8019/8000: Difference between revisions

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useful to be able to look up
 
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explained that/why 183edo may be less preferable to 118edo
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'''8019/8000''' is a comma in the 2.3.5.11 subgroup, equal to ([[11/8]])/([[10/9]])<sup>3</sup>. In terms of microtempering the 2.3.5.11 subgroup, it may combine well with the [[schisma]] due to the schisma equating three [[9/8]]'s with a [[64/45]]. This combination may be desirable as it gives lower-complexity interpretations of the most complex tritones in the [[5-limit]]: those corresponding to (10/9)<sup>3</sup> and [[729/512|(9/8)<sup>3</sup>]], the similarity being due to both stacking three of one of the two simplest 5-limit whole tones. For tempering both, [[118edo]] and [[183edo]] are recommendable, although [[65edo]] provides a less accurate tuning at the benefit of a more manageable number of tones.
'''8019/8000''' is a comma in the 2.3.5.11 subgroup, equal to ([[11/8]])/([[10/9]])<sup>3</sup>.
 
== Temperaments ==
In terms of microtempering the 2.3.5.11 subgroup, it may combine well with the [[schisma]] as doing so gives lower-complexity interpretations to the [[5-limit]] "tritones" of (10/9)<sup>3</sup> and [[729/512|(9/8)<sup>3</sup>]] and their octave-complements, which results in the 53&65 temperament in the 2.3.5.11 subgroup. (The term "tritones" is being used here in the sense of stacking 3 tones, as calling (10/9)<sup>3</sup> a "tritone" is questionable.) For optimising this temperament, [[183edo]] is recommendable, although [[65edo]] provides a less accurate tuning at the benefit of a more manageable number of tones. If extended to the full [[11-limit|11-]] or [[13-limit]], it is closely related to [[Schismatic family#Bischismic|Bischismic]], which also tempers [[3136/3125]].


== See also ==
== See also ==

Revision as of 02:33, 6 April 2021

Interval information
Ratio 8019/8000
Factorization 2-6 × 36 × 5-3 × 11
Monzo [-6 6 -3 0 1
Size in cents 4.106806¢
Name(s) missing ? 
FJS name [math]\displaystyle{ \text{d1}^{11}_{5,5,5} }[/math]
Special properties reduced
Tenney height (log2 nd) 25.935
Weil height (log2 max(n, d)) 25.9384
Wilson height (sopfr(nd)) 56
Open this interval in xen-calc

8019/8000 is a comma in the 2.3.5.11 subgroup, equal to (11/8)/(10/9)3.

Temperaments

In terms of microtempering the 2.3.5.11 subgroup, it may combine well with the schisma as doing so gives lower-complexity interpretations to the 5-limit "tritones" of (10/9)3 and (9/8)3 and their octave-complements, which results in the 53&65 temperament in the 2.3.5.11 subgroup. (The term "tritones" is being used here in the sense of stacking 3 tones, as calling (10/9)3 a "tritone" is questionable.) For optimising this temperament, 183edo is recommendable, although 65edo provides a less accurate tuning at the benefit of a more manageable number of tones. If extended to the full 11- or 13-limit, it is closely related to Bischismic, which also tempers 3136/3125.

See also