3136/3125: Difference between revisions
→Orion: made gen 17/16 not 17/1 and similarly 28/25 not 56/25 |
m →Hemimean orion: clarify |
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==== [[Hemimean family#Hemimean orion|Hemimean orion]] ==== | ==== [[Hemimean family#Hemimean orion|Hemimean orion]] ==== | ||
As tempering either [[256/255|S16]]/[[324/323|S18]] = [[1216/1215]] or [[324/323|S18]]/[[400/399|S20]] = [[1701/1700]] implies the other in the context of orion with the effect of extending to include prime 3 in the subgroup and as this therefore gives us both S16 = S18 = S20 and S17 = S19, it can be considered natural to add these commas, because {S16/S18, S17/S19, S18/S20} implies all the aforementioned commas of orion. However, this is an extension of hemimean because the ~17/16 generator of orion is no longer present and instead we have a ~3/2 generator. | As tempering either [[256/255|S16]]/[[324/323|S18]] = [[1216/1215]] or [[324/323|S18]]/[[400/399|S20]] = [[1701/1700]] implies the other in the context of orion with the effect of extending to include prime 3 in the subgroup and as this therefore gives us both S16 = S18 = S20 and S17 = S19, it can be considered natural to add these commas, because {S16/S18, S17/S19, S18/S20} implies all the aforementioned commas of orion. However, this is an extension of hemimean because the ~17/16 generator of orion is no longer present and instead we have a ~3/2 generator. (The temperament orion is described next on this page.) | ||
Subgroup: 2.3.5.7.17.19 | Subgroup: 2.3.5.7.17.19 | ||