FROM EDO-SYSTEM TO rational system

If we consider a (otonal) increasing/constant rational system with
n.n=12 and a 12-edo:

RATIONAL

EDO

R

C

R

C

12

12

1

1

1

0

1

0

13

12

13

12

1.083333

138.5727

1.059463

100

14

12

7

6

1.166667

266.8709

1.122462

200

15

12

5

4

1.25

386.3137

1.189207

300

16

12

4

3

1.333333

498.045

1.259921

400

17

12

17

12

1.416667

603.0004

1.33484

500

18

12

3

2

1.5

701.955

1.414214

600

19

12

19

12

1.583333

795.558

1.498307

700

20

12

5

3

1.666667

884.3587

1.587401

800

21

12

7

4

1.75

968.8259

1.681793

900

22

12

11

6

1.833333

1049.363

1.781797

1000

23

12

23

12

1.916667

1126.319

1.887749

1100

24

12

2

1

2

1200

2

1200

1- after plotting them we see a straight line related to 12-edo and a
curved line over it for the rational system (dashed lines):

2-now substract edo from rational and divide difference by numbers from
1 to .....:

if you divide the difference by 1 and substract from rational you have
edo, for dividing to numbers greater than 1 you have curves going to be
the rational system:

12-EDO

12- RDO(D/C)

0

0

0

0

0

100

106.4288

119.2863

133.7511

138.5727

200

211.1452

233.4355

258.512

266.8709

300

314.3856

343.1569

375.5245

386.3137

400

416.3408

449.0225

485.7894

498.045

500

517.1667

551.5002

590.1254

603.0004

600

616.9925

650.9775

689.2106

701.955

700

715.9263

747.779

783.6133

795.558

800

814.0598

842.1794

873.8139

884.3587

900

911.471

934.413

960.2227

968.8259

1000

1008.227

1024.681

1043.193

1049.363

1100

1104.387

1113.16

1123.029

1126.319

1200

1200

1200

1200

1200

3-so we will have a spectrum of systems here , between edo and
rational.if you divide the difference by 2 and substract from rational
you will have a curve in the middle of these two .

4-this process can be done for (utonal)constant/decreasing rational
system and edo systems, utonal system cover the area below the edo.so we
have in this 3 equal-degree systems:

Utonal< ---> edo<----->otonal

Shaahin Mohaajeri

Tombak Player & Researcher , Composer

www.geocities.com/acousticsoftombak

My tombak musics : www.rhythmweb.com/gdg

My articles in ''Harmonytalk'':

www.harmonytalk.com/archives/000296.html

www.harmonytalk.com/archives/000288.html

My article in DrumDojo:

www.drumdojo.com/world/persia/tonbak_acoustics.htm

Reminds me of Dan Stearns . . .

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@k...> wrote:
>
>
>
>
>
> If we consider a (otonal) increasing/constant rational system with
> n.n=12 and a 12-edo:
>
>
>
> RATIONAL
>
> EDO
>
>
>
>
>
>
>
>
>
> R
>
> C
>
> R
>
> C
>
> 12
>
> 12
>
> 1
>
> 1
>
> 1
>
> 0
>
> 1
>
> 0
>
> 13
>
> 12
>
> 13
>
> 12
>
> 1.083333
>
> 138.5727
>
> 1.059463
>
> 100
>
> 14
>
> 12
>
> 7
>
> 6
>
> 1.166667
>
> 266.8709
>
> 1.122462
>
> 200
>
> 15
>
> 12
>
> 5
>
> 4
>
> 1.25
>
> 386.3137
>
> 1.189207
>
> 300
>
> 16
>
> 12
>
> 4
>
> 3
>
> 1.333333
>
> 498.045
>
> 1.259921
>
> 400
>
> 17
>
> 12
>
> 17
>
> 12
>
> 1.416667
>
> 603.0004
>
> 1.33484
>
> 500
>
> 18
>
> 12
>
> 3
>
> 2
>
> 1.5
>
> 701.955
>
> 1.414214
>
> 600
>
> 19
>
> 12
>
> 19
>
> 12
>
> 1.583333
>
> 795.558
>
> 1.498307
>
> 700
>
> 20
>
> 12
>
> 5
>
> 3
>
> 1.666667
>
> 884.3587
>
> 1.587401
>
> 800
>
> 21
>
> 12
>
> 7
>
> 4
>
> 1.75
>
> 968.8259
>
> 1.681793
>
> 900
>
> 22
>
> 12
>
> 11
>
> 6
>
> 1.833333
>
> 1049.363
>
> 1.781797
>
> 1000
>
> 23
>
> 12
>
> 23
>
> 12
>
> 1.916667
>
> 1126.319
>
> 1.887749
>
> 1100
>
> 24
>
> 12
>
> 2
>
> 1
>
> 2
>
> 1200
>
> 2
>
> 1200
>
>
>
> 1- after plotting them we see a straight line related to 12-edo and
a
> curved line over it for the rational system (dashed lines):
>
>
>
> 2-now substract edo from rational and divide difference by numbers
from
> 1 to .....:
>
> if you divide the difference by 1 and substract from rational you
have
> edo, for dividing to numbers greater than 1 you have curves going
to be
> the rational system:
>
>
>
> 12-EDO
>
>
>
>
>
>
>
>
>
> 12- RDO(D/C)
>
> 0
>
> 0
>
> 0
>
> 0
>
> 0
>
>
>
> 100
>
> 106.4288
>
> 119.2863
>
> 133.7511
>
> 138.5727
>
>
>
> 200
>
> 211.1452
>
> 233.4355
>
> 258.512
>
> 266.8709
>
>
>
> 300
>
> 314.3856
>
> 343.1569
>
> 375.5245
>
> 386.3137
>
>
>
> 400
>
> 416.3408
>
> 449.0225
>
> 485.7894
>
> 498.045
>
>
>
> 500
>
> 517.1667
>
> 551.5002
>
> 590.1254
>
> 603.0004
>
>
>
> 600
>
> 616.9925
>
> 650.9775
>
> 689.2106
>
> 701.955
>
>
>
> 700
>
> 715.9263
>
> 747.779
>
> 783.6133
>
> 795.558
>
>
>
> 800
>
> 814.0598
>
> 842.1794
>
> 873.8139
>
> 884.3587
>
>
>
> 900
>
> 911.471
>
> 934.413
>
> 960.2227
>
> 968.8259
>
>
>
> 1000
>
> 1008.227
>
> 1024.681
>
> 1043.193
>
> 1049.363
>
>
>
> 1100
>
> 1104.387
>
> 1113.16
>
> 1123.029
>
> 1126.319
>
>
>
> 1200
>
> 1200
>
> 1200
>
> 1200
>
> 1200
>
>
>
>
>
> 3-so we will have a spectrum of systems here , between edo and
> rational.if you divide the difference by 2 and substract from
rational
> you will have a curve in the middle of these two .
>
> 4-this process can be done for (utonal)constant/decreasing rational
> system and edo systems, utonal system cover the area below the
edo.so we
> have in this 3 equal-degree systems:
>
> Utonal< ---> edo<----->otonal
>
>
>
> Shaahin Mohaajeri
>
>
>
> Tombak Player & Researcher , Composer
>
> www.geocities.com/acousticsoftombak
>
> My tombak musics : www.rhythmweb.com/gdg
>
> My articles in ''Harmonytalk'':
>
> www.harmonytalk.com/archives/000296.html
>
> www.harmonytalk.com/archives/000288.html
>
> My article in DrumDojo:
>
> www.drumdojo.com/world/persia/tonbak_acoustics.htm
>

On Wed, 19 Oct 2005, "Mohajeri Shahin" wrote:
>
> If we consider a (otonal) increasing/constant rational system with
> n.n=12 and a 12-edo:
>
> RATIONAL
>
> EDO
>
... [data snipt]

Mohajeri,

IMO, this information would have been easier to understand if you had
placed it in two (or more) columns, rather than just one.

... [data snipt]

>
> 1- after plotting them we see a straight line related to 12-edo and a
> curved line over it for the rational system (dashed lines):
>
> 2-now substract edo from rational and divide difference by numbers from
> 1 to .....:
>
> if you divide the difference by 1 and substract from rational you have
> edo, for dividing to numbers greater than 1 you have curves going to be
> the rational system:
>
> 12-EDO
>
> 12- RDO(D/C)
>
... [data snipt]

Same comment.

> 3-so we will have a spectrum of systems here , between edo and
> rational.

Very neat and interesting! This exposition would benefit by your
including the graphs to demonstrate the relationships between the
tunings.

> ... if you divide the difference by 2 and substract from rational
> you will have a curve in the middle of these two .

Not entirely sure which difference you mean us to divide. You're
producing some kind of average, between a rational tuning on one
hand, and a what? on the other. Is one such average special in
any way?

> 4-this process can be done for (utonal)constant/decreasing rational
> system and edo systems, utonal system cover the area below the edo.

Again, a graph would make this clearer, showing the otonal and utonal
curve families above and below the EDO.

> ... so we have in this 3 equal-degree systems:
>
> Utonal< ---> edo<----->otonal

I'd love to see the same information presented using tables and
graphs!

Regards,
Yahya

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Hi Yahya and Mohajeri,

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
>
> Mohajeri,
>
> IMO, this information would have been easier to understand
> if you had placed it in two (or more) columns, rather than
> just one.

Mohajeri's original post actually contained the data in
multi-column tables in HTML format. It was altered to the
horribly-formatted single column when you received it in
email. I warned him before about using fancy graphics when
posting to this list.

Stuff here should always be presented in the simplest
plain ASCII, using periods (dots) instead of spaces to
separate columns in multi-column tables.

That way the presentation of the data will never be altered,
other than lines being truncated and running on to the next
line when someone quotes the table and the "greater-than"
signs (right angle brackets) are added at the beginning of
the lines.

I really do wish others posting here would spend as much
time and effort on the presentation of their posts as i do.
It makes a difference.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hi all,

On Fri, 21 Oct 2005, "monz" wrote:
>
> Hi Yahya and Mohajeri,
>
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> <yahya@m...> wrote:
> >
> > Mohajeri,
> >
> > IMO, this information would have been easier to understand
> > if you had placed it in two (or more) columns, rather than
> > just one.
>
> Mohajeri's original post actually contained the data in
> multi-column tables in HTML format. It was altered to the
> horribly-formatted single column when you received it in
> email. I warned him before about using fancy graphics when
> posting to this list.
>
> Stuff here should always be presented in the simplest
> plain ASCII, using periods (dots) instead of spaces to
> separate columns in multi-column tables.
>
> That way the presentation of the data will never be altered,
> other than lines being truncated and running on to the next
> line when someone quotes the table and the "greater-than"
> signs (right angle brackets) are added at the beginning of
> the lines.
>
> I really do wish others posting here would spend as much
> time and effort on the presentation of their posts as i do.
> It makes a difference.

Thanks, Monz,

Your method - using dots instead of spaces - at least should
make lines cohere reasonably well. I usually use a few spaces,
and not more than three columns, understanding that the
result may be rather ragged, depending on the fonts that
readers use when viewing it. Your dot-joined columns can also
appear ragged in the same way.

What a pity that we usually find text easier to read in a
proportionally-spaced font, whilst formatting data in columns
in plain text requires the use of a monospaced font!

If I thought that everyone reading and writing on all the lists
I use could view HTML without problems, I'd use it like a shot.
But since I don't expect this to happen for a few year yet, I
read most mailing list digests as plain text.

---

Mohajeri,

I apologise for any implication that you did not take enough
trouble to format your data! I will look up your messages
on Yahoo.

---

Regards,
Yahya

--
No virus found in this outgoing message.
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Version: 7.0.344 / Virus Database: 267.12.4/146 - Release Date: 21/10/05

Hi Yahya and Mohajeri,

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:

> Your method - using dots instead of spaces - at least
> should make lines cohere reasonably well. I usually
> use a few spaces, and not more than three columns,
> understanding that the result may be rather ragged,
> depending on the fonts that readers use when viewing it.
> Your dot-joined columns can also appear ragged in the
> same way.

Yes, of course the font used by the viewer will affect
the final appearance, no matter how painstakingly one
tries to format tables.

However, it goes beyond that when reading posts on the
Yahoo interface, because Yahoo actually *removes* additional
spaces on the regular view! That's exactly why i use dots.

Note that Yahoo does preserve the original number of
spaces somewhere, because if you click "Reply" you do
get tables and diagrams formatted as they were originally
written.

> What a pity that we usually find text easier to read in a
> proportionally-spaced font, whilst formatting data in columns
> in plain text requires the use of a monospaced font!

Yes, it is unfortunate ... but having been a member here
for 7 years now, i'm used to reading everything in Courier
font. 21st-century progress, eh?

In fact, i've gotten so used to creating "ASCII-art" in
the form of diagrams and tables here, that now i use it
in other places too! When writing Csound files (which are
just plain text files which allow comments), i often create
ASCII flowcharts of the instruments, and put them as
comments right into the file. Here's an example (just
open it with Notepad or another text editor to see it):

/tuning/files/monz/d-j_3-25.csd

-monz
http://tonalsoft.com
Tonescape microtonal music software

On Sun, 23 Oct 2005 "monz" wrote:
> Hi Yahya and Mohajeri,
>
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz"
> <yahya@m...> wrote:
>
> > Your method - using dots instead of spaces - at least
> > should make lines cohere reasonably well. I usually
> > use a few spaces, and not more than three columns,
> > understanding that the result may be rather ragged,
> > depending on the fonts that readers use when viewing it.
> > Your dot-joined columns can also appear ragged in the
> > same way.
>
> Yes, of course the font used by the viewer will affect
> the final appearance, no matter how painstakingly one
> tries to format tables.
>
> However, it goes beyond that when reading posts on the
> Yahoo interface, because Yahoo actually *removes* additional
> spaces on the regular view! That's exactly why i use dots.

OK, point taken. If we separate columns with the string
" ... " (space, dot, dot, dot, space), we can expect that to
survive Yahoo's mangling. I'll do that in future.

> Note that Yahoo does preserve the original number of
> spaces somewhere, because if you click "Reply" you do
> get tables and diagrams formatted as they were originally
> written.

I only go to the Yahoo interface when I have plenty of time ...
that is, rarely.

> > What a pity that we usually find text easier to read in a
> > proportionally-spaced font, whilst formatting data in columns
> > in plain text requires the use of a monospaced font!
>
> Yes, it is unfortunate ... but having been a member here
> for 7 years now, i'm used to reading everything in Courier
> font. 21st-century progress, eh?
>
> In fact, i've gotten so used to creating "ASCII-art" in
> the form of diagrams and tables here, that now i use it
> in other places too! When writing Csound files (which are
> just plain text files which allow comments), i often create
> ASCII flowcharts of the instruments, and put them as
> comments right into the file. Here's an example (just
> open it with Notepad or another text editor to see it):
>
> /tuning/files/monz/d-j_3-25.csd

But doesn't that also use tabs to delimit columns? 8-0

I notice in this example you have set a CSound option
-s meaning "use short integer calculation". Does this
affect CSound's pitch resolution - can you use long
integers instead?

Regards,
Yahya

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