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Tempering out this comma in the 17-limit results in the rank-6 '''noellismic temperament''', or in the 2.3.5.7.17 subgroup, the rank-4 '''noellic temperament'''. In either case [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below.  
Tempering out this comma in the 17-limit results in the rank-6 '''noellismic temperament''', or in the 2.3.5.7.17 subgroup, the rank-4 '''noellic temperament'''. In either case [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below.  


=== Noellismic ===
=== Noellic ===
[[Subgroup]]: 2.3.5.7.11.13.17
[[Subgroup]]: 2.3.5.7.17


[[Mapping]]:
{{Mapping|legend=2| 1 0 0 0 -3 | 0 1 0 0 -2 | 0 0 1 0 2 | 0 0 0 1 2 }}
<br>[{{val| 1 0 0 0 0 0 -3 }}
<br>{{val| 0 1 0 0 0 0 -2 }}
<br>{{val| 0 0 1 0 0 0 2 }}
<br>{{val| 0 0 0 1 0 0 2 }}
<br>{{val| 0 0 0 0 1 0 0 }}
<br>{{val| 0 0 0 0 0 1 0 }}


Mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
: sval mapping generators: ~2, ~3, ~5, ~7


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468, ~11/8 = 551.3179, ~13/8 = 840.5277
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468


{{Optimal ET sequence|legend=1| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }}
{{Optimal ET sequence|legend=1| 19g, 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }}


=== Noellic ===
=== Noellismic ===
[[Subgroup]]: 2.3.5.7.17
[[Subgroup]]: 2.3.5.7.11.13.17


[[Sval]] [[mapping]]:  
[[Mapping]]: <br>
<br>[{{val| 1 0 0 0 -3 }}
{| class="right-all"
<br>{{val| 0 1 0 0 -2 }}
|-
<br>{{val| 0 0 1 0 2 }}
| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || -3 || ],
<br>{{val| 0 0 0 1 2 }}
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || -2 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 2 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 2 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
|}


Sval mapping generators: ~2, ~3, ~5, ~7
: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468, ~11/8 = 551.3179, ~13/8 = 840.5277


{{Optimal ET sequence|legend=1| 19g, 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }}
{{Optimal ET sequence|legend=1| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }}


== Etymology ==
== Etymology ==
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[[Category:Noellismic]]
[[Category:Noellismic]]
[[Category:Commas referencing a famous use of a number]]
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