Talk:17L 2s
Alphatricot/Alphatrident
Alphatricot/Alphatrident is in the vicinity of 176edo, but I can't figure out how to get it into the MOS tuning spectrum table (I know the template has a way to do it, because I've seen it elsewhere, but it's undocumented, and when I looked at the page source where I saw it elsewhere, it seemed unintuitive how it was used there).
Added: Lucius Chiaraviglio (talk) 06:04, 28 April 2025 (UTC)
I am going to try to see if this will work. Using this as a staging area to make sure I get the template parameters right rather than experiment on the real page and botch the whole thing:
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 10\19 | 631.579 | 568.421 | 1:1 | 1.000 | Equalized 17L 2s | |||||
| 59\112 | 632.143 | 567.857 | 6:5 | 1.200 | ||||||
| 49\93 | 632.258 | 567.742 | 5:4 | 1.250 | ||||||
| 88\167 | 632.335 | 567.665 | 9:7 | 1.286 | ||||||
| 39\74 | 632.432 | 567.568 | 4:3 | 1.333 | Supersoft 17L 2s | |||||
| 107\203 | 632.512 | 567.488 | 11:8 | 1.375 | ||||||
| 68\129 | 632.558 | 567.442 | 7:5 | 1.400 | ||||||
| 97\184 | 632.609 | 567.391 | 10:7 | 1.429 | ||||||
| 29\55 | 632.727 | 567.273 | 3:2 | 1.500 | Soft 17L 2s | |||||
| 106\201 | 632.836 | 567.164 | 11:7 | 1.571 | ||||||
| 77\146 | 632.877 | 567.123 | 8:5 | 1.600 | ||||||
| 125\237 | 632.911 | 567.089 | 13:8 | 1.625 | ||||||
| 48\91 | 632.967 | 567.033 | 5:3 | 1.667 | Semisoft 17L 2s | |||||
| 115\218 | 633.028 | 566.972 | 12:7 | 1.714 | ||||||
| 67\127 | 633.071 | 566.929 | 7:4 | 1.750 | ||||||
| 86\163 | 633.129 | 566.871 | 9:5 | 1.800 | ||||||
| 19\36 | 633.333 | 566.667 | 2:1 | 2.000 | Basic 17L 2s Scales with tunings softer than this are proper | |||||
| 85\161 | 633.540 | 566.460 | 9:4 | 2.250 | ||||||
| 66\125 | 633.600 | 566.400 | 7:3 | 2.333 | ||||||
| 113\214 | 633.645 | 566.355 | 12:5 | 2.400 | ||||||
| 47\89 | 633.708 | 566.292 | 5:2 | 2.500 | Semihard 17L 2s | |||||
| 122\231 | 633.766 | 566.234 | 13:5 | 2.600 | ||||||
| 75\142 | 633.803 | 566.197 | 8:3 | 2.667 | ||||||
| 103\195 | 633.846 | 566.154 | 11:4 | 2.750 | ||||||
| 28\53 | 633.962 | 566.038 | 3:1 | 3.000 | Hard 17L 2s | |||||
| 93\176 | 634.091 | 565.909 | 10:3 | 3.333 | Alphatricot/Alphatrident is around here | |||||
| 65\123 | 634.146 | 565.854 | 7:2 | 3.500 | ||||||
| 102\193 | 634.197 | 565.803 | 11:3 | 3.667 | ||||||
| 37\70 | 634.286 | 565.714 | 4:1 | 4.000 | Superhard 17L 2s | |||||
| 83\157 | 634.395 | 565.605 | 9:2 | 4.500 | ||||||
| 46\87 | 634.483 | 565.517 | 5:1 | 5.000 | ||||||
| 55\104 | 634.615 | 565.385 | 6:1 | 6.000 | ||||||
| 9\17 | 635.294 | 564.706 | 1:0 | → ∞ | Collapsed 17L 2s | |||||
Well, it seems to work despite me not being able to figure out how to tell MOS tuning spectrum what the MOS is (extracts from the page it is embedded in? — but this is a Talk page), but I had better leave this for a bit for review before committing it to the real page. (This is for review of the Comment entries I put in the table from the music theory perspective, as well as making sure that this displays properly on other people's computers.)
Proposed text to add to introduction section
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 (although just barely in the case of 36/25, which is near just in the equalized endpoint 19edo), while the simple ratio 13/9 is off-scale sharp. The Alphatricot family uses ~59049/40960 as a generator.
Added: Lucius Chiaraviglio (talk) 06:19, 28 April 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 19:24, 29 April 2025 (UTC)