323/256: Difference between revisions

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Mark as mathematical interest. Infobox to the top. Expand on its relation to the Pyth. M3
 
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{{Mathematical interest}}
'''323/256''', or the '''octave-reduced 323rd harmonic''', is a 19-limit major third that very closely approximates the 12edo major third. It is constructed by stacking [[17/16]] and [[19/16]], two JI intervals that approximate the 12edo minor second and minor third well, respectively.{{Infobox Interval
{{Infobox Interval
| Color name = noso 4th, 19o17o4
| Color name = noso 4th, 19o17o4
| Name = octave-reduced 323rd harmonic
| Name = octave-reduced 323rd harmonic
}}
}}
'''323/256''', or the '''octave-reduced 323rd harmonic''', is a [[19-limit]] major third that is close to the [[12edo]] major third. It is constructed by stacking [[17/16]] and [[19/16]], two JI intervals that approximate the 12edo minor second and minor third well, respectively. It is flat of the [[81/64|Pythagorean major third]] by [[324/323]].

Latest revision as of 09:11, 29 July 2026

This page presents a topic of primarily mathematical interest.

While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown.

Interval information
Ratio 323/256
Subgroup monzo 2.17.19 [-8 1 1
Size in cents 402.4684¢
Name octave-reduced 323rd harmonic
Color name noso 4th, 19o17o4
FJS name [math]\displaystyle{ \text{d4}^{17,19} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 16.3354
Weil norm (log2 max(n, d)) 16.6708
Wilson norm (sopfr(nd)) 52
Open this interval in xen-calc

323/256, or the octave-reduced 323rd harmonic, is a 19-limit major third that is close to the 12edo major third. It is constructed by stacking 17/16 and 19/16, two JI intervals that approximate the 12edo minor second and minor third well, respectively. It is flat of the Pythagorean major third by 324/323.