1559edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| Line 32: | Line 24: | ||
| {{monzo| 38 -2 -15 }}, {{monzo| 71 -99 37 }} | | {{monzo| 38 -2 -15 }}, {{monzo| 71 -99 37 }} | ||
| {{mapping| 1559 2471 3620 }} | | {{mapping| 1559 2471 3620 }} | ||
| | | −0.0196 | ||
| 0.0155 | | 0.0155 | ||
| 2.01 | | 2.01 | ||
| Line 39: | Line 31: | ||
| 43046721/43025920, 78125000/78121827, 12884901888/12867859375 | | 43046721/43025920, 78125000/78121827, 12884901888/12867859375 | ||
| {{mapping| 1559 2471 3620 4377 }} | | {{mapping| 1559 2471 3620 4377 }} | ||
| | | −0.0376 | ||
| 0.0339 | | 0.0339 | ||
| 4.40 | | 4.40 | ||
| Line 46: | Line 38: | ||
| 3025/3024, 180224/180075, 50014503/50000000, 56953125/56942116 | | 3025/3024, 180224/180075, 50014503/50000000, 56953125/56942116 | ||
| {{mapping| 1559 2471 3620 4377 5393 }} | | {{mapping| 1559 2471 3620 4377 5393 }} | ||
| | | −0.0188 | ||
| 0.0483 | | 0.0483 | ||
| 6.27 | | 6.27 | ||
| Line 53: | Line 45: | ||
| 1716/1715, 3025/3024, 4096/4095, 492128/492075, 5282739/5281250 | | 1716/1715, 3025/3024, 4096/4095, 492128/492075, 5282739/5281250 | ||
| {{mapping| 1559 2471 3620 4377 5393 5769 }} | | {{mapping| 1559 2471 3620 4377 5393 5769 }} | ||
| | | −0.0162 | ||
| 0.0445 | | 0.0445 | ||
| 5.78 | | 5.78 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 78: | Line 64: | ||
| 8000/6561 | | 8000/6561 | ||
| [[Raider]] | | [[Raider]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "confluenceprettype" from ''albumwithoutspaces'' (2024) | * "confluenceprettype" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/0jCzkUrwVEHevs7xAWgsvh Spotify] | [https://francium223.bandcamp.com/track/confluenceprettype Bandcamp] | [https://www.youtube.com/watch?v=4rxv7ec4BEM YouTube] – luna[25] in 1559edo tuning | ||
[[Category:Listen]] | |||
Revision as of 02:29, 16 November 2024
| ← 1558edo | 1559edo | 1560edo → |
Theory
1559edo is consistent to the 9-odd-limit. Using the patent val, it tempers out [38 -2 -15⟩ (luna comma) and [71 -99 37⟩ (raider comma) in the 5-limit; 43046721/43025920, 78125000/78121827 and [32 1 -6 -7⟩ in the 7-limit, 3025/3024, 180224/180075, 50014503/50000000 and 56953125/56942116 in the 11-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.033 | +0.088 | +0.257 | -0.195 | +0.011 | -0.273 | +0.370 | -0.179 | +0.314 | +0.314 |
| Relative (%) | +0.0 | +4.3 | +11.4 | +33.4 | -25.4 | +1.4 | -35.5 | +48.1 | -23.3 | +40.8 | +40.8 | |
| Steps (reduced) |
1559 (0) |
2471 (912) |
3620 (502) |
4377 (1259) |
5393 (716) |
5769 (1092) |
6372 (136) |
6623 (387) |
7052 (816) |
7574 (1338) |
7724 (1488) | |
Subsets and supersets
1559edo is the 246th prime edo.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [2471 -1559⟩ | [⟨1559 2471]] | -0.0106 | 0.0106 | 1.38 |- | 2.3.5 | [38 -2 -15⟩, [71 -99 37⟩ | [⟨1559 2471 3620]] | −0.0196 | 0.0155 | 2.01 |- | 2.3.5.7 | 43046721/43025920, 78125000/78121827, 12884901888/12867859375 | [⟨1559 2471 3620 4377]] | −0.0376 | 0.0339 | 4.40 |- | 2.3.5.7.11 | 3025/3024, 180224/180075, 50014503/50000000, 56953125/56942116 | [⟨1559 2471 3620 4377 5393]] | −0.0188 | 0.0483 | 6.27 |- | 2.3.5.7.11.13 | 1716/1715, 3025/3024, 4096/4095, 492128/492075, 5282739/5281250 | [⟨1559 2471 3620 4377 5393 5769]] | −0.0162 | 0.0445 | 5.78 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin |- | 1 | 251\1559 | 193.201 | 262144/234375 | Luna |- | 1 | 446\1559 | 343.297 | 8000/6561 | Raider Template:Rank-2 end Template:Orf