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:

Scale tree and tuning spectrum of 17L 2s

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)

There are several points that should be discussed.

• With this phrasing, it will not be possible to express the generator of m-chromatic as 3/2.
• From a regular temperament theory perspective, in order for the generator to be 36/25, it is necessary to prohibit 6/5 in this case. For example, it would be a 2.3.25-subgroup hanson. (Hanson normally means alpha-hexacot.)
• I don't think the size of just interval that represent the generator of the temperament need to fall within an exact range. 2.3.25-restricted hanson's generator is …~36/25(631.28c)~625/432(639.39c)~…, and 2.3.25.13-restricted cata's generator is …~36/25~13/9(636.62c)~…, both of which seem to fit this mos.

--Dummy index (talk) 13:30, 1 May 2025 (UTC)

I also noticed that problem with 36/25 (unless you make a nonstandard subgroup notation extension that lets you use both a prime and a multiple of that prime or both flat and sharp versions of that prime, depending upon a simple selection rule). Probably should add a note about that to what I proposed above. With respect to fitting into the range, if you DON'T do that (and depending upon generator constitution, often even if you do), you end up with an awful lot of EDOs where the generator doesn't map correctly — for instance, both 23/16 and 13/9 have spotty mapping in this tuning table (although at least covering enough EDOs to be useful for a decent subset of it), while the Alphatricot generator doesn't map correctly for anything other than a very narrow band close to 53edo. I've been working on this under Musical Mad Science under my user page (but it's nowhere near ready to put here or on any other official page), and found that 62/43 maps correctly to almost everything (and the very small number of exceptions are candidates for wart rescue). Lucius Chiaraviglio (talk) 15:25, 1 May 2025 (UTC)

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). In some cases, the analogous treatment might be needed for the 9th harmonic as well (such as when using ~13/9 with 112edo).

Added: Lucius Chiaraviglio (talk) 15:14, 2 May 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 15:31, 2 May 2025 (UTC)