45/28: Difference between revisions

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{{Infobox Interval

| Name = septimal wide minor sixth, marvel-ptolemaic minor sixth, ~~hemifamity~~ augmented fifth

| Name = septimal wide minor sixth, marvel-ptolemaic minor sixth, aberschismic augmented fifth

| Color name = ry5, ruyo 5th

}}

'''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'''.

'''45/28''', conventionally known as 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]]. However, it functions more commonly as an augmented fifth, sharp of the [[6561/4096|Pythagorean augmented fifth]] by an [[aberschisma]]. This gives rise to the more precise name '''aberschismic augmented fifth''', and in fact it arises as the result of stacking certain [[9-odd-limit]] consonances – of [[5/4]] and [[9/7]], and of [[9/8]] and [[10/7]].

== Temperaments ==

[[Marvel]] tempering equates this interval with the [[8/5|classical minor sixth]] and turns chords like 1–5/4–8/5 or 1–5/4–14/9 into [[essentially tempered chord]]s.

== Approximation ==

This interval is only a third of a [[cent]] sharper than 13\19, the minor sixth of [[19edo]].

== See also ==

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[[Category:Augmented fifth]]

[[Category:Aberschismic]]

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 {{Infobox Interval
-| Name = septimal wide minor sixth, marvel-ptolemaic minor sixth, hemifamity augmented fifth
+| Name = septimal wide minor sixth, marvel-ptolemaic minor sixth, aberschismic augmented fifth
 | Color name = ry5, ruyo 5th
 }}
-'''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'''.
+'''45/28''', conventionally known as 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]]. However, it functions more commonly as an augmented fifth, sharp of the [[6561/4096|Pythagorean augmented fifth]] by an [[aberschisma]]. This gives rise to the more precise name '''aberschismic augmented fifth''', and in fact it arises as the result of stacking certain [[9-odd-limit]] consonances – of [[5/4]] and [[9/7]], and of [[9/8]] and [[10/7]].
+== Temperaments ==
+[[Marvel]] tempering equates this interval with the [[8/5|classical minor sixth]] and turns chords like 1–5/4–8/5 or 1–5/4–14/9 into [[essentially tempered chord]]s.
+== Approximation ==
+This interval is only a third of a [[cent]] sharper than 13\19, the minor sixth of [[19edo]].
+{{Interval edo approximation|45/28}}
 == See also ==
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 [[Category:Augmented fifth]]
 [[Category:Aberschismic]]
 {{Todo|add sound example}}