56/45: Difference between revisions

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{{Infobox Interval

| Name = septimal narrow major third, marvel-ptolemaic major third, ~~hemifamity~~ diminished fourth

| Name = septimal narrow major third, marvel-ptolemaic major third, aberschismic diminished fourth

| Color name = zg4, zogu 4th

| Sound = jid_56_45_pluck_adu_dr220.mp3

}}

'''56/45''', the '''septimal narrow major third''', or '''marvel-ptolemaic major third''', is the interval between various [[9-odd-limit]] consonances – [[5/4]] and [[14/9]], [[9/7]] and [[8/5]], [[9/8]] and [[7/5]], and [[10/7]] and [[16/9]] – with it also being [[6/5]] away from the marvelous fifth, [[112/75]]. It is flat of the [[81/64|Pythagorean major third]] by [[3645/3584]], namely a [[81/80|syntonic comma]] plus a [[225/224|marvel comma]]. [[Marvel]] tempering makes all of these intervals into classical major thirds, and turns chords like 1–5/4–8/5 or 1–5/4–14/9 into [[essentially tempered dyadic chord]]s. It is a third of a cent flatter than the 6\19 major third of [[19edo]]; however, it functionally doubles as a type of diminished fourth, flat of the [[8192/6561|Pythagorean diminished fourth]] by [[5120/5103]]. This gives rise to the name '''hemifamity diminished fourth'''.

'''56/45''', conventionally known as the '''septimal narrow major third''' or '''marvel-ptolemaic major third''', is flat of the [[81/64|Pythagorean major third]] by [[3645/3584]], namely a [[81/80|syntonic comma]] plus a [[225/224|marvel comma]]. However, it functions more commonly as a diminished fourth, flat of the [[8192/6561|Pythagorean diminished fourth]] by an [[aberschisma]]. This gives rise to the more precise name '''aberschismic diminished fourth''', and in fact it arises as the interval between various [[9-odd-limit]] consonances – between [[5/4]] and [[14/9]], between [[9/7]] and [[8/5]], between [[9/8]] and [[7/5]], and between [[10/7]] and [[16/9]] – with it also being [[6/5]] away from the marvelous fifth, [[112/75]].

According to [[Ozan Yarman]], the perde segah of [[Arabic, Turkish, Persian music|Turkish maqam music]] should range from 56/45 to 5/4.

== Temperaments ==

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

== Approximation ==

This interval is a third of a cent flatter than 6\19, the major third of [[19edo]].

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = septimal narrow major third, marvel-ptolemaic major third, hemifamity diminished fourth
+| Name = septimal narrow major third, marvel-ptolemaic major third, aberschismic diminished fourth
 | Color name = zg4, zogu 4th
 | Sound = jid_56_45_pluck_adu_dr220.mp3
 }}
-'''56/45''', the '''septimal narrow major third''', or '''marvel-ptolemaic major third''', is the interval between various [[9-odd-limit]] consonances – [[5/4]] and [[14/9]], [[9/7]] and [[8/5]], [[9/8]] and [[7/5]], and [[10/7]] and [[16/9]] – with it also being [[6/5]] away from the marvelous fifth, [[112/75]]. It is flat of the [[81/64|Pythagorean major third]] by [[3645/3584]], namely a [[81/80|syntonic comma]] plus a [[225/224|marvel comma]]. [[Marvel]] tempering makes all of these intervals into classical major thirds, and turns chords like 1–5/4–8/5 or 1–5/4–14/9 into [[essentially tempered dyadic chord]]s. It is a third of a cent flatter than the 6\19 major third of [[19edo]]; however, it functionally doubles as a type of diminished fourth, flat of the [[8192/6561|Pythagorean diminished fourth]] by [[5120/5103]]. This gives rise to the name '''hemifamity diminished fourth'''.
+'''56/45''', conventionally known as the '''septimal narrow major third''' or '''marvel-ptolemaic major third''', is flat of the [[81/64|Pythagorean major third]] by [[3645/3584]], namely a [[81/80|syntonic comma]] plus a [[225/224|marvel comma]]. However, it functions more commonly as a diminished fourth, flat of the [[8192/6561|Pythagorean diminished fourth]] by an [[aberschisma]]. This gives rise to the more precise name '''aberschismic diminished fourth''', and in fact it arises as the interval between various [[9-odd-limit]] consonances – between [[5/4]] and [[14/9]], between [[9/7]] and [[8/5]], between [[9/8]] and [[7/5]], and between [[10/7]] and [[16/9]] – with it also being [[6/5]] away from the marvelous fifth, [[112/75]].
 According to [[Ozan Yarman]], the perde segah of [[Arabic, Turkish, Persian music|Turkish maqam music]] should range from 56/45 to 5/4.
+== Temperaments ==
+[[Marvel]] tempering equates this interval with the [[5/4|classical major third]] and turns chords like 1–5/4–8/5 or 1–5/4–14/9 into [[essentially tempered chord]]s.
 == Approximation ==
+This interval is a third of a cent flatter than 6\19, the major third of [[19edo]].
 {{Interval edo approximation|56/45}}