40/39: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| JI glyph =
| Ratio = 40/39
| Ratio = 40/39
| Monzo = 3 -1 1 0 0 -1
| Monzo = 3 -1 1 0 0 -1
| Cents = 43.83105
| Cents = 43.83105
| Name = tridecimal 1/5-tone, <br> tridecimal minor diesis
| Name = tridecimal 1/5-tone, <br> tridecimal minor diesis
| Color name =  
| Color name = 3uy1, thuyo unison
| FJS name =  
| FJS name = A1<sup>5</sup><sub>13</sub>
| Sound =  
| Sound =  
}}
}}
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[[Category:13-limit]]
[[Category:13-limit]]
[[Category:interval]]
[[Category:Superparticular]]
[[Category:superparticular]]
 
[[category:todo:clarify]] <!-- subsystem?? -->
{{todo|clarify}} <!-- subsystem?? -->

Revision as of 19:42, 19 December 2021

Interval information
Ratio 40/39
Factorization 23 × 3-1 × 5 × 13-1
Monzo [3 -1 1 0 0 -1
Size in cents 43.83105¢
Names tridecimal 1/5-tone,
tridecimal minor diesis
Color name 3uy1, thuyo unison
FJS name [math]\displaystyle{ \text{A1}^{5}_{13} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 10.6073
Weil height (log2 max(n, d)) 10.6439
Wilson height (sopfr(nd)) 27
Open this interval in xen-calc

40/39 is the difference between the third octave of the third 5/4 (40 = 5 ⋅ 23) and the fifth of the thirteenth partial of the same root (39 = 13 ⋅ 3). Possibility to change from subsystem 4 to subsystem 3 (or 5 to 13).