2197/2187: Difference between revisions

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Aura (talk | contribs)
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Made it more clear that 2197/2187 is the Threedie itself.
Flirora (talk | contribs)
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add infobox + cleanup
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The '''Threedie''', which is the interval '''2197/2187''' (13^3/3^7), is a 3.13 analog of the 2.5 [[128/125|diesis]], 2^7/5^3. Tempering by it, instead of chopping the octave into three sharp 5/4s, chops the tritave (3) into three slightly flat 13/9s, since (13/9)^3/3 = 2197/2187. 596 provides the optimal patent val for the corresponding rank five temperament.
{{Infobox Interval
| Icon =
| Ratio = 2197/2187
| Monzo = 0 -7 0 0 0 3
| Cents = 7.89798
| Name = threedie
| Color name =
| FJS name = dd2<sup>13,13,13</sup>
| Sound =
}}
 
The '''threedie''', '''2197/2187''', is a 3.13 analog of the 2.5 [[128/125|diesis]]. Analogously to tempering the diesis, which divides the octave into three sharp 5/4s, tempering the threedie divides the [[tritave]] into three slightly flat 13/9s, since (13/9)<sup>3</sup>/3 = 2197/2187. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.

Revision as of 05:48, 10 March 2021

Interval information
Ratio 2197/2187
Factorization 3-7 × 133
Monzo [0 -7 0 0 0 3⟩
Size in cents 7.897979¢
Name threedie
FJS name [math]\displaystyle{ \text{dd2}^{13,13,13} }[/math]
Special properties reduced
Tenney height (log2 nd) 22.1961
Weil height (log2 max(n, d)) 22.2026
Wilson height (sopfr(nd)) 60
Open this interval in xen-calc

The threedie, 2197/2187, is a 3.13 analog of the 2.5 diesis. Analogously to tempering the diesis, which divides the octave into three sharp 5/4s, tempering the threedie divides the tritave into three slightly flat 13/9s, since (13/9)3/3 = 2197/2187. 596edo provides the optimal patent val for the corresponding rank-5 temperament.

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