56/45: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

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

~~| Ratio = 56/45~~

| Color name = zg4, zogu 4th

~~| Monzo = 3 -2 -1 1~~

~~| Cents = 378.60219~~

| Name = septimal narrow major third, ~~<br> marvelous~~ major third

| Color name =

| 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''', the '''septimal narrow major third''', or '''marvelous major third''', is the interval between various 9-limit consonances: 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9. [[Marvel]] tempering makes all of these intervals into major thirds like any other, and turns chords like 1-5/4-8/5 or 1-5/4-14/9 into [[Dyadic_chord|essentially tempered dyadic chords]]. The 56/45 third is [[6/5]] away from the marvelous fifth, [[112/75]], and may also be called the marvelous major third. It is a third of a cent flatter than the 6\19 major third of [[19et]]. According to [[Ozan Yarman]], the perde segah of ~~Turkish~~ [[maqam music]] should range from 56/45.

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

== Approximation ==

== See also ==

* [[45/28]] – its [[octave complement]]

* [[45/28]] -- its octave complement

* [[135/112]] – its [[fifth complement]]

* [[135/112]] -- its fifth complement

* [[Gallery of just intervals]]

~~[[Category:7-limit]]~~

~~[[Category:Just interval]]~~

[[Category:Third]]

[[Category:Major third]]

[[Category:~~19edo~~]]

[[Category:Fourth]]

[[Category:Diminished fourth]]

[[Category:Aberschismic]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = septimal narrow major third, marvel-ptolemaic major third, hemifamity diminished fourth
-| Ratio = 56/45
+| Color name = zg4, zogu 4th
-| Monzo = 3 -2 -1 1
-| Cents = 378.60219
-| Name = septimal narrow major third, <br> marvelous major third
-| Color name =
 | 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''', the '''septimal narrow major third''', or '''marvelous major third''', is the interval between various 9-limit consonances: 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9. [[Marvel]] tempering makes all of these intervals into major thirds like any other, and turns chords like 1-5/4-8/5 or 1-5/4-14/9 into [[Dyadic_chord|essentially tempered dyadic chords]]. The 56/45 third is [[6/5]] away from the marvelous fifth, [[112/75]], and may also be called the marvelous major third. It is a third of a cent flatter than the 6\19 major third of [[19et]].  According to [[Ozan Yarman]], the perde segah of Turkish [[maqam music]] should range from 56/45.
+According to [[Ozan Yarman]], the perde segah of [[Arabic, Turkish, Persian music|Turkish maqam music]] should range from 56/45 to 5/4.
+== Approximation ==
+{{Interval edo approximation|56/45}}
 == See also ==
+* [[45/28]] – its [[octave complement]]
-* [[45/28]] -- its octave complement
+* [[135/112]] – its [[fifth complement]]
-* [[135/112]]  -- its fifth complement
 * [[Gallery of just intervals]]
-[[Category:7-limit]]
-[[Category:Just interval]]
 [[Category:Third]]
 [[Category:Major third]]
-[[Category:19edo]]
+[[Category:Fourth]]
+[[Category:Diminished fourth]]
+[[Category:Aberschismic]]