Yahoo Tuning Groups Ultimate Backup tuning to make ADL and EDL systems using scala , RE: [tuning] Re: ozan's 18 out of 79 tone improved system

You can make ADL and EDL systems using scala as below :

File - new-harmonic scale

If the first harmonic > last harmonic you have ADL system

If not you have EDL system

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

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf
Of Ozan Yarman
Sent: Monday, April 10, 2006 10:04 PM
To: tuning@yahoogroups.com
Subject: [tuning] Re: ozan's 18 out of 79 tone improved system

Brother, what you propose is this:

0: 1/1 0.000 unison, perfect prime
1: 17/16 104.955 17th harmonic
2: 119/110 136.150
3: 119/106 200.277
4: 119/100 301.154
5: 17/14 336.130 supraminor third
6: 119/95 389.955
7: 119/89 502.901
8: 119/87 542.249
9: 17/12 603.000 2nd septendecimal tritone
10: 75/52 634.055
11: 3/2 701.955 perfect fifth
12: 75/47 809.076
13: 75/46 846.308
14: 150/89 903.702
15: 30/17 983.313
16: 75/41 1045.520
17: 150/79 1110.046
18: 2/1 1200.000 octave

Compared with 18 out of my 79-tone system, the maximum difference is 7
cents:

1: 1: 0.929 cents 0.928770 0.1492 Hertz, 8.9501
cycles/min.
2: 2: -0.013 cents -0.012849 0.0021 Hertz, 0.1260
cycles/min.
3: 3: -3.635 cents -3.634720 0.6160 Hertz, 36.9600
cycles/min.
4: 4: 1.372 cents 1.372351 0.2469 Hertz, 14.8136
cycles/min.
5: 5: -3.351 cents -3.350643 0.6143 Hertz, 36.8557
cycles/min.
6: 6: 3.330 cents 3.329524 0.6309 Hertz, 37.8529
cycles/min.
7: 7: -3.733 cents -3.732908 0.7535 Hertz, 45.2076
cycles/min.
8: 8: 2.298 cents 2.298109 0.4753 Hertz, 28.5208
cycles/min.
9: 9: 2.052 cents 2.052071 0.4396 Hertz, 26.3750
cycles/min.
10: 10: 1.250 cents 1.250333 0.2726 Hertz, 16.3575
cycles/min.
11: 11: -0.000 cents -0.000000 0.0000 Hertz, 0.0000
cycles/min.
12: 12: -1.237 cents -1.236626 0.2981 Hertz, 17.8864
cycles/min.
13: 13: 6.910 cents 6.910038 1.7060 Hertz, 102.3591
cycles/min.
14: 14: -5.105 cents -5.105251 1.2984 Hertz, 77.9029
cycles/min.
15: 15: 6.042 cents 6.041624 1.6140 Hertz, 96.8411
cycles/min.
16: 16: 4.340 cents 4.340146 1.2013 Hertz, 72.0779
cycles/min.
17: 17: 0.320 cents 0.319889 0.0918 Hertz, 5.5078
cycles/min.
18: 18: 1.123 cents 1.123290 0.3396 Hertz, 20.3769
cycles/min.
Mode: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Total absolute difference : 47.0392 cents
Average absolute difference: 2.6133 cents
Root mean square difference: 3.2940 cents
Highest absolute difference: 6.9100 cents
Number of notes different: 17

I'm sure there is a better EDL cardinality that we can agree upon.

Manuel, can you implement New Scale|EDL into SCALA?

Cordially,

Ozan

----- Original Message -----

From: Mohajeri Shahin <mailto:shahinm@kayson-ir.com>

To: tuning@yahoogroups.com

Sent: 10 Nisan 2006 Pazartesi 6:32

Subject: ozan's 18 out of 79 tone improved system :RE: [tuning]
Re: reality of using tuning systems in fretted instruments

Dear ozan

Thanks for your comments , your 18 out of 79 tone improved
system is nearly parts of 119-EDL and 150-EDL . so for fretting
instrument , considering compensation, we must fret according to these 2
to have a sounding around your system :

119-EDL :

0: -- 1/1 -- 0.000 unison, perfect prime

7: -- 17/16 -- 104.955 17th harmonic

9: -- 119/110 -- 136.150

13: -- 119/106 -- 200.277

19: -- 119/100 -- 301.154

21: -- 17/14 -- 336.130 supraminor third

24: -- 119/95 -- 389.955

30: -- 119/89 -- 502.901

32: -- 119/87 -- 542.249

35: -- 17/12 -- 603.000 2nd septendecimal
tritone

__________________________________________________________________

150-EDL:

46: 75/52 -- 634.055

50: 3/2 -- 701.955 perfect fifth

56: 75/47 -- 809.076

58: 75/46 -- 846.308

61: 150/89 -- 903.702

65: 30/17 -- 983.313

68: 75/41 -- 1045.520

71: 150/79 -- 1110.046

75: 2/1 -- 1200.000 octave

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

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🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

Hi ozan

If I understood correctly , yes we can go beyond octave .but going into different cardinalities considering octave equivalency.have a Look at the example in ADL:

------6/12-7/12-8/12--.....12/12-13/12-----24/12-25/12-26/12-----48/12

(6/3 or 6/6)...........(12/6 or 12/12) .........(24/12 or 24/24)...........(48/24 or 48/48).......

Yes , ADO , EDO and EDL are with different natures .

If you consider 12-ado and 24-edl you have C1(ADO)+C11(EDL)=1200 CENT SO Cn(ADO)+C(12-n)(EDL)=1200 that is the trend of successive interval difference in EDL is increasingly but in ADO vice versa.

But about adl , assume to divide octave of string length of 64 cm to 8-ADL and the first part is L cm from nut on string , the others are :

L,L+D,L+2D,.....,L+7D

AND SUM OF ALL THESE LENGTH MUST BE 32.after calculating we have these cents :

54.96442754

128.2982447

222.3637231

340.5515592

487.7705829

671.3128903

902.4869839

1200

Good sounding !! IF YOU START FROM 222.363 YOU CAN HAVE A FLAT FIFTH OF ABOUT 680 CENT.

In ADL like EDL the trend of successive interval difference is increasingly . you know that in EDO it is constant.so we see that ADO , EDO , ADL and EDL are with different natures.

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

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Ozan Yarman
Sent: Saturday, April 15, 2006 12:07 AM
To: Tuning List
Subject: Re: to make ADL and EDL systems using scala , RE: [tuning] Re: ozan's 18 out of 79 tone improved system

So now we have Arithmetic as well as Equal Divisions of the Octave (ADO-EDO) and Lenght (ADL-EDL)... provided that we are talking about the ideal string of infinitesimal thickness. What about pipes and reeds?

And also, do we need to normalize a scale by 2/1 as a necessity of these definitions? Why not just say harmonic and sub-harmonic scales?

----- Original Message -----

From: Mohajeri Shahin <mailto:shahinm@kayson-ir.com>

To: tuning@yahoogroups.com

Sent: 12 Nisan 2006 Çarşamba 9:18

Subject: to make ADL and EDL systems using scala , RE: [tuning] Re: ozan's 18 out of 79 tone improved system

You can make ADL and EDL systems using scala as below :

File - new-harmonic scale

If the first harmonic > last harmonic you have ADL system

If not you have EDL system

Shaahin Mohaajeri

________________________________

YAHOO! GROUPS LINKS

* Visit your group "tuning </tuning> " on the web.

* To unsubscribe from this group, send an email to:
tuning-unsubscribe@yahoogroups.com <mailto:tuning-unsubscribe@yahoogroups.com?subject=Unsubscribe>

* Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service <http://docs.yahoo.com/info/terms/> .

________________________________

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

Thank you for the explanations brother. It'll take some time for me to process them of course.

Cordially,
Oz.
----- Original Message -----
From: Mohajeri Shahin
To: tuning@yahoogroups.com
Sent: 15 Nisan 2006 Cumartesi 10:46
Subject: RE: to make ADL and EDL systems using scala , RE: [tuning] Re: ozan's 18 out of 79 tone improved system

Hi ozan

If I understood correctly , yes we can go beyond octave .but going into different cardinalities considering octave equivalency.have a Look at the example in ADL:

------6/12—7/12—8/12--…..12/12—13/12-----24/12—25/12—26/12-----48/12

(6/3 or 6/6)………..(12/6 or 12/12) ………(24/12 or 24/24)………..(48/24 or 48/48)…….

Yes , ADO , EDO and EDL are with different natures .

If you consider 12-ado and 24-edl you have C1(ADO)+C11(EDL)=1200 CENT SO Cn(ADO)+C(12-n)(EDL)=1200 that is the trend of successive interval difference in EDL is increasingly but in ADO vice versa.

But about adl , assume to divide octave of string length of 64 cm to 8-ADL and the first part is L cm from nut on string , the others are :

L,L+D,L+2D,…..,L+7D

AND SUM OF ALL THESE LENGTH MUST BE 32.after calculating we have these cents :

54.96442754

128.2982447

222.3637231

340.5515592

487.7705829

671.3128903

902.4869839

1200

Good sounding !! IF YOU START FROM 222.363 YOU CAN HAVE A FLAT FIFTH OF ABOUT 680 CENT.

In ADL like EDL the trend of successive interval difference is increasingly . you know that in EDO it is constant.so we see that ADO , EDO , ADL and EDL are with different natures.

Shaahin Mohaajeri