User:Godtone/optimal edo sequences: Difference between revisions

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In the below I detail the <code>optimal_edo_sequence</code>s for a large range of odd-limits (19 thru 123). However, the formatting requires some explanation. I was originally specifically interested in how [[fifth-chroma temperaments]] {{nowrap| {{EDOs| 77, 80, 84(, 87, 94) }} }} fare relative to each-other, to get a sense of what their relative strengths and weaknesses are. Therefore I list which of those five [[edo]]s appear in the sequence separately, followed by what edos appear after them (to get a sense of what the smallest edos that are improvements are). However, this excludes edos smaller than 94 (other than 77, 80, 84 and 87 ofc), so I later did a sequence for smaller edos (in the 1 to 94 range) for completeness. A notable edo appearing frequently in ~~this list~~ (which is excluded in the first lists for being < 94) is [[89edo]], which interestingly splits 25/24 either into 4 or 6 depending on if you use the flat or sharp mapping of 5/4 (respectively), so that it's almost like it's approximately fifth-chroma in resolution. I also only calculate with pure-octave and patent vals, but since I know the correct high-limit val for 80edo (one of my favourite tuning systems), I use that val for it instead.

In the below I detail the <code>optimal_edo_sequence</code>s for a large range of odd-limits (19 thru 123). However, the formatting requires some explanation. I was originally specifically interested in how [[fifth-chroma temperaments]] {{nowrap| {{EDOs| 77, 80, 84(, 87, 94) }} }} fare relative to each-other, to get a sense of what their relative strengths and weaknesses are. Therefore I list which of those five [[edo]]s appear in the sequence separately, followed by what edos appear after them (to get a sense of what the smallest edos that are improvements are). However, this excludes edos smaller than 94 (other than 77, 80, 84 and 87 ofc), so I later did a sequence for smaller edos (in the 1 to 94 range) for completeness. A notable edo appearing frequently in these sequences (which is excluded in the first lists for being < 94) is [[89edo]], which interestingly splits 25/24 either into 4 or 6 depending on if you use the flat or sharp mapping of 5/4 (respectively), so that it's almost like it's approximately fifth-chroma in resolution. This is also notable because other than [[82edo]], it's the only edo to appear relatively frequently which is in the 77 to 94 range other than 77, 80, 84, 87, 94. I also only calculate with pure-octave and patent vals, but [[User:Godtone#RINGER_80|since I know]] the correct high-limit val for 80edo (as it's one of my favourite tuning systems), I use that val for it instead.

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	In the below I detail the <code>optimal_edo_sequence</code>s for a large range of odd-limits (19 thru 123). However, the formatting requires some explanation. I was originally specifically interested in how [[fifth-chroma temperaments]] {{nowrap\| {{EDOs\| 77, 80, 84(, 87, 94) }} }} fare relative to each-other, to get a sense of what their relative strengths and weaknesses are. Therefore I list which of those five [[edo]]s appear in the sequence separately, followed by what edos appear after them (to get a sense of what the smallest edos that are improvements are). However, this excludes edos smaller than 94 (other than 77, 80, 84 and 87 ofc), so I later did a sequence for smaller edos (in the 1 to 94 range) for completeness. A notable edo appearing frequently in ~~this list~~ (which is excluded in the first lists for being < 94) is [[89edo]], which interestingly splits 25/24 either into 4 or 6 depending on if you use the flat or sharp mapping of 5/4 (respectively), so that it's almost like it's approximately fifth-chroma in resolution. I also only calculate with pure-octave and patent vals, but since I know the correct high-limit val for 80edo (one of my favourite tuning systems), I use that val for it instead.		In the below I detail the <code>optimal_edo_sequence</code>s for a large range of odd-limits (19 thru 123). However, the formatting requires some explanation. I was originally specifically interested in how [[fifth-chroma temperaments]] {{nowrap\| {{EDOs\| 77, 80, 84(, 87, 94) }} }} fare relative to each-other, to get a sense of what their relative strengths and weaknesses are. Therefore I list which of those five [[edo]]s appear in the sequence separately, followed by what edos appear after them (to get a sense of what the smallest edos that are improvements are). However, this excludes edos smaller than 94 (other than 77, 80, 84 and 87 ofc), so I later did a sequence for smaller edos (in the 1 to 94 range) for completeness. A notable edo appearing frequently in these sequences (which is excluded in the first lists for being < 94) is [[89edo]], which interestingly splits 25/24 either into 4 or 6 depending on if you use the flat or sharp mapping of 5/4 (respectively), so that it's almost like it's approximately fifth-chroma in resolution. This is also notable because other than [[82edo]], it's the only edo to appear relatively frequently which is in the 77 to 94 range other than 77, 80, 84, 87, 94. I also only calculate with pure-octave and patent vals, but [[User:Godtone#RINGER_80\|since I know]] the correct high-limit val for 80edo (as it's one of my favourite tuning systems), I use that val for it instead.

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