Xenharmonic Wiki

Marvel family: Difference between revisions

← Older editNewer edit →

FloraC (talk | contribs)

4 user groups
27,047 edits
VisualWikitext
mNo edit summary
Formatting and some cleanup
Line 1: Line 1:
__FORCETOC__
{{interwiki
[[de:Marvel]]
| de = Marvel
 
| en = Marvel family
| es =
| ja =
}}
The '''marvel family''' is the set of temperaments that temper out the [[7-limit]] ''marvel comma'' ([[225/224]] = {{monzo|-5 2 2 -1}}) which is also named ''septimal kleisma''. These temperaments hence equate [[16/15]] and [[15/14]], or equivalently they equate two [[5/4]]'s and one [[14/9]]. The marvel comma is noteworthy in that it is tempered out by many common edos and rank-2 temperaments.
The '''marvel family''' is the set of temperaments that temper out the [[7-limit]] ''marvel comma'' ([[225/224]] = {{monzo|-5 2 2 -1}}) which is also named ''septimal kleisma''. These temperaments hence equate [[16/15]] and [[15/14]], or equivalently they equate two [[5/4]]'s and one [[14/9]]. The marvel comma is noteworthy in that it is tempered out by many common edos and rank-2 temperaments.


The marvel comma can also be viewed as a comma of the 2.9.25.7 subgroup. Hence it is tempered out by any subset edos of marvel-supporting edos that have this subgroup, such as [[11edo]] and [[17edo]] which are subsets of [[22edo]] and [[34edo]] which temper out the marvel comma.
The marvel comma can also be viewed as a comma of the 2.9.25.7 subgroup. Hence it is tempered out by any subset edos of marvel-supporting edos that have this subgroup, such as [[11edo]] and [[17edo]] which are subsets of [[22edo]] and [[34edo]] which temper out the marvel comma.


=Marvel=
= Marvel =
The head of the marvel family is marvel, which tempers out [[225/224]]. Marvel has a [[Normal lists|normal list basis]] of [2, 3, 5]; hence a [[Harmonic Limit|5-limit]] scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by [[197edo]].
The head of the marvel family is marvel, which tempers out [[225/224]]. Marvel has a [[Normal lists|normal list basis]] of [2, 3, 5]; hence a [[Harmonic Limit|5-limit]] scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by [[197edo]].


Line 13: Line 16:
See also [[Marvel temperaments]].
See also [[Marvel temperaments]].


==Vital statistics==
== Vital statistics ==
[[Comma]] c = 225/224
[[Comma]] c = 225/224


Line 50: Line 53:
Scales: [[marvel9]], [[marvel10]], [[marvel11]], [[marvel12]], [[marvel19]], [[marvel22]], [[pump12_1]], [[pump12_2]], [[pump13]], [[pump14]], [[pump15]], [[pump16]], [[pump17]], [[pump18]]
Scales: [[marvel9]], [[marvel10]], [[marvel11]], [[marvel12]], [[marvel19]], [[marvel22]], [[pump12_1]], [[pump12_2]], [[pump13]], [[pump14]], [[pump15]], [[pump16]], [[pump17]], [[pump18]]


==[[Minkowski blocks]]==
== [[Minkowski blocks]] ==
{2, 3, 5} subgroup
{2, 3, 5} subgroup


Line 79: Line 82:
41: 34171875/33554432, 3125/3072
41: 34171875/33554432, 3125/3072


==Music==
== Music ==
* [http://chrisvaisvil.com/?p=314 Semimarvelous Blue Drawf] by [[Chris Vaisvil]]
* [http://chrisvaisvil.com/?p=314 Semimarvelous Blue Drawf] by [[Chris Vaisvil]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/marvel10_2.mp3 notJoelTaylorsTreeSpirit-Marvel10-2] by [[Billy Stiltner]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/marvel10_2.mp3 notJoelTaylorsTreeSpirit-Marvel10-2] by [[Billy Stiltner]]


==11-limit (Unimarv)==
= 11-limit (Unimarv) =
[[Commas]]: 225/224, 385/384
[[Commas]]: 225/224, 385/384


Line 115: Line 118:
Scales: [[marvel22_11]], [[unimarv19]], [[unimarv22]]
Scales: [[marvel22_11]], [[unimarv19]], [[unimarv22]]


===Hobbit bases===
=== Hobbit bases ===
{2, 3, 5} subgroup
{2, 3, 5} subgroup


Line 130: Line 133:
41: 3125/3072, 34171875/33554432
41: 3125/3072, 34171875/33554432


==13-limit==
== 13-limit ==
Commas: 225/224, 385/384, 351/350
Commas: 225/224, 385/384, 351/350


Line 145: Line 148:
[[Spectrum]]: 5/4, 4/3, 16/15, 15/14, 9/7, 6/5, 7/6, 11/8, 7/5, 9/8, 8/7, 10/9, 12/11, 13/10, 11/10, 15/11, 16/13, 11/9, 15/13, 14/13, 13/12, 14/11, 18/13, 13/11
[[Spectrum]]: 5/4, 4/3, 16/15, 15/14, 9/7, 6/5, 7/6, 11/8, 7/5, 9/8, 8/7, 10/9, 12/11, 13/10, 11/10, 15/11, 16/13, 11/9, 15/13, 14/13, 13/12, 14/11, 18/13, 13/11


=Hecate=
== Hecate ==
Commas: 225/224, 385/384, 325/324
Commas: 225/224, 385/384, 325/324


Line 162: Line 165:
[[Spectrum]]: 4/3, 5/4, 16/15, 15/14, 6/5, 9/8, 7/5, 9/7, 7/6, 10/9, 8/7, 18/13, 11/8, 12/11, 13/12, 11/9, 11/10, 15/13, 15/11, 16/13, 13/11, 14/13, 13/10, 14/11
[[Spectrum]]: 4/3, 5/4, 16/15, 15/14, 6/5, 9/8, 7/5, 9/7, 7/6, 10/9, 8/7, 18/13, 11/8, 12/11, 13/12, 11/9, 11/10, 15/13, 15/11, 16/13, 13/11, 14/13, 13/10, 14/11


==17-limit==
=== 17-limit ===
Commas: 225/224, 385/384, 325/324, 595/594
Commas: 225/224, 385/384, 325/324, 595/594


Line 171: Line 174:
Badness: 0.000869
Badness: 0.000869


==Enodia==
=== Enodia ===
Commas: 225/224, 385/384, 325/324, 375/374
Commas: 225/224, 385/384, 325/324, 375/374


Line 180: Line 183:
Badness: .000917
Badness: .000917


=Marvelcat=
== Marvelcat ==
Commas: 169/168, 225/224, 385/384
Commas: 169/168, 225/224, 385/384


Line 189: Line 192:
Badness: 0.0009997
Badness: 0.0009997


=Marvell=
== Marvell ==
Commas: 225/224, 385/384, 1573/1568
Commas: 225/224, 385/384, 1573/1568


Line 202: Line 205:
Badness: 0.000862
Badness: 0.000862


=Isis=
== Isis ==
Commas: 225/224, 385/384, 275/273
Commas: 225/224, 385/384, 275/273


Line 213: Line 216:
Projection pairs: 7 225/32 11 4096/375 13 131072/10125
Projection pairs: 7 225/32 11 4096/375 13 131072/10125


=Deecee=
== Deecee ==
Commas: 225/224, 385/384, 364/363
Commas: 225/224, 385/384, 364/363


Line 228: Line 231:
Projection pairs: 7 225/32 11 4096/375 13 134217728/10546875
Projection pairs: 7 225/32 11 4096/375 13 134217728/10546875


=Mirage=
== Tripod ==
Commas: 105/104, 144/143, 196/195
 
13-limit eigenmonzo subgroup: 2.9/7.13/11
 
15-limit eigenmonzo subgroup: 2.5/3.13/11
 
Map: [<1 0 0 -5 12 -8|, <0 1 0 2 -1 3|, <0 0 1 2 -3 3|]
 
{{EDOs|legend=1| 9, 10, 19, 31, 41, 72f, 81, 91, 122f, 163df }}
 
Badness: 0.000745
 
Projection pairs: 7 225/32 11 4096/375 13 3375/256
 
== Other eleven limit marvel children ==
The second comma of the [[Normal lists|normal comma list]] defines which 11-limit family member we are looking at.
* 4125/4096 gives unidecimal marvel,
* 91125/90112 gives prodigy,
* 5632/5625 gives minerva, and
* 243/242 gives spectacle.
 
= Mirage =
Commas: 225/224, 243/242, 385/384
Commas: 225/224, 243/242, 385/384


Line 237: Line 262:
Badness: 0.000738
Badness: 0.000738


=Minerva=
= Minerva =
[[Comma]]s: 99/98, 176/175
[[Comma]]s: 99/98, 176/175


Line 262: Line 287:
Scales: [[minerva12]], [[minerva22x]]
Scales: [[minerva12]], [[minerva22x]]


==Athene==
== Athene ==
Commas: 99/98, 176/175, 275/273
Commas: 99/98, 176/175, 275/273


Line 277: Line 302:
[[Projection pair]]s: 7 225/32 11 5625/512 13 625/48
[[Projection pair]]s: 7 225/32 11 5625/512 13 625/48


==Other eleven limit marvel children==
= Spectacle =
The second comma of the [[Normal lists|normal comma list]] defines which 11-limit family member we are looking at. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 spectacle.
 
=Spectacle=
[[Comma]]s: 225/224, 243/242
[[Comma]]s: 225/224, 243/242


Line 447: Line 469:


Badness: 0.001075
Badness: 0.001075
=Tripod=
Commas: 105/104, 144/143, 196/195
13-limit eigenmonzo subgroup: 2.9/7.13/11
15-limit eigenmonzo subgroup: 2.5/3.13/11
Map: [<1 0 0 -5 12 -8|, <0 1 0 2 -1 3|, <0 0 1 2 -3 3|]
{{EDOs|legend=1| 9, 10, 19, 31, 41, 72f, 81, 91, 122f, 163df }}
Badness: 0.000745
Projection pairs: 7 225/32 11 4096/375 13 3375/256


=Prodigy=
=Prodigy=
Line 496: Line 503:
Scales: [[prodigy11]], [[prodigy12]], [[prodigy29]]
Scales: [[prodigy11]], [[prodigy12]], [[prodigy29]]


==Hobbit bases==
=== Hobbit bases ===
{2, 3, 5} subgroup
{2, 3, 5} subgroup


Retrieved from "https://en.xen.wiki/w/Marvel_family"