AFDO: Difference between revisions

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Arithmetic ~~rational~~ divisions of ~~octave~~

'''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.

~~ARDO (which is simplified as ADO) is an intervallic system considered as~~

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

~~arithmetic sequence with divisions of system as terms of sequence.~~

If the first division is R1 (~~wich~~ is ratio of C/C) and the last , Rn (~~wich~~ is ratio of 2C/C), with common difference of d

(which is 1/C), we have :

R2 = R1+d

<math>

R_2 = R_1 + d \\

R3= R1+2d

R_3= R_1 + 2d \\

R_4 = R_1 + 3d \\

R4 = R1+3d

\vdots \\

R_n = R_1 + (n-1)d

~~………~~

</math>

Rn = R1+(n-1)d

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.

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The above picture shows that ADO system is classified as :

- System with unequal **epimorios** (**Superparticular**) divisions.

*System with unequal **epimorios** (**Superparticular**) divisions.

*System based on ascending series of superparticular ratios with descending sizes.

- System based on ascending series of superparticular ratios with descending sizes.

*System which covers superparticular ratios between harmonic of number C (in this example 12)to harmonic of Number 2C(in this example 24).

*An spreadsheet showing relation between harmonics , superparticular ratios and ADO system

- System which covers superparticular ratios between harmonic of number C (in this example 12)to harmonic of Number 2C(in this example 24).

*The Overtone Series

- An spreadsheet showing relation between harmonics , superparticular ratios and ADO system

- The Overtone Series

Relation between Otonality and ADO system

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[[Category:ADO]]

[[Category:todo:cleanup]]

[[Category:todo:Change table images to wikitables]]

@@ Line 1: / Line 1: @@
-Arithmetic rational divisions of octave
+'''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.
-ARDO (which is simplified as ADO) is an intervallic system considered as
+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
-arithmetic sequence with divisions of system as terms of sequence.
-If the first division is R1 (wich is ratio of C/C) and the last , Rn (wich is ratio of 2C/C), with common difference of d
 (which is 1/C), we have :
-R2 = R1+d
+<math>
+R_2 = R_1 + d \\
-R3= R1+2d
+R_3= R_1 + 2d \\
+R_4 = R_1 + 3d \\
-R4 = R1+3d
+\vdots \\
+R_n = R_1 + (n-1)d
-………
+</math>
-Rn = R1+(n-1)d
 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.
@@ Line 50: / Line 44: @@
 The above picture shows that ADO system is classified as :
-- System with unequal **epimorios** (**Superparticular**) divisions.
+*System with unequal **epimorios** (**Superparticular**) divisions.
+*System based on ascending series of superparticular ratios with descending sizes.
-- System based on ascending series of superparticular ratios with descending sizes.
+*System which covers superparticular ratios between harmonic of number C (in this example 12)to harmonic of Number 2C(in this example 24).
+*An spreadsheet showing relation between harmonics , superparticular ratios and ADO system
-- System which covers superparticular ratios between harmonic of number C (in this example 12)to harmonic of Number 2C(in this example 24).
+*The Overtone Series
-- An spreadsheet showing relation between harmonics , superparticular ratios and ADO system
-- The Overtone Series
 Relation between Otonality and ADO system
@@ Line 73: / Line 63: @@
 [[Category:ADO]]
 [[Category:todo:cleanup]]
+[[Category:todo:Change table images to wikitables]]