Xenharmonic Wiki

Marvel family: Difference between revisions

← Older editNewer edit →
VisualWikitext
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
m →Apollo: fix link
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
reworked: intro reworded to make name giving marvel comma stand out, introduced (improved) EDOs template
Line 2: Line 2:
[[de:Marvel]]
[[de:Marvel]]


The '''marvel family''' is the set of temperaments that temper out the [[7-limit]] comma [[225/224|225/224]] = {{monzo|-5 2 2 -1}}, the [[septimal_kleisma|septimal kleisma]] or [[marvel_comma|marvel comma]]. 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|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|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]].


Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to [[Kleismic_family|catakleismic temperament]]. Another temperament which does little damage to tuning accuracy is [[Pythagorean_family|compton temperament]], for which [[240edo|240edo]] may be used.
Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to [[catakleismic temperament]]. Another temperament which does little damage to tuning accuracy is [[compton temperament]], for which [[240edo]] may be used.


See also [[Marvel_temperaments|Marvel temperaments]].
See also [[Marvel temperaments]].


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


Related linear temperament: [[Kleismic_family|catakleismic temperament]]
Related linear temperament: [[catakleismic temperament]]


7-limit minimax: 3 and 5 1/4c flat, 7 just
7-limit minimax: 3 and 5 1/4c flat, 7 just
Line 21: Line 22:
[|1 0 0 0>, |5/4 1/2 -1/2 1/4>, |5/4 -1/2 1/2 1/4>, |0 0 0 1>]
[|1 0 0 0>, |5/4 1/2 -1/2 1/4>, |5/4 -1/2 1/2 1/4>, |0 0 0 1>]


[[Eigenmonzo_subgroup|Eigenmonzo subgroup]]: 2.5/3.7
[[Eigenmonzo subgroup]]: 2.5/3.7


9-limit minimax: 3 1/6c flat, 5 1/3c flat, 7 just
9-limit minimax: 3 1/6c flat, 5 1/3c flat, 7 just
Line 27: Line 28:
[|1 0 0 0>, |5/6 2/3 -1/3 1/6>, |5/3 -2/3 1/3 1/3>, |0 0 0 1>]
[|1 0 0 0>, |5/6 2/3 -1/3 1/6>, |5/3 -2/3 1/3 1/3>, |0 0 0 1>]


[[Eigenmonzo_subgroup|Eigenmonzo subgroup]]: 2.9/5.7
[[Eigenmonzo subgroup]]: 2.9/5.7


Lattice basis: secor length 1.256, 3/2 length 1.369
Lattice basis: secor length 1.256, 3/2 length 1.369
Line 39: Line 40:
Generators: 2, 3, 5
Generators: 2, 3, 5


[[EDO|EDOs]]: [[10edo|10]], [[12edo|12]], [[19edo|19]], [[22edo|22]], [[31edo|31]], [[41edo|41]],[[72edo|72]], [[197edo|197]], [[269edo|269c]]
{{EDOs|legend=1| 10, 12, 19, 22, 31, 41, 72, 197, 269c }}


Badness: 0.0000365
Badness: 0.0000365


[[Projection_pair|Projection pair]]s: 7 225/32
[[Projection pair]]s: 7 225/32


[[Spectrum_of_a_temperament|Spectrum]]: 4/3, 5/4, 7/5, 7/6, 8/7, 6/5, 9/8, 9/7, 10/9
[[Spectrum]]: 4/3, 5/4, 7/5, 7/6, 8/7, 6/5, 9/8, 9/7, 10/9


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


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


Line 79: Line 80:


==Music==
==Music==
[http://chrisvaisvil.com/?p=314 Semimarvelous Blue Drawf] by [[Chris_Vaisvil|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|Billy Stiltner]]


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


Related linear temperament: [[Kleismic_family|catakleismic temperament]]
Related linear temperament: [[catakleismic temperament]]


[[Minimax_tuning|Minimax tuning]]:
[[Minimax tuning]]:


[|1 0 0 0 0>, |4/3 8/9 -1/3 0 -1/9>, |8/3 -2/9 1/3 0 -2/9>,
[|1 0 0 0 0>, |4/3 8/9 -1/3 0 -1/9>, |8/3 -2/9 1/3 0 -2/9>,
|3 4/3 0 0 -2/3>, |8/3 -2/9 -2/3 0 7/9>]
|3 4/3 0 0 -2/3>, |8/3 -2/9 -2/3 0 7/9>]


[[Eigenmonzo_subgroup|Eigenmonzo subgroup]]: 2.9/5.11/9
[[Eigenmonzo subgroup]]: 2.9/5.11/9


Lattice basis: secor length 1.0364 5/4 length 1.0759
Lattice basis: secor length 1.0364 5/4 length 1.0759
Line 103: Line 103:
Map: [<1 0 0 -5 12|, <0 1 0 2 -1|, <0 0 1 2 -3|]
Map: [<1 0 0 -5 12|, <0 1 0 2 -1|, <0 0 1 2 -3|]


[[generator|Generators]]: 2, 3, 5
[[Generator]]s: 2, 3, 5


[[EDO|Edos]]: [[10edo|10]], [[12edo|12e]], [[19edo|19]], [[22edo|22]], [[31edo|31]], [[41edo|41]], [[53edo|53]], [[72edo|72]], [[166edo|166]], [[197edo|197e]], [[269edo|269ce]], [[341edo|341ce]]
{{EDOs|legend=1| 10, 12e, 19, 22, 31, 41, 53, 72, 166, 197e, 269ce, 341ce }}


Badness: 0.000255
Badness: 0.000255


[[Projection_pair|Projection pair]]s: 7 225/32 11 4096/375
[[Projection pair]]s: 7 225/32 11 4096/375


[[Spectrum_of_a_temperament|Spectrum]]: 5/4, 4/3, 7/6, 8/7, 7/5, 6/5, 9/7, 12/11, 9/8, 11/8, 11/9, 10/9, 11/10, 14/11
[[Spectrum]]: 5/4, 4/3, 7/6, 8/7, 7/5, 6/5, 9/7, 12/11, 9/8, 11/8, 11/9, 10/9, 11/10, 14/11


Scales: [[marvel22_11|marvel22_11]], [[unimarv19|unimarv19]], [[unimarv22|unimarv22]]
Scales: [[marvel22_11]], [[unimarv19]], [[unimarv22]]


===Hobbit bases===
===Hobbit bases===
Line 139: Line 139:
Map: [<1 0 0 -5 12 -4|, <0 1 0 2 -1 -1|, <0 0 1 2 -3 4|]
Map: [<1 0 0 -5 12 -4|, <0 1 0 2 -1 -1|, <0 0 1 2 -3 4|]


EDOs: 19, 22, 31, 50, 53, 72, 103, [[175edo|175f]], [[300edo|300cef]], [[403bcef|403bcef]]
{{EDOs|legend=1| 19, 22, 31, 50, 53, 72, 103, 175f, 300cef, 403bcef }}


Badness: 0.000690
Badness: 0.000690


[[Spectrum_of_a_temperament|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=
Line 154: Line 154:
Map: [<1 0 0 -5 12 2|, <0 1 0 2 -1 4|, <0 0 1 2 -3 -2|]
Map: [<1 0 0 -5 12 2|, <0 1 0 2 -1 4|, <0 0 1 2 -3 -2|]


EDOs: 19, 41, 53, 72, 113, 125f, 166, 238cf, 404cef
{{EDOs|legend=1| 19, 41, 53, 72, 113, 125f, 166, 238cf, 404cef }}


Badness: 0.000721
Badness: 0.000721
Line 160: Line 160:
Projection pairs: 7 225/32 11 4096/375 13 324/25
Projection pairs: 7 225/32 11 4096/375 13 324/25


[[Spectrum_of_a_temperament|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==
Line 167: Line 167:
Map: [<1 0 0 -5 12 2 18|, <0 1 0 2 -1 4 0|, <0 0 1 2 -3 -2 -6|]
Map: [<1 0 0 -5 12 2 18|, <0 1 0 2 -1 4 0|, <0 0 1 2 -3 -2 -6|]


EDOs: 19, 41, 53g, 72, 113, 166g, 238cfg, 351cfg, 404cefg
{{EDOs|legend=1| 19, 41, 53g, 72, 113, 166g, 238cfg, 351cfg, 404cefg }}


Badness: 0.000869
Badness: 0.000869
Line 176: Line 176:
Map: [<1 0 0 -5 12 2 18|, <0 1 0 2 -1 4 0|, <0 0 1 2 -3 -2 6|]
Map: [<1 0 0 -5 12 2 18|, <0 1 0 2 -1 4 0|, <0 0 1 2 -3 -2 6|]


EDOs: 41g, 53, 72, 125f, 166g, 238cfg, 363cefg, 404cefg
{{EDOs|legend=1| 41g, 53, 72, 125f, 166g, 238cfg, 363cefg, 404cefg }}


Badness: .000917
Badness: .000917
Line 185: Line 185:
Map: [<1 0 0 -5 12 -|, <0 2 0 4 -2 3|, <0 0 1 2 -3 1|]
Map: [<1 0 0 -5 12 -|, <0 2 0 4 -2 3|, <0 0 1 2 -3 1|]


EDOs: 9, 10, 19, 44, 53, 72, 125f, 197ef, 269cef
{{EDOs|legend=1| 9, 10, 19, 44, 53, 72, 125f, 197ef, 269cef }}


Badness: 0.0009997
Badness: 0.0009997
Line 198: Line 198:
Map: [<1 0 0 -5 12 -29|, <0 1 0 2 -1 6|, <0 0 1 2 -3 10|]
Map: [<1 0 0 -5 12 -29|, <0 1 0 2 -1 6|, <0 0 1 2 -3 10|]


EDOs: 9, 31, [[63edo|63]], 72, [[103edo|103]], [[166edo|166]], [[238edo|238cf]], [[269edo|269ce]], 507bcef, 610bcef
{{EDOs|legend=1| 9, 31, 63, 72, 103, 166, 238cf, 269ce, 507bcef, 610bcef }}


Badness: 0.000862
Badness: 0.000862
Line 207: Line 207:
Map: [<1 0 0 -5 12 17|, <0 1 0 2 -1 4|, <0 0 1 2 -3 -3|]
Map: [<1 0 0 -5 12 17|, <0 1 0 2 -1 4|, <0 0 1 2 -3 -3|]


EDOs: 10, 22, 31, 41, 53, 94
{{EDOs|legend=1| 10, 22, 31, 41, 53, 94 }}


Badness: 0.000866
Badness: 0.000866
Line 222: Line 222:
Map: [<1 0 0 -5 12 27|, <0 1 0 2 -1 -3|, <0 0 1 2 -3 -8|]
Map: [<1 0 0 -5 12 27|, <0 1 0 2 -1 -3|, <0 0 1 2 -3 -8|]


EDOs: 9, 22, 41, 63, 72, [[185edo|185cf]], [[257edo|257cf]]
{{EDOs|legend=1| 9, 22, 41, 63, 72, 185cf, 257cf }}


Badness: 0.000920
Badness: 0.000920
Line 233: Line 233:
Map: [<1 1 3 3 2 0|, <0 6 -7 -2 15 0|, <0 0 0 0 0 1|]
Map: [<1 1 3 3 2 0|, <0 6 -7 -2 15 0|, <0 0 0 0 0 1|]


EDOs: 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef
{{EDOs|legend=1| 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef }}


Badness: 0.000738
Badness: 0.000738


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


Related linear temperament: [[Semicomma_family|orwell]]
Related linear temperament: [[Semicomma family#Orwell|orwell]]


[[Eigenmonzo_subgroup|Eigenmonzo subgroup]]: 2.7/5.11/9
[[Eigenmonzo subgroup]]: 2.7/5.11/9


Lattice basis: 16/15 length 0.8997 5/4 length 1.0457
Lattice basis: 16/15 length 0.8997 5/4 length 1.0457
Line 252: Line 252:
Map: [<1 0 0 -5 -9|, <0 1 0 2 2|, <0 0 1 2 4|]
Map: [<1 0 0 -5 -9|, <0 1 0 2 2|, <0 0 1 2 4|]


[[generator|Generators]]: 2, 3, 5
[[Generator]]s: 2, 3, 5


[[EDO|EDOs]]: [[9edo|9]], [[12edo|12]], [[21edo|21]], [[22edo|22]], [[31edo|31]], [[43edo|43]], [[53edo|53]], [[74edo|74]], [[75edo|75]], [[96edo|96]], [[127edo|127]]
{{EDOs|legend=1| 9, 12, 21, 22, 31, 43, 53, 74, 75, 96, 127 }}


Badness: 0.000381
Badness: 0.000381


[[Projection_pair|Projection pair]]s: 7 225/32 11 5625/512
[[Projection pair]]s: 7 225/32 11 5625/512


Scales: [[minerva12|minerva12]], [[minerva22x|minerva22x]]
Scales: [[minerva12]], [[minerva22x]]


==Athene==
==Athene==
Line 271: Line 271:
Map: [<1 0 0 -5 -9 -4|, <0 1 0 2 2 -1|, <0 0 1 2 4 4|]
Map: [<1 0 0 -5 -9 -4|, <0 1 0 2 2 -1|, <0 0 1 2 4 4|]


EDOs: 22, 31, 53, 84e, 118d, 149df, 171de, 202def
{{EDOs|legend=1| 22, 31, 53, 84e, 118d, 149df, 171de, 202def }}


Badness: 0.000818
Badness: 0.000818


[[Projection_pair|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==
==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. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 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=
=Spectacle=
[[Comma|Commas]]: 225/224, 243/242
[[Comma]]s: 225/224, 243/242


Related linear temperament: [[Marvel_temperaments|marvo]]
Related linear temperament: [[Marvel temperaments#Marvo|marvo]]


[[Minimax_tuning|Minimax tuning]]:
[[Minimax tuning]]:


[|1 0 0 0 0>, |1/5 0 0 0 2/5>, |2/5 -2 1 0 4/5>, |-19/5 -4 2 0 12/5>, |0 0 0 0 1>]
[|1 0 0 0 0>, |1/5 0 0 0 2/5>, |2/5 -2 1 0 4/5>, |-19/5 -4 2 0 12/5>, |0 0 0 0 1>]


[[Eigenmonzo_subgroup|Eigenmonzo subgroup]]: 2.9/5.11
[[Eigenmonzo subgroup]]: 2.9/5.11


Map: [<1 1 0 -3 2|, <0 2 0 4 5|, <0 0 1 2 0|]
Map: [<1 1 0 -3 2|, <0 2 0 4 5|, <0 0 1 2 0|]


[[generator|Generators]]: 2, 11/9, 5
[[Generator]]s: 2, 11/9, 5


[[EDO|EDOs]]: [[10edo|10]], [[31edo|31]], [[41edo|41]], [[72edo|72]], [[240edo|240]], [[259edo|259b]], [[269edo|269ce]], [[310edo|310c]], [[331edo|331bc]], [[353edo|353c]], [[497edo|497bc]], [[569edo|569bc]]
{{EDOs|legend=1| 10, 31, 41, 72, 240, 259b, 269ce, 310c, 331bc, 353c, 497bc, 569bc }}


Badness: 0.000499
Badness: 0.000499
Line 301: Line 301:
Projection pairs: 3 242/81 7 366025/52488 11 644204/59049 to 2.5.11/9
Projection pairs: 3 242/81 7 366025/52488 11 644204/59049 to 2.5.11/9


Scales: [[spectacle31|spectacle31]]
Scales: [[spectacle31]]


==13-limit==
==13-limit==
Line 308: Line 308:
Map: [<1 1 0 -3 2 -5|, <0 2 0 4 5 -2|, <0 0 1 2 0 4|]
Map: [<1 1 0 -3 2 -5|, <0 2 0 4 5 -2|, <0 0 1 2 0 4|]


EDOs: 31, 72, 103, 175f, 209, 240
{{EDOs|legend=1| 31, 72, 103, 175f, 209, 240 }}


Badness: 0.001009
Badness: 0.001009


=Apollo=
=Apollo=
[[Comma|Commas]]: 100/99, 225/224
[[Comma]]s: 100/99, 225/224


Related linear temperament: [[Magic]]
Related linear temperament: [[Magic]]
Line 321: Line 321:
Map: [<1 0 0 -5 2|, <0 1 0 2 -2|, <0 0 1 2 2|]
Map: [<1 0 0 -5 2|, <0 1 0 2 -2|, <0 0 1 2 2|]


EDOs: 12, 19, 22, 41, [[104edo|104edo]], [[157edo|157ce]], [[198edo|198ce]], [[220edo|220ce]], [[261edo|261ce]]
{{EDOs|legend=1| 12, 19, 22, 41, 104, 157ce, 198ce, 220ce, 261ce }}


Projection pairs: 7 225/32 11 100/9
Projection pairs: 7 225/32 11 100/9


==13-limit==
==13-limit==
[[Comma|Commas]]: 100/99, 225/224, 245/243
[[Comma]]s: 100/99, 225/224, 245/243


Eigenmonzo subgroup: 2.11/9.13/9
Eigenmonzo subgroup: 2.11/9.13/9
Line 332: Line 332:
Map: [<1 0 0 -5 2 7|, <0 1 0 2 -2 -5|, <0 0 1 2 2 2|]
Map: [<1 0 0 -5 2 7|, <0 1 0 2 -2 -5|, <0 0 1 2 2 2|]


EDOs: 22, 29, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef
{{EDOs|legend=1| 22, 29, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef }}


Projection pairs: 7 225/32 11 100/9 13 3200/243
Projection pairs: 7 225/32 11 100/9 13 3200/243
Line 341: Line 341:
Map: [<1 0 1 -3 2|, <0 1 1 4 1|, <0 0 2 4 1|]
Map: [<1 0 1 -3 2|, <0 1 1 4 1|, <0 0 2 4 1|]


EDOs: {{EDOs|9, 20, 22, 31, 53}}
{{EDOs|legend=1| 9, 20, 22, 31, 53 }}


== 13-limit ==
== 13-limit ==
Line 348: Line 348:
Map: [<1 0 1 -3 2 -5|, <0 1 1 4 1 6|, <0 0 2 4 1 6|]
Map: [<1 0 1 -3 2 -5|, <0 1 1 4 1 6|, <0 0 2 4 1 6|]


EDOs: {{EDOs|9, 20, 29, 31}}
{{EDOs|legend=1| 9, 20, 29, 31 }}


== Diana ==
== Diana ==
Line 355: Line 355:
Map: [<1 0 1 -3 2 7|, <0 1 1 4 1 -2|, <0 0 2 4 1 1|]
Map: [<1 0 1 -3 2 7|, <0 1 1 4 1 -2|, <0 0 2 4 1 1|]


EDOs: {{EDOs|22, 29, 31, 53}}
{{EDOs|legend=1| 22, 29, 31, 53 }}


=Potassium=
=Potassium=
Line 364: Line 364:
Map: [&lt;1 0 0 -5 -2|, &lt;0 1 0 2 2|, &lt;0 0 1 2 1|]
Map: [&lt;1 0 0 -5 -2|, &lt;0 1 0 2 2|, &lt;0 0 1 2 1|]


EDOs: 9, 10, 12, 19, 31e, 50e
{{EDOs|legend=1| 9, 10, 12, 19, 31e, 50e }}


Badness: 0.000464
Badness: 0.000464
Line 379: Line 379:
Map: [&lt;1 0 0 -5 -2 -8|, &lt;0 1 0 2 2 3|, &lt;0 0 1 2 1 3|]
Map: [&lt;1 0 0 -5 -2 -8|, &lt;0 1 0 2 2 3|, &lt;0 0 1 2 1 3|]


EDOs: 9, 10, 19, 31e, 50e
{{EDOs|legend=1| 9, 10, 19, 31e, 50e }}


Badness: 0.000733
Badness: 0.000733
Line 390: Line 390:
Map: [&lt;2 0 0 -10 -7|, &lt;0 1 0 2 0|, &lt;0 0 1 2 3|]
Map: [&lt;2 0 0 -10 -7|, &lt;0 1 0 2 0|, &lt;0 0 1 2 3|]


EDOs: 12, 22, 50, 72, 166, 238c, 310c
{{EDOs|legend=1| 12, 22, 50, 72, 166, 238c, 310c }}


Badness: 0.000743
Badness: 0.000743
Line 399: Line 399:
Map: [&lt;1 0 1 -3 0|, &lt;0 6 5 22 0|, &lt;0 0 0 0 1|]
Map: [&lt;1 0 1 -3 0|, &lt;0 6 5 22 0|, &lt;0 0 0 0 1|]


EDOs: 19, 53, 72, 197e, 269ce
{{EDOs|legend=1| 19, 53, 72, 197e, 269ce }}


Badness: 0.001275
Badness: 0.001275
Line 408: Line 408:
Map: [&lt;1 0 1 -3 0 0|, &lt;0 6 5 22 0 14|, &lt;0 0 0 0 1 0|]
Map: [&lt;1 0 1 -3 0 0|, &lt;0 6 5 22 0 14|, &lt;0 0 0 0 1 0|]


EDOs: 19, 53, 72, 125f, 197ef, 269cef
{{EDOs|legend=1| 19, 53, 72, 125f, 197ef, 269cef }}


Badness: 0.000916
Badness: 0.000916
Line 417: Line 417:
Map: [&lt;1 0 0 -5 9|, &lt;0 2 0 4 -7|, &lt;0 0 1 2 0|]
Map: [&lt;1 0 0 -5 9|, &lt;0 2 0 4 -7|, &lt;0 0 1 2 0|]


EDOs: 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce
{{EDOs|legend=1| 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce }}


Badness: 0.00154
Badness: 0.00154
Line 426: Line 426:
Map: [&lt;1 0 0 -5 9 -1|, &lt;0 2 0 4 -7 3|, &lt;0 0 1 2 0 1|]
Map: [&lt;1 0 0 -5 9 -1|, &lt;0 2 0 4 -7 3|, &lt;0 0 1 2 0 1|]


EDOs: 19, 29, 43, 53, 72, 125f, 197ef, 269cef
{{EDOs|legend=1| 19, 29, 43, 53, 72, 125f, 197ef, 269cef }}


Badness: 0.001062
Badness: 0.001062
Line 435: Line 435:
Map: [&lt;1 0 0 -5 -3|, &lt;0 1 0 2 7|, &lt;0 0 1 2 -2|]
Map: [&lt;1 0 0 -5 -3|, &lt;0 1 0 2 7|, &lt;0 0 1 2 -2|]


EDOs: 41, 53, 94, 229c, 248ce, 289ce, 342ce, 383ce
{{EDOs|legend=1| 41, 53, 94, 229c, 248ce, 289ce, 342ce, 383ce }}


Badness: 0.001250
Badness: 0.001250
Line 444: Line 444:
Map: [&lt;1 0 0 -5 -3 2|, &lt;0 1 0 2 7 4|, &lt;0 0 1 2 -2 -2|]
Map: [&lt;1 0 0 -5 -3 2|, &lt;0 1 0 2 7 4|, &lt;0 0 1 2 -2 -2|]


EDOs: 41, 53, 94, 429cdef, 523cdef
{{EDOs|legend=1| 41, 53, 94, 429cdef, 523cdef }}


Badness: 0.001075
Badness: 0.001075
Line 457: Line 457:
Map: [&lt;1 0 0 -5 12 -8|, &lt;0 1 0 2 -1 3|, &lt;0 0 1 2 -3 3|]
Map: [&lt;1 0 0 -5 12 -8|, &lt;0 1 0 2 -1 3|, &lt;0 0 1 2 -3 3|]


EDOs: 9, 10, 19, 31, 41, 72f, [[81edo|81]], [[91edo|91]], [[122edo|122f]], [[163edo|163df]]
{{EDOs|legend=1| 9, 10, 19, 31, 41, 72f, 81, 91, 122f, 163df }}


Badness: 0.000745
Badness: 0.000745
Line 464: Line 464:


=Prodigy=
=Prodigy=
Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to [[Gamelismic_clan|miracle temperament]]. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle.
Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to [[miracle temperament]]. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle.


[[Comma|Commas]]: 225/224, 441/440
[[Comma]]s: 225/224, 441/440


Related linear temperament: [[Gamelismic_clan|miracle]]
Related linear temperament: [[Gamelismic clan#Miracle|miracle]]


[[Minimax_tuning|Minimax tuning]]:
[[Minimax tuning]]:


[|1 0 0 0 0&gt;, |13/12 1/2 -1/4 0 1/12&gt;,
[|1 0 0 0 0&gt;, |13/12 1/2 -1/4 0 1/12&gt;,
Line 476: Line 476:
|3/2 -1 1/2 0 1/2&gt;, |0 0 0 0 1&gt;]
|3/2 -1 1/2 0 1/2&gt;, |0 0 0 0 1&gt;]


[[Eigenmonzo_subgroup|Eigenmonzo subgroup]]: 2.9/5.11
[[Eigenmonzo subgroup]]: 2.9/5.11


Lattice basis: secor length 0.9111, 3/2 length 0.9477
Lattice basis: secor length 0.9111, 3/2 length 0.9477
Line 486: Line 486:
Map: [&lt;1 0 0 -5 -13|, &lt;0 1 0 2 6|, &lt;0 0 1 2 3|]
Map: [&lt;1 0 0 -5 -13|, &lt;0 1 0 2 6|, &lt;0 0 1 2 3|]


[[generator|Generators]]: 2, 3, 5
[[Generator]]s: 2, 3, 5


[[EDO|EDOs]]: [[10edo|10]], [[12edo|12]], [[29edo|29]], [[31edo|31]], [[41edo|41]], [[72edo|72]], [[247edo|247c]], [[319edo|319bcde]], [[391edo|391bcde]], [[463edo|463bcde]]
{{EDOs|legend=1| 10, 12, 29, 31, 41, 72, 247c, 319bcde, 391bcde, 463bcde }}


Badness: 0.000344
Badness: 0.000344


[[Projection_pair|Projection pair]]s: 7 225/32 11 91125/8192
[[Projection pair]]s: 7 225/32 11 91125/8192


Scales: [[prodigy11|prodigy11]], [[prodigy12|prodigy12]], [[prodigy29|prodigy29]]
Scales: [[prodigy11]], [[prodigy12]], [[prodigy29]]


==Hobbit bases==
==Hobbit bases==
Line 508: Line 508:
Map: [&lt;1 0 0 -5 -13 -8|, &lt;0 1 0 2 6 3|, &lt;0 0 1 2 3 3|]
Map: [&lt;1 0 0 -5 -13 -8|, &lt;0 1 0 2 6 3|, &lt;0 0 1 2 3 3|]


EDOs: 10, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233cdef, 274cdef, 305cdef
{{EDOs|legend=1| 10, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233cdef, 274cdef, 305cdef }}


Badness: 0.000736
Badness: 0.000736
Line 517: Line 517:
Map: [&lt;1 0 0 -5 -13 -23|, &lt;0 1 0 2 6 11|, &lt;0 0 1 2 3 4|]
Map: [&lt;1 0 0 -5 -13 -23|, &lt;0 1 0 2 6 11|, &lt;0 0 1 2 3 4|]


EDOs: 29, 41, 72, 113, 185cf, 341cf, 413bcf, 526bcdf
{{EDOs|legend=1| 29, 41, 72, 113, 185cf, 341cf, 413bcf, 526bcdf }}


Badness: 0.000900
Badness: 0.000900
Line 526: Line 526:
Map: [&lt;1 0 0 -5 -13 -4|, &lt;0 1 0 2 6 -1|, &lt;0 0 1 2 3 4|]
Map: [&lt;1 0 0 -5 -13 -4|, &lt;0 1 0 2 6 -1|, &lt;0 0 1 2 3 4|]


EDOs: 31, 72, 103, 175f
{{EDOs|legend=1| 31, 72, 103, 175f }}


Badness: 0.000889
Badness: 0.000889
Retrieved from "https://en.xen.wiki/w/Marvel_family"