AFDO: Difference between revisions

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'''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 interval ratios is equal, rather than the distance between their logarithms like in EDO systems. All ADOs are subsets of [[just intonation]]. ADOs with more divisors such as [[Highly_composite_equal_division|highly composite]] ADOs generally have more useful just intervals.

'''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 [[12ado]] the first degree is [[13/12]], the second is 14/12 ([[7/6]]), and so on. For an ADO system, the distance between interval ratios is equal, rather than the distance between their logarithms like in EDO systems. All ADOs are subsets of [[just intonation]]. ADOs with more divisors such as [[Highly_composite_equal_division|highly composite]] ADOs generally have more useful just intervals.

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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An ADO has step sizes of [[superparticular ratios]] with increasing numerators. For example, [[5ado]] has step sizes of [[6/5]], [[7/6]], [[8/7]], and [[9/8]].

== Relation ~~between~~ otonality ~~and ADO system~~ ==

== Relation to otonality & harmonic series ==

We can consider ADO system as otonal system. Otonality is a term introduced by Harry Partch to describe chords whose notes are the overtones (multiples) of a given fixed tone.Considering ADO , an Otonality is a collection of pitches which can be expressed in ratios that have equal denominators. For example, 1/1, 5/4, and 3/2 form an ~~Otonality~~ because they can be written as 4/4, 5/4, 6/4. Every Otonality is therefore part of the harmonic series~~. nominator here is called "numerary nexus"~~.An ~~Otonality~~ corresponds to an **arithmetic series** of frequencies or a harmonic series of wavelengths or distances on a string instrument.

We can consider ADO system as otonal system. Otonality is a term introduced by Harry Partch to describe chords whose notes are the overtones (multiples) of a given fixed tone.Considering ADO , an Otonality is a collection of pitches which can be expressed in ratios that have equal denominators. For example, 1/1, 5/4, and 3/2 form an otonality because they can be written as 4/4, 5/4, 6/4. Every Otonality is therefore part of the harmonic series. An otonality corresponds to an arithmetic series of frequencies or a harmonic series of wavelengths or distances on a string instrument.

- [http://240edo.googlepages.com/ADO-EDL.XLS Fret position calculator] (excel sheet ) based on EDL system and string length

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-'''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 interval ratios is equal, rather than the distance between their logarithms like in EDO systems. All ADOs are subsets of [[just intonation]]. ADOs with more divisors such as [[Highly_composite_equal_division|highly composite]] ADOs generally have more useful just intervals.
+'''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 [[12ado]] the first degree is [[13/12]], the second is 14/12 ([[7/6]]), and so on. For an ADO system, the distance between interval ratios is equal, rather than the distance between their logarithms like in EDO systems. All ADOs are subsets of [[just intonation]]. ADOs with more divisors such as [[Highly_composite_equal_division|highly composite]] ADOs generally have more useful just intervals.
 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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 An ADO has step sizes of [[superparticular ratios]] with increasing numerators. For example, [[5ado]] has step sizes of [[6/5]], [[7/6]], [[8/7]], and [[9/8]].
-== Relation between otonality and ADO system ==
+== Relation to otonality & harmonic series ==
-We can consider ADO system as otonal system. Otonality is a term introduced by Harry Partch to describe chords whose notes are the overtones (multiples) of a given fixed tone.Considering ADO , an Otonality is a collection of pitches which can be expressed in ratios that have equal denominators. For example, 1/1, 5/4, and 3/2 form an Otonality because they can be written as 4/4, 5/4, 6/4. Every Otonality is therefore part of the harmonic series. nominator here is called "numerary nexus".An Otonality corresponds to an **arithmetic series** of frequencies or a harmonic series of wavelengths or distances on a string instrument.
+We can consider ADO system as otonal system. Otonality is a term introduced by Harry Partch to describe chords whose notes are the overtones (multiples) of a given fixed tone.Considering ADO , an Otonality is a collection of pitches which can be expressed in ratios that have equal denominators. For example, 1/1, 5/4, and 3/2 form an otonality because they can be written as 4/4, 5/4, 6/4. Every Otonality is therefore part of the harmonic series. An otonality corresponds to an arithmetic series of frequencies or a harmonic series of wavelengths or distances on a string instrument.
 - [http://240edo.googlepages.com/ADO-EDL.XLS Fret position calculator] (excel sheet ) based on EDL system and string length