Oscillorwell: Difference between revisions
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AthiTrydhen (talk | contribs) Created page with "'''Oscillorwell''' is a family of 22 tone temperaments with sinusoidally varying generators. == Oscillorwell, 3/2 repeating version == The formula for the nth generator is 12..." |
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'''Oscillorwell''' is a family of 22 tone | {{Novelty}} | ||
'''Oscillorwell''' is a family of [[Category:22-tone scales|22 tone]] [[temperament]]s with sinusoidally varying [[generator]]s. | |||
== Oscillorwell, 3/2 repeating version == | == Oscillorwell, 3/2 repeating version == | ||
The formula for the nth generator is 1200*log(7/6,2) + 9.674*sin(pi n/7)^2, where the factor is chosen so that every seventh generator would form a just 3/2. | The formula for the nth generator is 1200*log(7/6,2) + 9.674*sin(pi n/7)^2, where the factor is chosen so that every seventh generator would form a [[just]] [[3/2]]. | ||
{| class="wikitable" | {| class="wikitable" | ||
|0 | |0.000 | ||
|- | |- | ||
|37. | |37.519 | ||
|- | |- | ||
|88. | |88.325 | ||
|- | |- | ||
|160. | |160.479 | ||
|- | |- | ||
|203.912 | |203.912 | ||
| Line 16: | Line 17: | ||
|266.871 | |266.871 | ||
|- | |- | ||
|310. | |310.304 | ||
|- | |- | ||
|364. | |364.391 | ||
|- | |- | ||
|433. | |433.264 | ||
|- | |- | ||
|470.783 | |470.783 | ||
|- | |- | ||
|535. | |535.563 | ||
|- | |- | ||
|586. | |586.370 | ||
|- | |- | ||
|637. | |637.176 | ||
|- | |- | ||
|701.956 | |701.956 | ||
|- | |- | ||
|739. | |739.475 | ||
|- | |- | ||
|808. | |808.348 | ||
|- | |- | ||
|862. | |862.435 | ||
|- | |- | ||
|905.868 | |905.868 | ||
| Line 42: | Line 43: | ||
|968.827 | |968.827 | ||
|- | |- | ||
|1012. | |1012.260 | ||
|- | |- | ||
|1084. | |1084.414 | ||
|- | |- | ||
|1135. | |1135.220 | ||
|} | |} | ||
== Oscillorwell, 7/4 repeating version == | == Oscillorwell, 7/4 repeating version == | ||
The formula for the nth generator is 1200*log(7/6,2) + 8.465*sin(pi n/8)^2, where the factor is chosen so that every eighth generator would form a just 7/4. | The formula for the nth generator is 1200*log(7/6,2) + 8.465*sin(pi n/8)^2, where the factor is chosen so that every eighth generator would form a just [[7/4]]. | ||
{| class="wikitable" | {| class="wikitable" | ||
|0 | |0.000 | ||
|- | |- | ||
|36. | |36.939 | ||
|- | |- | ||
|76. | |76.870 | ||
|- | |- | ||
|162. | |162.743 | ||
|- | |- | ||
|202. | |202.674 | ||
|- | |- | ||
|268. | |268.111 | ||
|- | |- | ||
|308. | |308.042 | ||
|- | |- | ||
|350. | |350.966 | ||
|- | |- | ||
|433. | |433.846 | ||
|- | |- | ||
|470.785 | |470.785 | ||
|- | |- | ||
|539. | |539.214 | ||
|- | |- | ||
|582. | |582.139 | ||
|- | |- | ||
|626. | |626.302 | ||
|- | |- | ||
|701.957 | |701.957 | ||
| Line 82: | Line 83: | ||
|737.656 | |737.656 | ||
|- | |- | ||
|813. | |813.311 | ||
|- | |- | ||
|857. | |857.475 | ||
|- | |- | ||
|900. | |900.399 | ||
|- | |- | ||
|968.828 | |968.828 | ||
|- | |- | ||
|1005. | |1005.767 | ||
|- | |- | ||
|1088. | |1088.647 | ||
|- | |- | ||
|1131. | |1131.571 | ||
|} | |} | ||
{{todo|inline=1|improve synopsis|add definition|improve layout|link}} | |||
[[Category:22-tone scales]] | |||
Latest revision as of 03:20, 12 January 2026
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This page presents a novelty topic.
It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks. |
Oscillorwell is a family of temperaments with sinusoidally varying generators.
Oscillorwell, 3/2 repeating version
The formula for the nth generator is 1200*log(7/6,2) + 9.674*sin(pi n/7)^2, where the factor is chosen so that every seventh generator would form a just 3/2.
| 0.000 |
| 37.519 |
| 88.325 |
| 160.479 |
| 203.912 |
| 266.871 |
| 310.304 |
| 364.391 |
| 433.264 |
| 470.783 |
| 535.563 |
| 586.370 |
| 637.176 |
| 701.956 |
| 739.475 |
| 808.348 |
| 862.435 |
| 905.868 |
| 968.827 |
| 1012.260 |
| 1084.414 |
| 1135.220 |
Oscillorwell, 7/4 repeating version
The formula for the nth generator is 1200*log(7/6,2) + 8.465*sin(pi n/8)^2, where the factor is chosen so that every eighth generator would form a just 7/4.
| 0.000 |
| 36.939 |
| 76.870 |
| 162.743 |
| 202.674 |
| 268.111 |
| 308.042 |
| 350.966 |
| 433.846 |
| 470.785 |
| 539.214 |
| 582.139 |
| 626.302 |
| 701.957 |
| 737.656 |
| 813.311 |
| 857.475 |
| 900.399 |
| 968.828 |
| 1005.767 |
| 1088.647 |
| 1131.571 |
|
Todo: improve synopsis, add definition, improve layout, link |