AFDO: Difference between revisions

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'''~~ARDO~~''' (which is ~~simplified as ADO) refers~~ to ~~Arithmetic Rational Divisions of~~ the ~~Octave~~. it is an ~~intervallic~~ system ~~considered as an arithmetic sequence with divisions of~~ the ~~system as terms of a sequence~~.

'''ADO''' (arithmetic divisions of the octave) is a tuning system which divides the octave arithmetically rather than logarithmically. For any C-ADO system, the m-th degree is equal to the ratio (C+m)/C. For example, in 12-ADO the first degree is [[13/12]], the second is 14/12 ([[7/6]]), and so on. For an ADO system, the distance between ratios is equal, rater than the distance between their logarithms like in EDO systems.

If the first division is <math>R_1</math> (which is ratio of C/C) and the last , <math>R_n</math> (which is ratio of 2C/C), with common difference of d

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</math>

Each consequent divisions like R4 and R3 have a difference of d with each other.The concept of division here is a bit different from EDO and other systems (which is the difference of cents of two consequent degree). In ADO, a division is frequency-related and is the ratio of each degree due to the first degree.For example ratio of 1.5 is the size of 3/2 in 12-ADO system.

If the first division has ratio of R1 and length of L1 and the last, Rn and Ln , we have: Ln = 1/Rn and if Rn >........> R3 > R2 > R1 so :

~~For any C-ADO system with **cardinality** of C, we have ratios related to different degrees of m as :~~

~~(C+m/C)~~

~~For example , in 12-ADO the ratio related to the first degree is 13/12 .~~

~~12-ADO can be shown as series like: 12:13:14:15:16:17:18:19:20:21:22:23:24 or 12 13 14 15 16 17 18 19 20 21 22 23 24 .~~

~~For an ADO intervallic system with n divisions we have unequal divisions of length by dividing string length ton unequal divisions based on each degree ratios.~~If the first division has ratio of R1 and length of L1 and the last, Rn and Ln , we have: Ln = 1/Rn and if Rn >........> R3 > R2 > R1 so :

L1 > L2 > L3 > …… > Ln

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-'''ARDO''' (which is simplified as ADO) refers to Arithmetic Rational Divisions of the Octave. it is an intervallic system considered as an arithmetic sequence with divisions of the system as terms of a sequence.
+'''ADO''' (arithmetic divisions of the octave) is a tuning system which divides the octave arithmetically rather than logarithmically.  For any C-ADO system, the m-th degree is equal to the ratio (C+m)/C. For example, in 12-ADO the first degree is [[13/12]], the second is 14/12 ([[7/6]]), and so on. For an ADO system, the distance between ratios is equal, rater than the distance between their logarithms like in EDO systems.
 If the first division is <math>R_1</math> (which is ratio of C/C) and the last , <math>R_n</math> (which is ratio of 2C/C), with common difference of d
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 </math>
-Each consequent divisions like R4 and R3 have a difference of d with each other.The concept of division here is a bit different from EDO and other systems (which is the difference of cents of two consequent degree). In ADO, a division is frequency-related and is the ratio of each degree due to the first degree.For example ratio of 1.5 is the size of 3/2 in 12-ADO system.
+If the first division has ratio of R1 and length of L1 and the last, Rn and Ln , we have: Ln = 1/Rn and if Rn &gt;........&gt; R3 &gt; R2 &gt; R1 so :
-For any C-ADO system with **cardinality** of C, we have ratios related to different degrees of m as :
-(C+m/C)
-For example , in 12-ADO the ratio related to the first degree is 13/12 .
--ADO can be shown as series like: 12:13:14:15:16:17:18:19:20:21:22:23:24 or 12 13 14 15 16 17 18 19 20 21 22 23 24 .
-For an ADO intervallic system with n divisions we have unequal divisions of length by dividing string length ton unequal divisions based on each degree ratios.If the first division has ratio of R1 and length of L1 and the last, Rn and Ln , we have: Ln = 1/Rn and if Rn &gt;........&gt; R3 &gt; R2 &gt; R1 so :
 L1 &gt; L2 &gt; L3 &gt; …… &gt; Ln