40/21: Difference between revisions

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{{Infobox Interval

~~| JI glyph =~~

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

~~| Ratio = 40/21~~

| Color name = ry7, ruyo 7th

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

~~| Cents = 1115.53281~~

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

| Color name =

~~| FJS name = M757~~

| Sound = jid_40_21_pluck_adu_dr220.mp3

}}

'''40/21''', the '''acute major seventh''', is a [[7-limit]] interval measuring about 1115.5 cents. Despite being approximated by the diminished octave in systems like [[septimal meantone]], and even being called the "'''small septimal diminished octave'''" by some musicians ~~through~~ analogy with [[21/20]] being called the "large septimal chroma", 40/21 is a major seventh in ~~both~~ [[Helmholtz-Ellis notation]] and [[Functional Just System]] ~~because it is sharp of~~ the [[243/128|Pythagorean major seventh (243/128)]] by [[5120/5103]].

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

== 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]].

== Approximation ==

== See also ==

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* [[Gallery of just intervals]]

~~[[Category:Interval]]~~

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

[[Category:Seventh]]

[[Category:Major seventh]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| JI glyph =
+| Name = septimal acute major seventh, small septimal diminished octave
-| Ratio = 40/21
+| Color name = ry7, ruyo 7th
-| Monzo = 3 -1 1 -1
-| Cents = 1115.53281
-| Name = acute major seventh, <br>small septimal diminished octave
-| Color name =
-| FJS name = M7<sup>5</sup><sub>7</sub>
 | Sound = jid_40_21_pluck_adu_dr220.mp3
 }}
-'''40/21''', the '''acute major seventh''', is a [[7-limit]] interval measuring about 1115.5 cents. Despite being approximated by the diminished octave in systems like [[septimal meantone]], and even being called the "'''small septimal diminished octave'''" by some musicians through analogy with [[21/20]] being called the "large septimal chroma", 40/21 is a major seventh in both [[Helmholtz-Ellis notation]] and [[Functional Just System]] because it is sharp of the [[243/128|Pythagorean major seventh (243/128)]] by [[5120/5103]].
+'''40/21''', the '''septimal acute major seventh''', is a [[7-limit]] interval measuring about 1115.5 cents.
+== 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]].
+== Approximation ==
+{{Interval edo approximation|40/21}}
 == See also ==
@@ Line 16: / Line 16: @@
 * [[Gallery of just intervals]]
-[[Category:Interval]]
-[[Category:7-limit]]
 [[Category:Seventh]]
 [[Category:Major seventh]]