224/135: Difference between revisions

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Created page with "{{Infobox Interval | JI glyph = | Ratio = 224/135 | Monzo = 5 -3 -1 1 | Cents = 876.64719 | Name = septimal narrow major sixth, <br> marvelous major sixth | Color name = | F..."
 
Update thanks to the establishment of the aberschisma
 
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{{Infobox Interval
{{Infobox Interval
| JI glyph =
| Name = septimal narrow major sixth, marvel-ptolemaic major sixth, aberschismic 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''', conventionally known as the '''septimal narrow major sixth''' or '''marvel-ptolemaic major sixth''', is a [[7-limit]] interval that 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 an [[aberschisma]]. This gives rise to the more precise name '''aberschismic diminished seventh'''. In fact it forms the difference between [[16/9]] and [[15/14]].  
'''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 ==
== 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:Aberschismic]]

Latest revision as of 19:48, 30 July 2026

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,
aberschismic 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

224/135, conventionally known as the septimal narrow major sixth or marvel-ptolemaic major sixth, is a 7-limit interval that 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 an aberschisma. This gives rise to the more precise name aberschismic diminished seventh. In fact it forms the difference between 16/9 and 15/14.

See also

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