40/21: Difference between revisions

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{{Infobox Interval

~~| Ratio = 40/21~~

| Name = septimal acute major seventh, aberschismic major seventh

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

~~| Cents = 1115.53281~~

| Name = septimal acute major seventh, ~~ small septimal diminished octave~~

| Color name = ry7, ruyo 7th

~~| FJS name = M757~~

| Sound = jid_40_21_pluck_adu_dr220.mp3

}}

'''40/21''', conventionally known as the '''septimal acute major seventh''', is an interval in [[7-limit]] [[just intonation]] measuring about 1115.5 [[cent]]s. Despite being approximated by the diminished octave in systems like septimal [[meantone]], and even being called the ''septimal diminished octave'' by some musicians due to analogy with [[21/20]] being called the "septimal chromatic semitone", 40/21 functions as a major seventh, as is supported by [[Sagittal notation]], [[Helmholtz–Ellis notation]] and [[Functional Just System]], viewed as the [[243/128|Pythagorean major seventh (243/128)]] altered by an [[aberschisma]]. This gives rise to the more precise name '''aberschismic major seventh'''.

~~'''40/21''', the '''septimal acute major seventh''', is a [[7-limit]] interval measuring about 1115.5 cents.~~

== Approximation ==

== ~~Terminology~~ ==

Despite being approximated by the diminished octave in systems like [[septimal meantone]], and even being called the '''small septimal diminished octave''' by some musicians due to analogy with [[21/20]] being called the "large septimal chroma", 40/21 is a major seventh in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz-Ellis notation]] and [[Functional Just System]], viewed as the [[243/128|Pythagorean major seventh (243/128)]] altered by [[5120/5103]].

== See also ==

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* [[Gallery of just intervals]]

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

[[Category:Seventh]]

[[Category:Major seventh]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 40/21
+| Name = septimal acute major seventh, aberschismic major seventh
-| Monzo = 3 -1 1 -1
-| Cents = 1115.53281
-| Name = septimal acute major seventh, <br>small septimal diminished octave
 | Color name = ry7, ruyo 7th
-| FJS name = M7<sup>5</sup><sub>7</sub>
 | Sound = jid_40_21_pluck_adu_dr220.mp3
 }}
+'''40/21''', conventionally known as the '''septimal acute major seventh''', is an interval in [[7-limit]] [[just intonation]] measuring about 1115.5 [[cent]]s. Despite being approximated by the diminished octave in systems like septimal [[meantone]], and even being called the ''septimal diminished octave'' by some musicians due to analogy with [[21/20]] being called the "septimal chromatic semitone", 40/21 functions as a major seventh, as is supported by [[Sagittal notation]], [[Helmholtz–Ellis notation]] and [[Functional Just System]], viewed as the [[243/128|Pythagorean major seventh (243/128)]] altered by an [[aberschisma]]. This gives rise to the more precise name '''aberschismic major seventh'''.
-'''40/21''', the '''septimal acute major seventh''', is a [[7-limit]] interval measuring about 1115.5 cents.
+== Approximation ==
+{{Interval edo approximation|40/21}}
-== Terminology ==
-Despite being approximated by the diminished octave in systems like [[septimal meantone]], and even being called the '''small septimal diminished octave''' by some musicians due to analogy with [[21/20]] being called the "large septimal chroma", 40/21 is a major seventh in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz-Ellis notation]] and [[Functional Just System]], viewed as the [[243/128|Pythagorean major seventh (243/128)]] altered by [[5120/5103]].
 == See also ==
@@ Line 18: / Line 13: @@
 * [[Gallery of just intervals]]
-[[Category:7-limit]]
 [[Category:Seventh]]
 [[Category:Major seventh]]