225/224: Difference between revisions

Line 3:

| Monzo = -5 2 2 -1

| Cents = 7.71152

| Name = septimal kleisma, marvel comma

| Name = septimal kleisma, marvel comma

| Color name = ryy-2, ruyoyo negative 2nd, Ruyoyo comma

| FJS name = d-2257

Line 11:

The interval of '''225/224''', the '''septimal kleisma''' or '''marvel comma''' is a [[7-limit]] [[superparticular]] ratio. It pops up as the difference between pairs of 7-limit ratios, for example as ([[15/14]])/([[16/15]]) or ([[45/32]])/([[7/5]]).

It is also the difference between [[81/80]] and [[126/125]] and is tempered out alongside these two commas in [[~~Meantone family#Septimal meantone|Septimal~~ meantone]]. ~~If we don't temper out this interval and instead repeatedly stack (and octave~~-~~reduce)~~ it~~, we get~~ [[~~311edo~~]]~~, where it is equal to 2 steps, meaning 311edo is a circle of 225~~/~~224's. Note that this is not true for 226/225 or 224/223, the adjacent superparticulars, as they accumulate too much error to close into a circle in 311edo~~.

It is also the difference between [[81/80]] and [[126/125]] and is tempered out alongside these two commas in [[septimal meantone]]. In the 11-limit, it factors neatly into ([[385/384]])([[540/539]]).

== Temperaments ==

Tempering out this comma leads to the [[marvel family]] of temperaments, which enables [[marvel chords]].

Tempering out this comma leads to the [[marvel family]] of temperaments, which enables [[marvel chords]]. See [[marvel temperaments]] for a collection of rank-2 temperaments where it is tempered out.

== Approximation ==

If we do not temper out this interval and instead repeatedly stack (and octave-reduce) it, we get [[311edo]], where it is equal to 2 steps, meaning 311edo is a circle of 225/224's. Note that this is not true for 226/225 or 224/223, the adjacent superparticulars, as they accumulate too much error to close into a circle in 311edo.

== See also ==

* [[Marvel family]], the family of rank-3 temperaments where it is tempered out

* [[Marvel temperaments]], a collection of rank-2 temperaments where it is tempered out

* [[Marvel chords]]

* [[Small comma]]

* [[Gallery of just intervals]]

@@ Line 3: / Line 3: @@
 | Monzo = -5 2 2 -1
 | Cents = 7.71152
-| Name = septimal kleisma, <br/> marvel comma
+| Name = septimal kleisma, <br>marvel comma
 | Color name = ryy-2, ruyoyo negative 2nd,<br> Ruyoyo comma
 | FJS name = d-2<sup>25</sup><sub>7</sub>
@@ Line 11: / Line 11: @@
 The interval of '''225/224''', the '''septimal kleisma''' or '''marvel comma''' is a [[7-limit]] [[superparticular]] ratio. It pops up as the difference between pairs of 7-limit ratios, for example as ([[15/14]])/([[16/15]]) or ([[45/32]])/([[7/5]]).
-It is also the difference between [[81/80]] and [[126/125]] and is tempered out alongside these two commas in [[Meantone family#Septimal meantone|Septimal meantone]]. If we don't temper out this interval and instead repeatedly stack (and octave-reduce) it, we get [[311edo]], where it is equal to 2 steps, meaning 311edo is a circle of 225/224's. Note that this is not true for 226/225 or 224/223, the adjacent superparticulars, as they accumulate too much error to close into a circle in 311edo.
+It is also the difference between [[81/80]] and [[126/125]] and is tempered out alongside these two commas in [[septimal meantone]]. In the 11-limit, it factors neatly into ([[385/384]])([[540/539]]).
 == Temperaments ==
-Tempering out this comma leads to the [[marvel family]] of temperaments, which enables [[marvel chords]].
+Tempering out this comma leads to the [[marvel family]] of temperaments, which enables [[marvel chords]]. See [[marvel temperaments]] for a collection of rank-2 temperaments where it is tempered out.
+== Approximation ==
+If we do not temper out this interval and instead repeatedly stack (and octave-reduce) it, we get [[311edo]], where it is equal to 2 steps, meaning 311edo is a circle of 225/224's. Note that this is not true for 226/225 or 224/223, the adjacent superparticulars, as they accumulate too much error to close into a circle in 311edo.
 == See also ==
-* [[Marvel family]], the family of rank-3 temperaments where it is tempered out
-* [[Marvel temperaments]], a collection of rank-2 temperaments where it is tempered out
-* [[Marvel chords]]
 * [[Small comma]]
 * [[Gallery of just intervals]]

225/224: Difference between revisions

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