Canopus: Difference between revisions
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{{ | {{Infobox regtemp | ||
| Title = Canopus | |||
| Subgroups = 3.5.7 | |||
| Comma basis = [[16875/16807]] | |||
| Edo join 1 = b13 | Edo join 2 = b88 | |||
| Mapping = 1; -5 -4 | |||
| Generators = 7/5 | |||
| Generators tuning = 583.986 | |||
| Optimization method = CWE | |||
| MOS scales = [[3L 1s (3/1-equivalent)|3L 1s <3/1>]], [[3L 4s (3/1-equivalent)|3L 4s <3/1>]], [[3L 7s (3/1-equivalent)|3L 7s <3/1>]] | |||
| Color name = | |||
| Odd limit 1 = 3.5.7 7 | Mistuning 1 = 1.40 | Complexity 1 = 7 | |||
| Odd limit 2 = 3.5.7 49 | Mistuning 2 = 2.80 | Complexity 2 = 13 | |||
}} | |||
'''Canopus''' is the [[Rank-2 temperament|rank two]] [[3.5.7 subgroup]] temperament [[Temper out|tempering out]] [[16875/16807]], the amount by which [[27/7]] exceeds four 7/5s. Having a generator of [[~]][[7/5|7:5]], it possesses non-trivial [[MOS]] of the families [[1L 2s (3/1-equivalent)|1L 2s]], [[3L 1s (3/1-equivalent)|3L 1s]], [[3L 4s (3/1-equivalent)|3L 4s]], [[3L 7s (3/1-equivalent)|3L 7s]], and (in most cases) [[10L 3s (3/1-equivalent)|10L 3s]]. As 16875/16807 = ([[540/539]])<sup>2</sup>*([[3025/3024]]), Canopus can be extended to the 3.5.7.11/4 subgroup extremely naturally by tempering out these two commas; prime 53 can additionally be incorporated by means of tempering out [[1325/1323]], equating (7/5)<sup>2</sup> = [[49/25]] to 53/27. | '''Canopus''' is the [[Rank-2 temperament|rank two]] [[3.5.7 subgroup]] temperament [[Temper out|tempering out]] [[16875/16807]], the amount by which [[27/7]] exceeds four 7/5s. Having a generator of [[~]][[7/5|7:5]], it possesses non-trivial [[MOS]] of the families [[1L 2s (3/1-equivalent)|1L 2s]], [[3L 1s (3/1-equivalent)|3L 1s]], [[3L 4s (3/1-equivalent)|3L 4s]], [[3L 7s (3/1-equivalent)|3L 7s]], and (in most cases) [[10L 3s (3/1-equivalent)|10L 3s]]. As 16875/16807 = ([[540/539]])<sup>2</sup>*([[3025/3024]]), Canopus can be extended to the 3.5.7.11/4 subgroup extremely naturally by tempering out these two commas; prime 53 can additionally be incorporated by means of tempering out [[1325/1323]], equating (7/5)<sup>2</sup> = [[49/25]] to 53/27. | ||
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In the below, tritave-reduced harmonics and subharmonics are indicated in '''bold'''. | In the below, tritave-reduced harmonics and subharmonics are indicated in '''bold'''. | ||
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{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
|+ style="font-size: 105%;" | Canopus | |+ style="font-size: 105%;" | Canopus | ||