56/45: Difference between revisions

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'''56/45'''

{{Infobox Interval

|3 -2 -~~1 1&gt~~;

| Name = septimal narrow major third, marvel-ptolemaic major third, hemifamity 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'''.

~~378~~.~~6022 cents~~

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

~~[[File:jid_56_45_pluck_adu_dr220.mp3]] [[:File:jid_56_45_pluck_adu_dr220.mp3~~|~~sound sample]]~~

== Approximation ==

~~According to~~ [[~~Ozan_Yarman|Ozan Yarman~~]]~~, the perde segah of Turkish maqam music should range from '''56/45''', which is flatter than~~ [[5/~~4|5/4~~]] ~~by the~~ [[~~septimal_kleisma|septimal kleisma~~]] of [[~~225/224|225/224~~]]~~, to 5/4. 56/45 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|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|6/5~~]] ~~away from the marvelous fifth,~~ [[~~112/75|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.~~

== See also ==

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

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

* [[Gallery of just intervals]]

[[Category:Third]]

[[Category:Major third]]

[[Category:Fourth]]

[[Category:Diminished fourth]]

[[Category:Aberschismic]]

@@ Line 1: / Line 1: @@
-'''56/45'''
+{{Infobox Interval
-|3 -2 -1 1&gt;
+| Name = septimal narrow major third, marvel-ptolemaic major third, hemifamity 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'''.
-.6022 cents
+According to [[Ozan Yarman]], the perde segah of [[Arabic, Turkish, Persian music|Turkish maqam music]] should range from 56/45 to 5/4.
-[[File:jid_56_45_pluck_adu_dr220.mp3]] [[:File:jid_56_45_pluck_adu_dr220.mp3|sound sample]]
+== Approximation ==
+{{Interval edo approximation|56/45}}
-According to [[Ozan_Yarman|Ozan Yarman]], the perde segah of Turkish maqam music should range from '''56/45''', which is flatter than [[5/4|5/4]] by the [[septimal_kleisma|septimal kleisma]] of [[225/224|225/224]], to 5/4. 56/45 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|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|6/5]] away from the marvelous fifth, [[112/75|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.
+== See also ==
+* [[45/28]] – its [[octave complement]]
+* [[135/112]] – its [[fifth complement]]
+* [[Gallery of just intervals]]
+[[Category:Third]]
+[[Category:Major third]]
+[[Category:Fourth]]
+[[Category:Diminished fourth]]
+[[Category:Aberschismic]]