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 ~~[[edo]]s~~ 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 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.

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Revision as of 17:48, 17 April 2025 view source Godtone (talk \| contribs) autopatrolled, emailconfirmed 2,289 edits Created page with "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 edos appear in the sequence separately, followed by wha..."		Revision as of 17:49, 17 April 2025 view source Godtone (talk \| contribs) autopatrolled, emailconfirmed 2,289 edits m delink repeat Newer edit →
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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 ~~[[edo]]s~~ 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 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.

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