by a weird alien musician who
> shares with Ozan mainly the curious view that medieval and later Near
> Eastern theorists are worth reading, and that the practices of
> quotidian
> performers (an adjective Ozan has taught me to love!) are worth
> studying and indeed measuring scientifically where possible and
> appropriate.
>
> First of all, to put things directly, Yarman-79 includes both pure
> fifths and a pathway for meantone through the "Baroque" fifths and
> fourths respectively about 1/3 Holdrian comma narrow and wide. He can
> thus have the steps or perdeler rast and segah about 380 cents apart,
> and connect them via a chain of four perfect fifths each impure by no
> more than 1/3 comma.
>
> Just try this in 72-EDO! As Paul Erlich summed things up about a
> decade ago, it isn't a meantone, and Ozan wants some meantone
> capabilities. While 383.33 cents might be an acceptable distance
> between rast and segah for Ozan's purposes, there's no way to connect
> these two steps at this distance with a chain of four fifths where one
> isn't impure by 16.67 cents -- over twice the 1/3 Holdrian comma of
> Yarman-79.
>
> I consider that pretty straightfoward, and I even quoted Paul Erlich,
> not to my knowledge a Near Eastern theorist!
>
> How about a 53-note circulating Pythagorean tuning, or 53-EDO, both of
> which might claim Near Eastern precedents (although I'm not sure I've
> seen Pythagorean schemes beyond 24 notes, a Pythagorean-53 would be my
> own preference if going in this direction)?
>
> Here the Ozanian literary canon -- and also his kanun -- supply two
> answers. The first is that 53-EDO, like 72-EDO, is not a meantone, and
> neither includes meantone capabilities. However, Yarman-79 has both
> many of the intervals of 53-EDO, plus that meantone option!
>
> Also, with 53-EDO, we are limited to two sizes of middle or Zalzalian
> or neutral intervals -- call them what we will. With a Pythagorean 53,
> we get four sizes, since there will be some variations by the
> 3.615-cent comma of Mercator, but still not the diversity of
> Yarman-79.
>
> For an alien focusing on curious concepts of mostly Arab and Persian
> tuning, life can be a bit simpler: I often get by with middle seconds
> of 132 or 154 cents, and middle thirds of 341 and 363 cents, even
> observing that maybe 363 cents, a near-just 37/30 as it happens
> although structurally more like a tempered 121/98, "isn't so far" from
> the classic Turkish 26/21. In fact, at least one Syrian 24-note
> scheme, that of Tawfiq al-Sabbagh, likewise has two sizes of middle or
> Zalzalian intervals -- but again, a lot less diversity than Yarman-79!
>
> Why not just tune 159-EDO, or an expertly tweaked variation to get
> some just fifths and fourths, as in Yarman-79? Here Ozan is seeking
> above all to choose a system that can actually be implemented on a
> practical qanun, as we know that Yarman-79 can.
>
> Getting back to musical values as opposed to practical implementation
> limits with instruments of interest, Ozan is quite rightly a sticker
> for the right shade or flavor of intonation in a given maqam as
> interpreted in the Ottoman tradition! I know as someone at times at
> the receiving end of that discernment.
>
> For example, I may think of 154-132-209 cents as a fine tetrachord for
> Maqam Huseyni: but Ozan will helpfully inform me that 165 cents for
> that lower middle step would be much more like it, as studies of
> Turkish performers have shown! While I may think of my quotidian
> tuning as fine for Arab music, or even invoke the steps of Ibn Sina's
> Mustaqim (9:8-13:12-128:117) as the basis for my very approximate
> permutation, Ozan and his colleagues can for their part cite actual
> Turkish practice! Of course, since I'm going for a "generic" Huseyni
> rather than the specific tradition that Ozan knows and embraces,
> there's
> no conflict in these views, and we would likely find various shades of
> tuning in different parts of the Near East.
>
> Actually I have found an attractive (for me) tuning that would do much
> more justice for an Osmanli Huseyni (i.e. an Ottoman Huseyni, if I'm
> correct) at 161-127-208 cents, which actually satisfies one of George
> Secor's criteria (at least if read literally, which here is to say
> generously) for a "near-just" temperament -- Peppermint doesn't quite
> meet the test, but does support 159-129-208, a better Turkish Huseyni
> than 154-132-209.
>
> In the new temperament I'm looking at, actually a spinoff of a recent
> thread about EDO's, the middle steps would be 127-138-151-161 cents,
> more variety than 132-154 cents but not the total kind of variety that
> Ozan needs. Indeed, he needn't spend one second showing why this
> scheme is no substitute for Yarman-79 when he could be more usefully
> preparing his Ethno2 demo or listening to some classic sharki as a
> welcome diversion!
>
> For one, any 24-note tuning I use for maqam music is likely either
> _not_ to be a meantone (or putting it another way, much more
> 17-EDO-like than meantone-like), or to be something like Zest-24 with
> 171-cent steps not so ideal for a maqam style (yes, Ozan does mention
> 32:29 in his writings, but not as an ideal middle second!).
>
> For Ozan's views and explanations, his own writings are the best
> source, not to speak of his own music on his 79-tone kanun or
> otherwise.
>
> That's a partial response until our Ozan gets undepleted.
>
> With many thanks,
>
> Margo Schulter
> mschulter@...
>
>
>
> ------------------------------------
>
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>
>
>

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:

> Additionally, I'd like to thank you, Cameron, for the best pretext >I've
> seen yet in favor of my regular temperament that gets 9/7 "wrong" >by a
> tad more than 5 cents, albeit in the more interesting direction:
> actually I'm getting 22/17 wrong by only 6.25 cents! As for my >clever
> "Peppermint" idea, if I would only stick with Keenan Pepper's high
> concept and make it a regular 24-note chain, I'd be only 0.395 cents
> off (so quoth Scala).

22/17 also puns with a 6/5 from 14/13 and with 5/4 from 28/27, ie, you could use 84/65 at about 444 cents. So, in a tuning based on interlocking tetrachords, you could get a very nice reordered chromatic tetrahord from 28/27 above the tonic of the first tetrachord (provided there's a 28/27 above the next conjunct tetrachord), for example. Sharp of 9/7 has just as many possibilities as splitting the difference with 14/11, IMO. Even higher in the region between 13/10 and 17/13 is the most multifacted interval of
them all for harmony, the number one "shadow interval", but a big pain to integrate into a tetrachordal structure, being so close to 4/3.

Thanks for another great post from you! I was singing along to your recently posted musical example by the way, it's very singable.

.........................--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:
>
> Hello, all.
>
> In recent days, the Tuning list has confronted the unpleasant
> phenomenon of atmospheric Ozan depletion. While some decades ago it
> was feared that the Supersonic Transport (SST) might result in the
> depletion of Earth's ozone layer, our Ozan layer is no less vital to
> the well-being of the Tuning list, protecting us from unmitigated
> doses of "ultraviolet radiation" that might reduce our thriving
> ecosystem to a 24-EDO or 72-EDO monoculture.
>
> The cause for our present problem, happily, is itself a great good:
> the super-sonic quality transport of Ethno2, inspiring a forthcoming
> demo from our worthy Ozan but also raising the issue of Ozan depletion
> if this same Ozan is asked to explain the limitations of equal
> temperaments even in the throes of preparing this demo.
>
> Therefore, to help us weather this temporary Ozan depletion problem, I
> now step forward to explain a few things about 72-EDO and Yarman-79,
> albeit definitely in an "unauthorized" version, and with notes on my
> own strange tastes in maqam music and tunings for which he is yet more
> absolutely not responsible, if that were possible! Ozan's writings, of
> course, are the ideal "authorized" source, and I would be delighted if
> this article raises more interest in them <http://www.ozanyarman.com/>.
>
> Also, taking a break from my own process of exploring and
> understanding Dastgah-e Segah, I send warmest greetings to Jacques,
> and congratulations on the creative force which Ethno2 is proving.
>
> Additionally, I'd like to thank you, Cameron, for the best pretext I've
> seen yet in favor of my regular temperament that gets 9/7 "wrong" by a
> tad more than 5 cents, albeit in the more interesting direction:
> actually I'm getting 22/17 wrong by only 6.25 cents! As for my clever
> "Peppermint" idea, if I would only stick with Keenan Pepper's high
> concept and make it a regular 24-note chain, I'd be only 0.395 cents
> off (so quoth Scala).
>
> Now back to the Ozanosphere which is the main focus. Why use Yarman-79,
> basically an ingeniously tweaked MOS of 159-EDO, rather than 72-EDO,
> or 43-EDO for Persian music, or for that matter my favorite nonequal
> scheme of the moment (which doubtless can be virtually cloned by some
> EDO with enough steps to do so)?
>
> Again, this is an _unauthorized_ version by a weird alien musician who
> shares with Ozan mainly the curious view that medieval and later Near
> Eastern theorists are worth reading, and that the practices of quotidian
> performers (an adjective Ozan has taught me to love!) are worth
> studying and indeed measuring scientifically where possible and
> appropriate.
>
> First of all, to put things directly, Yarman-79 includes both pure
> fifths and a pathway for meantone through the "Baroque" fifths and
> fourths respectively about 1/3 Holdrian comma narrow and wide. He can
> thus have the steps or perdeler rast and segah about 380 cents apart,
> and connect them via a chain of four perfect fifths each impure by no
> more than 1/3 comma.
>
> Just try this in 72-EDO! As Paul Erlich summed things up about a
> decade ago, it isn't a meantone, and Ozan wants some meantone
> capabilities. While 383.33 cents might be an acceptable distance
> between rast and segah for Ozan's purposes, there's no way to connect
> these two steps at this distance with a chain of four fifths where one
> isn't impure by 16.67 cents -- over twice the 1/3 Holdrian comma of
> Yarman-79.
>
> I consider that pretty straightfoward, and I even quoted Paul Erlich,
> not to my knowledge a Near Eastern theorist!
>
> How about a 53-note circulating Pythagorean tuning, or 53-EDO, both of
> which might claim Near Eastern precedents (although I'm not sure I've
> seen Pythagorean schemes beyond 24 notes, a Pythagorean-53 would be my
> own preference if going in this direction)?
>
> Here the Ozanian literary canon -- and also his kanun -- supply two
> answers. The first is that 53-EDO, like 72-EDO, is not a meantone, and
> neither includes meantone capabilities. However, Yarman-79 has both
> many of the intervals of 53-EDO, plus that meantone option!
>
> Also, with 53-EDO, we are limited to two sizes of middle or Zalzalian
> or neutral intervals -- call them what we will. With a Pythagorean 53,
> we get four sizes, since there will be some variations by the
> 3.615-cent comma of Mercator, but still not the diversity of
> Yarman-79.
>
> For an alien focusing on curious concepts of mostly Arab and Persian
> tuning, life can be a bit simpler: I often get by with middle seconds
> of 132 or 154 cents, and middle thirds of 341 and 363 cents, even
> observing that maybe 363 cents, a near-just 37/30 as it happens
> although structurally more like a tempered 121/98, "isn't so far" from
> the classic Turkish 26/21. In fact, at least one Syrian 24-note
> scheme, that of Tawfiq al-Sabbagh, likewise has two sizes of middle or
> Zalzalian intervals -- but again, a lot less diversity than Yarman-79!
>
> Why not just tune 159-EDO, or an expertly tweaked variation to get
> some just fifths and fourths, as in Yarman-79? Here Ozan is seeking
> above all to choose a system that can actually be implemented on a
> practical qanun, as we know that Yarman-79 can.
>
> Getting back to musical values as opposed to practical implementation
> limits with instruments of interest, Ozan is quite rightly a sticker
> for the right shade or flavor of intonation in a given maqam as
> interpreted in the Ottoman tradition! I know as someone at times at
> the receiving end of that discernment.
>
> For example, I may think of 154-132-209 cents as a fine tetrachord for
> Maqam Huseyni: but Ozan will helpfully inform me that 165 cents for
> that lower middle step would be much more like it, as studies of
> Turkish performers have shown! While I may think of my quotidian
> tuning as fine for Arab music, or even invoke the steps of Ibn Sina's
> Mustaqim (9:8-13:12-128:117) as the basis for my very approximate
> permutation, Ozan and his colleagues can for their part cite actual
> Turkish practice! Of course, since I'm going for a "generic" Huseyni
> rather than the specific tradition that Ozan knows and embraces, there's
> no conflict in these views, and we would likely find various shades of
> tuning in different parts of the Near East.
>
> Actually I have found an attractive (for me) tuning that would do much
> more justice for an Osmanli Huseyni (i.e. an Ottoman Huseyni, if I'm
> correct) at 161-127-208 cents, which actually satisfies one of George
> Secor's criteria (at least if read literally, which here is to say
> generously) for a "near-just" temperament -- Peppermint doesn't quite
> meet the test, but does support 159-129-208, a better Turkish Huseyni
> than 154-132-209.
>
> In the new temperament I'm looking at, actually a spinoff of a recent
> thread about EDO's, the middle steps would be 127-138-151-161 cents,
> more variety than 132-154 cents but not the total kind of variety that
> Ozan needs. Indeed, he needn't spend one second showing why this
> scheme is no substitute for Yarman-79 when he could be more usefully
> preparing his Ethno2 demo or listening to some classic sharki as a
> welcome diversion!
>
> For one, any 24-note tuning I use for maqam music is likely either
> _not_ to be a meantone (or putting it another way, much more
> 17-EDO-like than meantone-like), or to be something like Zest-24 with
> 171-cent steps not so ideal for a maqam style (yes, Ozan does mention
> 32:29 in his writings, but not as an ideal middle second!).
>
> For Ozan's views and explanations, his own writings are the best
> source, not to speak of his own music on his 79-tone kanun or
> otherwise.
>
> That's a partial response until our Ozan gets undepleted.
>
> With many thanks,
>
> Margo Schulter
> mschulter@...
>

> 22/17 also puns with a 6/5 from 14/13 and with 5/4 from 28/27, ie,
> you could use 84/65 at about 444 cents. So, in a tuning based on
> interlocking tetrachords, you could get a very nice reordered
> chromatic tetrahord from 28/27 above the tonic of the first
> tetrachord (provided there's a 28/27 above the next conjunct
> tetrachord), for example.

Hi, Cameron. Another ratio close to 22/17 is 128/99 at about 445
cents, which comes up in Zephyr-24, a superset of the 1-3-7-9-11-13
eikosany.

One context where an interval around 9/7 or 128/99 often comes up --
with 352/273 at 440 cents a "tempering" of either I often seem to use
as either a rational ratio or very close irrational approximation --
is in what I call Huzam Jadid or "New Huzam," meaning that the larger
and smaller neutral steps are reversed from their usual placement
based on Rast:

Sikah Jadid Zirkula Mustaqim
|----------|---------------|---------|
C* D E F G* A B C*
0 154 363 440 705 859 1068 1200
154 209 77 264 154 209 132

This is one of the maqamat in the Sikah family, with a Sikah trichord,
middle Hijaz tetrachord (here a variant known as "Zirkula" with the
middle step around 7/6 but the semitone around 22/21 first and the
largish neutral second around 12/11 last), and a trichord of Rast,
or here Mustaqim (with a tone plus a smaller neutral second, rather
than the larger one typical of Rast), to fill out the "textbook" octave version. This is the regular "e-based" tuning, with a chain of
24 notes formed by fifths at 704.607 cents.

If we do this in Keenan Pepper's regular tuning, using an unmodified
24-note chain of fifths at 704.096 cents, then we get:

Sikah Jadid Zirkula Mustaqim
|----------|---------------|---------|
C* D E F G* A B C*
0 159 367 447 704 863 1071 1200
159 208 80 257 159 208 129

This has a virtually just 22/17 and 13/7, plus a middle step of
the Hijaz (i.e. Zirkula) tetrachord at a near-just 297/256.

> Sharp of 9/7 has just as many possibilities as splitting the
> difference with 14/11, IMO.

Well, in these 24-note systems, there tends to be a regular major
third (e.g. F-A) at around 14/11, plus a fourth-less-diesis
(e.g. C*-F) somewhere around 9/7, 352/273, or 22/17. These two
intervals in a given system, if it's strictly regular (a 23-fifth
chain), will differ by the 17-comma, which represents 64/63 or 78/77
or 99/98, etc.

> Even higher in the region between 13/10 and 17/13 is the most
> multifacted interval of them all for harmony, the number one
> "shadow interval", but a big pain to integrate into a tetrachordal
> structure, being so close to 4/3.

One trick I've had pointed out to me is that 13/5 can have a very
special quality because of the octave spacing, in my experience making
a very nice wide major tenth expanding to a 12th while a comparably
wide major sixth expands to an octave. Keenan Pepper's regular tuning
has a near-just 17/13 along with the 22/17. In 13-EDO, I found that
the same interval represents both a wide major third and 4/3 -- and
with the right timbres, it was quite pleasant!

By the way, I recall that in another post you mentioned a kind
of tetrachord with something like 18:17 and 8:7 steps -- which
would leave a step slightly larger than 11:10 to complete
a pure 4:3 fourth (~99-231-168 cents). Another division that
occurred to me, as it might appear on a monochord, would be

68 64 56 51
105 231 162
1/1 17/16 17/14 4/3
0 105 336 498

> Thanks for another great post from you! I was singing along to your
> recently posted musical example by the way, it's very singable.

This is very helpful and welcome feedback, because my first goal in a
maqam improvisation is to have a "vocal-like" quality.

With many thanks,

Margo