224/135: Difference between revisions

Interval information
Ratio	224/135
Factorization	25 × 3-3 × 5-1 × 7
Monzo	[5 -3 -1 1⟩
Size in cents	876.6472¢
Names	septimal narrow major sixth,; marvel-ptolemaic major sixth,; hemifamity diminished seventh
Color name	zg7, zogu 7th
FJS name	[math]\displaystyle{ \text{d7}^{7}_{5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	14.8842
Weil norm (log2 max(n, d))	15.6147
Wilson norm (sopfr(nd))	31
	Open this interval in xen-calc

Revision as of 12:43, 6 January 2026

224/135, the septimal narrow major sixth, or marvel-ptolemaic major sixth, is a 7-limit interval that forms the difference between 16/9 and 15/14. It is flat of the Pythagorean major sixth by 3645/3584, i.e. a syntonic comma plus a marvel comma. This interval functionally doubles as a type of diminished seventh, flat of the Pythagorean diminished seventh by 5120/5103. This gives rise to the name hemifamity diminished seventh.

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 {{Infobox Interval
-| JI glyph =
+| Name = septimal narrow major sixth, marvel-ptolemaic major sixth, hemifamity diminished seventh
-| Ratio = 224/135
+| Color name = zg7, zogu 7th
-| Monzo = 5 -3 -1 1
-| Cents = 876.64719
-| Name = septimal narrow major sixth, <br> marvelous major sixth
-| Color name =
-| FJS name =
-| Sound =
 }}
+'''224/135''', the '''septimal narrow major sixth''', or '''marvel-ptolemaic major sixth''', is a [[7-limit]] interval that forms the difference between [[16/9]] and [[15/14]]. It is flat of the [[27/16|Pythagorean major sixth]] by [[3645/3584]], i.e. a [[81/80|syntonic comma]] plus a [[225/224|marvel comma]]. This interval functionally doubles as a type of diminished seventh, flat of the [[32768/19683|Pythagorean diminished seventh]] by [[5120/5103]]. This gives rise to the name '''hemifamity diminished seventh'''.
-'''224/135''', the '''septimal narrow minor sixth''', or '''marvelous minor sixth''', is a [[7-limit]] interval that forms the difference between [[7/4]] and [[135/128]], and between [[16/9]] and [[15/14]].  Given that 135/128 is a type of chromatic semitone, this means 224/135 is functionally a type of diminished seventh.
 == See also ==
+* [[135/112]] – its octave complement
+* [[Gallery of just intervals]]
-* [[135/112]] -- its octave complement
+[[Category:Sixth]]
-* [[Gallery of just intervals]]
+[[Category:Major sixth]]
+[[Category:Seventh]]
+[[Category:Diminished seventh]]
+[[Category:Hemifamity]]