from edo to rational

Hi

I tried to do as monzo told , but may be very bad because of lack of my
skill.

If we consider 2 equall-degree systems of edo and rdo(rational
divisions of octave)(otonal=i/c , utonal=c/d)

And:

cR= cent of rational intervals

cE= cent of equally divided intervals

K=any positive numbers from 1 to infinity

And considering :

1- C' =cR-cE

2- C'K= C'/k

3- New c=cR-C' K

if k=1 , system=edo

if k goes to infinity , system will change gradually to rational

12-EDO

R cE

1 0

1.059463094 100

1.122462048 200

1.189207115 300

1.25992105 400

1.334839854 500

1.414213562 600

1.498307077 700

1.587401052 800

1.681792831 900

1.781797436 1000

1.887748625 1100

2 1200

12-rdo(i/c)((otonal)) R cR

12 12 1 1 1
0

13 12 13 12 1.083333333 138.5726609

14 12 7 6 1.166666667 266.8709056

15 12 5 4 1.25
386.3137139

16 12 4 3 1.333333333 498.0449991

17 12 17 12 1.416666667 603.0004086

18 12 3 2 1.5
701.9550009

19 12 19 12 1.583333333 795.5580153

20 12 5 3 1.666666667 884.358713

21 12 7 4 1.75
968.8259065

22 12 11 6 1.833333333 1049.362941

23 12 23 12 1.916666667 1126.319346

24 12 2 1 2
1200

We have:

k=1.2
k=2 k=8
k=10000

C'=cR-cE C'/1.2 NEWc1 C'/2
NEW c2 C'/8 NEW c3 C'/10000
NEW c4

0 0 0 0
0 0 0 0
0

38.5726609 32.14388409 106.4287768 19.28633045
119.2863305 4.821582613 133.7510783 0.003857266
138.5688036

66.8709056 55.72575467 211.1451509 33.4354528
233.4354528 8.3588632 258.5120424 0.006687091
266.8642185

86.31371386 71.92809489 314.385619 43.15685693
343.1568569 10.78921423 375.5244996 0.008631371
386.3050825

98.04499913 81.70416595 416.3408332 49.02249957
449.0224996 12.25562489 485.7893742 0.0098045
498.0351946

103.0004086 85.83367386 517.1667348 51.50020432
551.5002043 12.87505108 590.1253576 0.010300041
602.9901086

101.9550009 84.96250072 616.9925001 50.97750043
650.9775004 12.74437511 689.2106258 0.0101955
701.9448054

95.55801527 79.63167939 715.9263359 47.77900763
747.7790076 11.94475191 783.6132634 0.009555802
795.5484595

84.358713 70.2989275 814.0597855 42.1793565
842.1793565 10.54483912 873.8138739 0.008435871
884.3502771

68.82590647 57.35492206 911.4709844 34.41295323
934.4129532 8.603238309 960.2226682 0.006882591
968.8190239

49.3629415 41.13578458 1008.227157 24.68147075
1024.681471 6.170367687 1043.192574 0.004936294
1049.358005

26.3193464 21.93278867 1104.386558 13.1596732
1113.159673 3.2899183 1123.029428 0.002631935
1126.316714

0 0 1200
0 1200 0 1200
0 1200

and the same for 12-rdo(c/d)((utonal))

and at the end , the result :

0 0 0
0 0 0 0
0 0

138.5726609 133.7510783 119.2863305 106.4287768 100
95.61344227 86.8403268 76.9705719 73.6806536

266.8709056 258.5120424 233.4354528 211.1451509 200
191.7728431 175.3185293 156.8074262 150.6370585

386.3137139 375.5244996 343.1568569 314.385619 300
288.5290156 265.5870468 239.7773318 231.1740935

498.0449991 485.7893742 449.0224996 416.3408332 400
385.9402145 357.8206435 326.1861261 315.641287

603.0004086 590.1253576 551.5002043 517.1667348 500
484.0736641 452.2209924 416.3867366 404.4419847

701.9550009 689.2106258 650.9775004 616.9925001 600
583.0074999 549.0224996 510.7893742 498.0449991

795.5580153 783.6132634 747.7790076 715.9263359 700
682.8332652 648.4997957 609.8746424 596.9995914

884.358713 873.8138739 842.1793565 814.0597855 800
783.6591668 750.9775004 714.2106258 701.9550009

968.8259065 960.2226682 934.4129532 911.4709844 900
885.614381 856.8431431 824.4755004 813.6862861

1049.362941 1043.192574 1024.681471 1008.227157 1000
988.8548491 966.5645472 941.4879576 933.1290944

1126.319346 1123.029428 1113.159673 1104.386558 1100
1093.571223 1080.71367 1066.248922 1061.427339

1200 1200 1200 1200
1200 1200 1200 1200
1200

OTONAL>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> EDO
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< UTONAL

The graph is like this but I can't upload it's excell format in the
files of group because of no enough space.

/ Edo(the line)

1200I / /

I / / /

Iotonal / / / utonal

I / / /

I / / /

I / / /

I / / /

I / /

0I/___________________________________________

1 13

we can also have different trends as result with c=cR+C' K or k as
negative numbers .

Shaahin Mohaajeri

Tombak Player & Researcher , Composer

www.geocities.com/acousticsoftombak

My tombak musics : www.rhythmweb.com/gdg <http://www.rhythmweb.com/gdg>

My articles in ''Harmonytalk'':

www.harmonytalk.com/archives/000296.html
<http://www.harmonytalk.com/archives/000296.html>

www.harmonytalk.com/archives/000288.html
<http://www.harmonytalk.com/archives/000288.html>

My article in DrumDojo:

www.drumdojo.com/world/persia/tonbak_acoustics.htm
<http://www.drumdojo.com/world/persia/tonbak_acoustics.htm>