Talk:Superpyth–22 equivalence continuum: Difference between revisions
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ArrowHead294 (talk | contribs) m ArrowHead294 moved page Talk:Superpyth-22 equivalence continuum to Talk:Superpyth–22 equivalence continuum: The dash in titles like these should be an en dash, not a hyphen-minus, since "superpyth" does not modify "22" |
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== Suggested rename and re-parametrization == | == Suggested rename and re-parametrization == | ||
This should be renamed and re-parametrized to 22 | This should be renamed and re-parametrized to superpyth-22 equivalence continuum: | ||
{| class="wikitable center-1 | {| class="wikitable center-1" | ||
|+Temperaments in the continuum | |+Temperaments in the continuum | ||
|- | |- | ||
| Line 25: | Line 25: | ||
| [[Diaschismic]] | | [[Diaschismic]] | ||
| 2048/2025 | | 2048/2025 | ||
| {{Monzo| - | | {{Monzo| 11 -4 -2 }} | ||
|- | |- | ||
| 3 | | 3 | ||
| Line 48: | Line 48: | ||
|} | |} | ||
Or doing it backwards, the 22 | Or doing it backwards, the quasisuper-22 equivalence continuum: | ||
{| class="wikitable center-1 | {| class="wikitable center-1" | ||
|+Temperaments in the continuum | |+Temperaments in the continuum | ||
|- | |- | ||
| Line 73: | Line 73: | ||
| [[Diaschismic]] | | [[Diaschismic]] | ||
| 2048/2025 | | 2048/2025 | ||
| {{Monzo| - | | {{Monzo| 11 -4 -2 }} | ||
|- | |- | ||
| 3 | | 3 | ||
| 22 & 29c | | 22 & 29c | ||
| | | | ||
| {{Monzo| 34 -17 -3 }} | | {{Monzo| 34 -17 -3 }} | ||
|- | |- | ||
| Line 99: | Line 99: | ||
# ''n'' = 1 should correspond to 1 or -1 in the next prime, and the comma should be smaller than that of ''n'' = 0. That seems to narrow the number of candidates down to 2. As we set one of them as ''n'' = 1, the other would be ''n'' = inf and vice versa. | # ''n'' = 1 should correspond to 1 or -1 in the next prime, and the comma should be smaller than that of ''n'' = 0. That seems to narrow the number of candidates down to 2. As we set one of them as ''n'' = 1, the other would be ''n'' = inf and vice versa. | ||
# As we decide which is ''n'' = 1 and which ''n'' = inf, we should try to keep the just value of ''n'' greater than 2. We might wanna present both tables in the page, one by ''n'', and the other would be ''n''/(''n'' + 1). | # As we decide which is ''n'' = 1 and which ''n'' = inf, we should try to keep the just value of ''n'' greater than 2. We might wanna present both tables in the page, one by ''n'', and the other would be ''n''/(''n'' + 1). | ||
So in this case the answer seems to be superpyth-22. Superpyth is also the smaller comma, as expected. | |||
[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:35, 16 April 2023 (UTC) | [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:35, 16 April 2023 (UTC) | ||
Honestly, you probably know more about this than I do, so I think we should go with your idea. You can move the page and implement your idea if you want. I mainly just wanted to see the hyper-accurate temperaments that can be extracted from 22-edo. I created this page to extend your idea of equivalence continua to 22-edo, a somewhat accurate temperament for 7-limit. | |||
--[[User:Royalmilktea|Royalmilktea]] ([[User talk:Royalmilktea|talk]]) 06:59, 9 May 2023 (UTC) | |||
Latest revision as of 16:51, 17 December 2024
Suggested rename and re-parametrization
This should be renamed and re-parametrized to superpyth-22 equivalence continuum:
| n | Temperament | Comma | |
|---|---|---|---|
| Ratio | Monzo | ||
| 0 | 22 & 22c | [35 -22⟩ | |
| 1 | Quasisuper | 8388608/7971615 | [23 -13 -1⟩ |
| 2 | Diaschismic | 2048/2025 | [11 -4 -2⟩ |
| 3 | Porcupine | 250/243 | [1 -5 3⟩ |
| 4 | Comic | 5120000/4782969 | [13 -14 4⟩ |
| … | … | … | … |
| ∞ | Superpyth | 20480/19683 | [12 -9 1⟩ |
Or doing it backwards, the quasisuper-22 equivalence continuum:
| n | Temperament | Comma | |
|---|---|---|---|
| Ratio | Monzo | ||
| 0 | 22 & 22c | [35 -22⟩ | |
| 1 | Superpyth | 20480/19683 | [12 -9 1⟩ |
| 2 | Diaschismic | 2048/2025 | [11 -4 -2⟩ |
| 3 | 22 & 29c | [34 -17 -3⟩ | |
| … | … | … | … |
| ∞ | Quasisuper | 8388608/7971615 | [23 -13 -1⟩ |
Or maybe we should call it superpyth-quasisuper based on the two "order-1" temperaments?
FloraC (talk) 08:21, 16 April 2023 (UTC)
Update: I've found some simple rules to follow:
- n = 0 should correspond to a 3-limit comma (or in general, the comma that's independent of the last prime).
- n = 1 should correspond to 1 or -1 in the next prime, and the comma should be smaller than that of n = 0. That seems to narrow the number of candidates down to 2. As we set one of them as n = 1, the other would be n = inf and vice versa.
- As we decide which is n = 1 and which n = inf, we should try to keep the just value of n greater than 2. We might wanna present both tables in the page, one by n, and the other would be n/(n + 1).
So in this case the answer seems to be superpyth-22. Superpyth is also the smaller comma, as expected.
FloraC (talk) 08:35, 16 April 2023 (UTC)
Honestly, you probably know more about this than I do, so I think we should go with your idea. You can move the page and implement your idea if you want. I mainly just wanted to see the hyper-accurate temperaments that can be extracted from 22-edo. I created this page to extend your idea of equivalence continua to 22-edo, a somewhat accurate temperament for 7-limit.
--Royalmilktea (talk) 06:59, 9 May 2023 (UTC)