752/729: Difference between revisions

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'''752/729''', or the '''47-limit ~quartertone comma (HEJI)''', is a 2.3.47 subgroup comma. It is the amount by which the octave-reduced 47th harmonic [[47/32]] exceeds the [[729/512|Pythagorean augmented fourth (729/512)]]. It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby quadracesimoseptimal (47-limit) interval.
'''752/729''', or the '''47-limit ~quartertone comma (HEJI)''', is a 2.3.47 subgroup comma. It is the amount by which the octave-reduced 47th harmonic [[47/32]] exceeds the [[729/512|Pythagorean augmented fourth (729/512)]]. Prior to March 2025, it was the formal comma to translate a Pythagorean interval to a nearby quadracesimoseptimal (47-limit) interval in [[Helmholtz–Ellis notation]].


[[Category:Commas named after their interval size]]
[[Category:Commas named after their interval size]]

Latest revision as of 13:39, 12 July 2025

Interval information
Ratio 752/729
Subgroup monzo 2.3.47 [4 -6 1
Size in cents 53.77662¢
Name 47-limit ~quartertone (HEJI)
Color name s47o2, safoso 2nd
FJS name [math]\displaystyle{ \text{m2}^{47} }[/math]
Special properties reduced
Tenney norm (log2 nd) 19.0644
Weil norm (log2 max(n, d)) 19.1092
Wilson norm (sopfr(nd)) 73
Comma size medium
Open this interval in xen-calc

752/729, or the 47-limit ~quartertone comma (HEJI), is a 2.3.47 subgroup comma. It is the amount by which the octave-reduced 47th harmonic 47/32 exceeds the Pythagorean augmented fourth (729/512). Prior to March 2025, it was the formal comma to translate a Pythagorean interval to a nearby quadracesimoseptimal (47-limit) interval in Helmholtz–Ellis notation.