45/28: Difference between revisions

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added color name
Make this marvel-ptolemaic until 3645/3584 has an accepted name
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{{Infobox Interval
{{Infobox Interval
| Name = septimal wide minor sixth, marvelous minor sixth
| Name = septimal wide minor sixth, marvel-ptolemaic minor sixth, hemifamity augmented fifth
| Color name = ry5, ruyo 5th
| Color name = ry5, ruyo 5th
}}
}}
'''45/28''', the '''septimal wide minor sixth''', or '''marvelous minor sixth''', is an interval that is only a third of a [[cent]] sharper than the 13\19 minor sixth of [[19edo]], however, it functionally doubles as a type of augmented fifth.
'''45/28''', the '''septimal wide minor sixth''', or '''marvel-ptolemaic minor sixth''', is an interval that is sharp of the [[128/81|Pythagorean minor sixth]] by [[3645/3584]], i.e. a [[81/80|syntonic comma]] plus a [[225/224|marvel comma]]. It is only a third of a [[cent]] sharper than the 13\19 minor sixth of [[19edo]]; however, it functionally doubles as a type of augmented fifth, sharp of the [[6561/4096|Pythagorean augmented fifth]] by [[5120/5103]]. This gives rise to the name '''hemifamity augmented fifth'''.  


== See also ==
== See also ==
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[[Category:Sixth]]
[[Category:Sixth]]
[[Category:Minor sixth]]
[[Category:Minor sixth]]
[[Category:Marvel]]
[[Category:Fifth]]
[[Category:Augmented fifth]]
[[Category:Hemifamity]]


{{Todo|add sound example}}
{{Todo|add sound example}}

Revision as of 12:31, 6 January 2026

Interval information
Ratio 45/28
Factorization 2-2 × 32 × 5 × 7-1
Monzo [-2 2 1 -1
Size in cents 821.3978¢
Names septimal wide minor sixth,
marvel-ptolemaic minor sixth,
hemifamity augmented fifth
Color name ry5, ruyo 5th
FJS name [math]\displaystyle{ \text{A5}^{5}_{7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 10.2992
Weil norm (log2 max(n, d)) 10.9837
Wilson norm (sopfr(nd)) 22
Open this interval in xen-calc

45/28, the septimal wide minor sixth, or marvel-ptolemaic minor sixth, is an interval that is sharp of the Pythagorean minor sixth by 3645/3584, i.e. a syntonic comma plus a marvel comma. It is only a third of a cent sharper than the 13\19 minor sixth of 19edo; however, it functionally doubles as a type of augmented fifth, sharp of the Pythagorean augmented fifth by 5120/5103. This gives rise to the name hemifamity augmented fifth.

See also