2edo: Difference between revisions

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== Theory ==

The 600 cents step of 2edo corresponds to <math>\sqrt{2} \approx 1.414</math> as a frequency ratio. It is the first edo that can be considered to have a [[prime number]] of divisions, since 1 is not a prime number due to having only itself as a factor. It is the first [[The Riemann zeta function and tuning #Zeta EDO lists|zeta integral edo]] and the first [[The Riemann zeta function and tuning #Zeta EDO lists|zeta gap edo]], and, in addition, it is also a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]], though 2edo is not the first to have this property, with that distinction instead going to [[1edo]].

The 600 cents step of 2edo corresponds to <math>\sqrt{2} \approx 1.414</math> as a frequency ratio. It is the first edo that can be considered to have a [[prime number]] of divisions and the first proper edo, since 1 is not a prime number due to having only itself as a factor and dividing by it returns the same number. It is the first [[The Riemann zeta function and tuning #Zeta EDO lists|zeta integral edo]] and the first [[The Riemann zeta function and tuning #Zeta EDO lists|zeta gap edo]], and, in addition, it is also a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]], though 2edo is not the first to have this property, with that distinction instead going to [[1edo]].

The harmony that is found in 2edo can be said to revolve around Tonic-Antitonic contrast, with the note at 600 cents away from the Tonic having a function akin to [[12edo]]'s diminished fifth. In addition, the full versions of the Antitonic chords of the two possible keys of 2edo are inversions of one another, which can lead to modulations. Furthermore, 2edo can also be used to give a skeletonized version of the 3-limit music such as was used in Medieval Europe, by mapping the fifth and therefore the fourth to 600 cents.

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 == Theory ==
-The 600 cents step of 2edo corresponds to <math>\sqrt{2} \approx 1.414</math> as a frequency ratio. It is the first edo that can be considered to have a [[prime number]] of divisions, since 1 is not a prime number due to having only itself as a factor. It is the first [[The Riemann zeta function and tuning #Zeta EDO lists|zeta integral edo]] and the first [[The Riemann zeta function and tuning #Zeta EDO lists|zeta gap edo]], and, in addition, it is also a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]], though 2edo is not the first to have this property, with that distinction instead going to [[1edo]].
+The 600 cents step of 2edo corresponds to <math>\sqrt{2} \approx 1.414</math> as a frequency ratio. It is the first edo that can be considered to have a [[prime number]] of divisions and the first proper edo, since 1 is not a prime number due to having only itself as a factor and dividing by it returns the same number. It is the first [[The Riemann zeta function and tuning #Zeta EDO lists|zeta integral edo]] and the first [[The Riemann zeta function and tuning #Zeta EDO lists|zeta gap edo]], and, in addition, it is also a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]], though 2edo is not the first to have this property, with that distinction instead going to [[1edo]].
 The harmony that is found in 2edo can be said to revolve around Tonic-Antitonic contrast, with the note at 600 cents away from the Tonic having a function akin to [[12edo]]'s diminished fifth. In addition, the full versions of the Antitonic chords of the two possible keys of 2edo are inversions of one another, which can lead to modulations. Furthermore, 2edo can also be used to give a skeletonized version of the 3-limit music such as was used in Medieval Europe, by mapping the fifth and therefore the fourth to 600 cents.