2edt: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''2EDT''', if the attempt is made to use it as an actual scale, would divide the [[3/1|tritave]] into two equal parts, each of size 950.9775 cents, which is to say sqrt(3) as a frequency ratio. If we want to consider it to be a temperament, it tempers out [[27/25]], equating 5/3 with 9/5.
{{EDO intro}}


==Factoids about 2EDT==
=== Theory ===
[[26/15]] and 45/26 are [[Nearest just interval|good rational representations]] of the square root of 3.


2EDT is closely related to the [[Very high accuracy temperaments|monzismic temperament]], which tempers out |54 -37 2>, the monzisma.
As a temperament in the 3.5 [[subgroup]], it tempers out [[27/25]], equating 5/3 with 9/5.
 
Since [[26/15]] is a convergent of sqrt(3), 26/15 (and its [[tritave complement]] 45/26) are good rational representations of the square root of 3. 2edt thus tempers out (26/15)<sup>2</sup> / (3/1) = [[676/675]], the island comma.
 
One step of 2edt is close to the optimal TE generator of [[Very high accuracy temperaments|monzismic temperament]], which tempers out {{monzo|54 -37 2}}, the monzisma.
 
===Odd harmonics===
{{Harmonics in equal|2|3|1|intervals=odd}}


[[Category:Edt]]
[[Category:Edt]]
[[Category:Edonoi]]
[[Category:Edonoi]]

Revision as of 09:28, 28 April 2024

← 1edt 2edt 3edt →
Prime factorization 2 (prime) (highly composite)
Step size 950.978 ¢ 
Octave 1\2edt (950.978 ¢)
(convergent)
Consistency limit 3
Distinct consistency limit 2

Template:EDO intro

Theory

As a temperament in the 3.5 subgroup, it tempers out 27/25, equating 5/3 with 9/5.

Since 26/15 is a convergent of sqrt(3), 26/15 (and its tritave complement 45/26) are good rational representations of the square root of 3. 2edt thus tempers out (26/15)2 / (3/1) = 676/675, the island comma.

One step of 2edt is close to the optimal TE generator of monzismic temperament, which tempers out [54 -37 2⟩, the monzisma.

Odd harmonics

Approximation of odd harmonics in 2edt
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0 +67 +435 +0 -347 +314 +67 -150 -343 +435 +278
Relative (%) +0.0 +7.0 +45.8 +0.0 -36.5 +33.1 +7.0 -15.8 -36.0 +45.8 +29.2
Steps
(reduced) 		2
(0) 		3
(1) 		4
(0) 		4
(0) 		4
(0) 		5
(1) 		5
(1) 		5
(1) 		5
(1) 		6
(0) 		6
(0)
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