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* Four of them make a tempered [[4/3]].
* Four of them make a tempered [[4/3]].


It is most naturally viewed as a 2.3.5.7.13 subgroup temperament (tempering out [[49/48]], [[65/64]] and [[225/224]]).
It is most naturally viewed as a 2.3.5.7.13 subgroup temperament, tempering out [[49/48]], [[65/64]] and [[91/90]]. This is called '''negra'''.  


It is an important temperament which is most notable for being in [[19edo]], where it is generated by the "diatonic half step" of 2\19, but can also be found (albeit not very accurately) in [[9edo]] and [[10edo]].
It is an important temperament which is most notable for being in [[19edo]], where it is generated by the "diatonic half step" of 2\19, but can also be found (albeit not very accurately) in [[9edo]] and [[10edo]].
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It forms 9-note MOS's at [[1L 8s]], with the mode ssssLssss being particularly useful as it has 4:5:6's on the 1/1 and 3/2, as well as 10-note MOS's at [[9L 1s]], which is also useful in that it makes 4:5:6 and 10:12:15 share the same "shape" of generic intervals in the scale (as in other rank-2 decatonic scales such as [[Pajara]] and [[Blackwood]] scales; this is because 5/4 and 6/5 get tempered to the same thing in [[10edo]]).
It forms 9-note MOS's at [[1L 8s]], with the mode ssssLssss being particularly useful as it has 4:5:6's on the 1/1 and 3/2, as well as 10-note MOS's at [[9L 1s]], which is also useful in that it makes 4:5:6 and 10:12:15 share the same "shape" of generic intervals in the scale (as in other rank-2 decatonic scales such as [[Pajara]] and [[Blackwood]] scales; this is because 5/4 and 6/5 get tempered to the same thing in [[10edo]]).


The 7-limit extensions can also be viewed as joining with the [[Marvel temperaments #Negri|Marvel temperament family]]; the tuning information below is also located there.
The 7-limit extension can also be viewed as joining with the [[Marvel temperaments #Negri|Marvel temperament family]]; the tuning information below is also located there. For the various 11-limit extensions, see [[negri extensions]].  


== Temperament data ==
== Temperament data ==
=== 5-limit ===
{{main| Marvel family #Negri }}


[[Comma|Comma]]s: 16875/16384
; 5-limit


[[POTE_tuning|POTE temperament]]: ~16/15 = 125.7549
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<div style="line-height:1.6;">Technical data</div>
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[[Map|Map]]: [&lt;1 2 2|, &lt;0 -4 3|]
Subgroup: 2.3.5


[[wedgie|Wedgie]]: &lt;&lt;4 -3 -14||
[[Comma list]]: 16875/16384


EDOs: [[9edo|9]], [[10edo|10]], [[19edo|19]], [[86edo|86]]
[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -4 3 }}]


=== 7-limit ===
[[Wedgie]]: {{wedgie| 4 -3 -14 }}
[[Comma|Comma]]s: 49/48, 225/224


[[POTE_tuning|POTE temperament]]: ~15/14 = 125.608
{{Val list|legend=1| 9, 10, 19, 67c, 86c, 105c }}


[[Map|Map]]: [&lt;1 2 2 3|, &lt;0 -4 3 -2|]
</div></div>


[[wedgie|Wedgie]]: &lt;&lt;4 -3 2 -14 -8 13||
; 7-limit


EDOs: [[9edo|9]], [[10edo|10]], [[19edo|19]], [[86edo|86]]
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<div style="line-height:1.6;">Technical data</div>
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=== 11-limit ===
Subgroup: 2.3.5.7
Commas: 45/44, 49/48, 56/55


[[POTE_tuning|POTE generator]]: ~15/14 = 126.474
[[Comma list]]: 49/48, 225/224


Map: [&lt;1 2 2 3 4|, &lt;0 -4 3 -2 -5|]
[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -4 3 -2 }}]


EDOs: 9, 10, 19
[[Wedgie]]: {{wedgie| 4 -3 2 -14 -8 13 }}


[[Badness|Badness]]: 0.0262
{{Val list|legend=1| 9, 10, 19, 48d, 67cdd, 86cdd }}


=== 13-limit ===
</div></div>
Commas: 45/44, 49/48, 56/55, 78/77


[[POTE_tuning|POTE generator]]: ~14/13 = 126.431
; 2.3.5.7.13 (negra)


Map: [&lt;1 2 2 3 4 4|, &lt;0 -4 3 -2 -5 -3|]
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


EDOs: 9, 10, 19
Subgroup: 2.3.5.7.13
 
[[Comma list]]: 49/48, 65/64, 91/90
 
[[Mapping]]: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -3 }}]
 
Gencom map: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}]
 
Gencom: [2 14/13; 49/48 65/64 91/90]
 
{{Val list|legend=1| 9, 10, 19, 48df, 67cddf, 86cddff }}
 
</div></div>


== Examples ==
== Examples ==
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