Talk:17L 2s: Difference between revisions
→Proposed text to add to introduction section: Proposed text to add to introduction section (revised) |
→Proposed text to add to introduction section (revised): Have already found 1 case of needing 2.3♯.3♭.5 |
||
| Line 28: | Line 28: | ||
==== Proposed text to add to introduction section (revised) ==== | ==== Proposed text to add to introduction section (revised) ==== | ||
From a regular temperament theory perspective, this scale is notable for corresponding to the mega chromatic scale of the [[Alphatricot family]] temperaments. Unfortunately, its generator does not have a convenient rational representation — the simple ratios [[23/16]] and even [[36/25]] are off-scale flat, while the simple ratio [[13/9]] is off-scale sharp. The Alphatricot family uses ~[[59049/40960]] as a generator. Note that although the comparitively simple 36/25 is just barely off-scale flat (being near just in the equalized endpoint [[19edo]]), using it effectively depends upon direct approximation of the 25th harmonic, while one might also need to use the 5th harmonic as opposed to its square, requiring the use of a 2.3.5♯.5♭ (or 2.3.5.25) subgroup temperament that includes a rule on when to use each flavor of 5th harmonic (or when to use the 5th harmonic and when to use direct approximation of the 25th harmonic). | From a regular temperament theory perspective, this scale is notable for corresponding to the mega chromatic scale of the [[Alphatricot family]] temperaments. Unfortunately, its generator does not have a convenient rational representation — the simple ratios [[23/16]] and even [[36/25]] are off-scale flat, while the simple ratio [[13/9]] is off-scale sharp. The Alphatricot family uses ~[[59049/40960]] as a generator. Note that although the comparitively simple 36/25 is just barely off-scale flat (being near just in the equalized endpoint [[19edo]]), using it effectively depends upon direct approximation of the 25th harmonic, while one might also need to use the 5th harmonic as opposed to its square, requiring the use of a 2.3.5♯.5♭ (or 2.3.5.25) subgroup temperament that includes a rule on when to use each flavor of 5th harmonic (or when to use the 5th harmonic and when to use direct approximation of the 25th harmonic). In some cases, the analogous treatment might be needed for the 9th harmonic as well (such as when using ~13/9 with [[112edo]]). | ||
Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:14, 2 May 2025 (UTC) | Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:14, 2 May 2025 (UTC)<br> | ||
Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:31, 2 May 2025 (UTC) | |||