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== Theory ==
== Theory ==
298edo has excellent representation of the 2.5.11.17.23.43.53.59 subgroup, with all the harmonics having errors of less than 10 r¢. It is a double of [[149edo]], the smallest uniquely consistent EDO in the 17-limit. In the 2.5.11.17.23.43.53.59 subgroup, 298edo tempers out 3176/3175, 3128/3125, 3128/3127, 32906/32065 and 76585/76582.
298edo is [[consistent]] in the 5-odd-limit, where it is [[enfactoring|enfactored]], with the same tuning as [[149edo]]. Since 149edo is notable for being the smallest edo distinctly consistent in the [[17-odd-limit]], 298edo is related to 149edo - it retains the mapping for 2.3.5.17 but differs on the mapping for harmonics [[7/4|7]], [[11/8|11]], [[13/8|13]]. 298edo tempers out the [[rastma]], splitting [[3/2]] inherited from 149edo into two steps representing [[11/9]]. It also tempers out the [[ratwolfsma]].


=== Patent val ===
The patent val supports the [[bison]] temperament and the rank-3 temperament [[hemimage]]. In the 2.5.11.13 subgroup, 298edo supports [[emka]]. In the full 13-limit, 298edo supports an unnamed 77 & 298 temperament with [[13/8]] as its generator.   
298edo's patent val is the lowest error val in the 17-limit among 298edo vals, but they differ on the mapping of the 7th, 11th, and 13th harmonics. Thus it can be viewed as a "spicy 149edo" as a result.   


The patent val in 298edo supports the [[bison]] temperament and the rank-3 temperament [[hemimage]]. In the 2.5.11.13 subgroup, 298edo supports [[emka]]. In the full 13-limit, 298edo supports an unnamed 77 & 298 temperament with [[13/8]] as its generator.
Aside from the patent val, there is a number of mappings to be considered. One can approach 298edo's vals as a double of 149edo again, by simply viewing its prime harmonics as variations from 149edo by its own half-step.


298edo tempers out the [[rastma]] and the [[ratwolfsma]], meaning it splits its perfect fifth which it inherits from 149edo, into two steps representing 11/9, and also supports the [[ratwolf triad]].
The 298d val, {{val|298 472 692 '''836''' 1031}}, which includes 149edo's 7-limit tuning, is better tuned than the patent val in the 11-limit (though not in the 17-limit). It supports [[hagrid]], in addition to the 31 & 298d variant and the 118 & 298d variant of [[hemithirds]]. Some of the commas it tempers out make for much more interesting temperaments than the patent val - for example it still tempers out 243/242, but now it adds [[1029/1024]], [[3136/3125]], and [[9801/9800]].  


=== Other vals ===
The 298cd val, {{val|298 472 '''691''' '''836''' 1031}} supports [[miracle]].  
Different temperaments can be extracted from 298edo by simply viewing its prime harmonics as variations from 149edo by its own half-step, although it is important to note that these vals are not better tuned than the patent val. 
 
The 298d val in 11-limit (149edo with 298edo 11/8) is better tuned than the patent val (although not in the 17-limit) and supports [[hagrid]], in addition to the 31 & 298d variant and the 118 & 298d variant of [[hemithirds]]. Some of the commas it tempers out make for much more interesting temperaments than the patent val. It still tempers out 243/242, but now it adds 1029/1024, 3136/3125, and 9801/9800.
 
The 298cd val supports [[miracle]].  


In higher limits, 298edo has excellent representation of the 2.5.11.17.23.43.53.59 subgroup, with all the harmonics having errors of less than 10 r¢. A comma basis for the 2.5.11.17.23.43.53.59 subgroup is {1376/1375, 3128/3127, 4301/4300, 25075/25069, 38743/38720, 58351/58300, 973360/972961}.
=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|298}}
{{Harmonics in equal|298}}
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