Edithistory:Alpha scale
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| oldid | date/time | username | edit summary |
|---|---|---|---|
| 1345069001 | 2026-03-24T03:38:44Z | Trumpetrep | Nominated for deletion; see [[:Wikipedia:Articles for deletion/Alpha scale]]. |
| 1344168539 | 2026-03-18T19:35:06Z | Jerdle | The ratio of the sizes of different intervals had been confused with the use of ratios as intervals, so clarified it. |
| 1216982622 | 2024-04-03T02:59:37Z | Maulwurf6 | /* top */Fixed typo |
| 1203959155 | 2024-02-06T02:16:19Z | Citation bot | Added publisher. | [[:en:WP:UCB|Use this bot]]. [[:en:WP:DBUG|Report bugs]]. | Suggested by Abductive | [[Category:Music theory stubs]] | #UCB_Category 38/216 |
| 1196305166 | 2024-01-17T02:16:19Z | Unbeatable101 | Rescuing 2 sources and tagging 0 as dead.) #IABot (v2.0.9.5 |
| 1192408842 | 2023-12-29T05:04:08Z | 107.122.85.71 | minor text edits; converted text refs to template form |
| 1176245265 | 2023-09-20T13:48:42Z | Bearcat | clean up |
| 1172394025 | 2023-08-26T20:09:08Z | 209.6.112.33 | understanding of harm. 7th in table was incorrect: it is based on the octave inversion per WC quote in article |
| 1171942856 | 2023-08-24T02:20:55Z | 209.6.112.33 | use same precision as in Beta scale; add table row for minor third |
| 1105998036 | 2022-08-22T19:08:42Z | TooManyFingers | Changed word order for clarity |
| 1089879484 | 2022-05-26T04:18:57Z | Antonissimo | /* top */ comma is not required before (or after) quotation if the sentence would flow normally without the quotation marks. |
| 1070825644 | 2022-02-09T13:25:20Z | 79.107.103.33 | MOS:BOLDSYN |
| 1070819608 | 2022-02-09T12:39:03Z | 79.107.103.33 | |
| 1027622736 | 2021-06-09T01:01:35Z | Dgcampbe | |
| 1005910412 | 2021-02-10T01:36:52Z | Awelotta | clarified the formula. Music: A Mathematical Offering also explains this process so not original research |
| 955481592 | 2020-05-08T02:06:57Z | 107.242.121.44 | fixed error in math notation |
| 878475113 | 2019-01-15T01:18:07Z | 86.145.58.211 | |
| 878474904 | 2019-01-15T01:16:24Z | 86.145.58.211 | |
| 876774822 | 2019-01-04T11:11:27Z | Hyacinth | B{{music|b}}, 1017.60 cents, |
| 876774362 | 2019-01-04T11:06:25Z | Hyacinth | E{{music|b}}, 315.64 cents, |
| 876262841 | 2019-01-01T06:34:40Z | Hyacinth | Twelve-tone equal temperament vs. just |
| 876262594 | 2019-01-01T06:31:14Z | Hyacinth | {{multiple image | align = | direction = vertical | width = | header = [[Chromatic circle]] | image1 = Alpha scale chromatic circle.png | caption1 = Comparing the alpha scale's approximations with the just values | image2 = 12-tet scale chromatic circle for comparison with alpha scale et al.png | caption2 = Twelve-tone equal temperament's approximations vs. just }} |
| 876262168 | 2019-01-01T06:25:32Z | Hyacinth | -" with the just minor third, major third, perfect fifth, and harmonic seventh" |
| 876258715 | 2019-01-01T05:40:51Z | Hyacinth | /* top */ [[File:Alpha scale chromatic circle.png|thumb|One octave of the alpha scale in the [[chromatic circle]] comparing the scale's approximations with the just minor third, major third, perfect fifth, and harmonic seventh]] |
| 876258574 | 2019-01-01T05:38:53Z | Hyacinth | [[File:Alpha scale chromatic circle.png|thumb|One octave of the alpha scale in the [[chromatic circle]] with the just minor third, major third, perfect fifth, and harmonic sevenths for comparison with the alpha scale's approximations]] |
| 875932161 | 2018-12-30T00:34:16Z | Hyacinth | /* top */ [[]] |
| 875932106 | 2018-12-30T00:33:32Z | Hyacinth | ({{audio|Alpha scale step on C.mid|Play}}) |
| 875930364 | 2018-12-30T00:15:15Z | Hyacinth | It is derived from approximating [[just interval]]s using multiples of a single interval without, as is standard in [[equal temperament]]s, requiring an [[octave]] (2:1). |
| 875927641 | 2018-12-29T23:48:39Z | Hyacinth | -x |
| 875926844 | 2018-12-29T23:41:47Z | Hyacinth | <math>x=\frac{9\log_2(3/2)+5\log_2(5/4)+4\log_2(6/5)}{9^2+5^2+4^2}\approx0.06497082462</math> and <math>0.06497082462\times1200=77.965</math> |
| 875923392 | 2018-12-29T23:14:58Z | Hyacinth | {{Quote|Carlos' α (alpha) scale arises from the approximation of 9/5 for the above ratio [{{sfrac|log<sub>2</sub> (3/2)|log<sub>2</sub> (5/4)}}{{=}}{{sfrac|ln(3/2)|ln(5/4)}}]. This means taking a value for the scale degree so that nine of them approximate a 3:2 perfect fifth, five of them approximate a 5:4 major third, and four of them approximate a 6:5 minor third. In order to make the approximation as good as possible we minimize the mean square deviation.<ref name="Benson"/>}} |
| 875920682 | 2018-12-29T22:48:21Z | Hyacinth | /* top */ -clarify |
| 875789370 | 2018-12-29T01:02:38Z | Hyacinth | {{Script|Grek|α}} |
| 875788913 | 2018-12-29T00:58:49Z | Hyacinth | "The idea was to split a minor third into tow equal parts. Then that was divided again." |
| 875527749 | 2018-12-27T05:35:33Z | Hyacinth | /* top */ group |
| 875526667 | 2018-12-27T05:23:09Z | Hyacinth | however |
| 875526579 | 2018-12-27T05:21:51Z | Hyacinth | /* top */ while |
| 875526555 | 2018-12-27T05:21:27Z | Hyacinth | /* top */ The alpha scale, "splits the minor third exactly in half (also into quarters)." |
| 875525979 | 2018-12-27T05:15:52Z | Hyacinth | <ref name="Three"> |
| 875525739 | 2018-12-27T05:13:08Z | Hyacinth | /* top */ {{clarify|date=December 2018|reason=A just minor third is 315.64 cents, and thus one fourth is 78.91 cents, not 78.}} |
| 875525326 | 2018-12-27T05:08:51Z | Hyacinth | Reverted edits by [[Special:Contribs/Hyacinth|Hyacinth]] ([[User talk:Hyacinth|talk]]) to last version by 82.132.213.32 |
| 875525113 | 2018-12-27T05:06:41Z | Hyacinth | fix numbers |
| 849021212 | 2018-07-05T23:27:46Z | 82.132.213.32 | The error should be positive for the septimal major 2nd and major 3rd and negative for the perfect 5th |
| 843636868 | 2018-05-30T12:54:43Z | 2A02:8108:11C0:603C:A940:299C:9B7D:9E4B | |
| 831836803 | 2018-03-22T12:29:48Z | 81.178.247.200 | the octave error should be +47.44 rather than -47.44. I think it was just a typo |
| 796480550 | 2017-08-21T03:44:36Z | 31.52.113.156 | |
| 782223567 | 2017-05-25T16:47:35Z | Magic links bot | Replace [[Help:Magic links|magic links]] with templates per [[Special:Permalink/772743896#Future of magic links|local RfC]] and [[:mw:Requests for comment/Future of magic links|MediaWiki RfC]] |
| 770030691 | 2017-03-13T01:05:33Z | Hyacinth | <br/> |
| 770019408 | 2017-03-12T23:30:40Z | Hyacinth | |align=center|-3 |
| 770018645 | 2017-03-12T23:24:59Z | Hyacinth | |- |align=center|octave |align=center|15 |align=center|1169.48 |align=center|2:1 |align=center|1200.00 |align=center|−30.52 |- |align=center|octave |align=center|16 |align=center|1247.44 |align=center|2:1 |align=center|1200.00 |align=center|−4 |
| 770018276 | 2017-03-12T23:21:49Z | Hyacinth | |- |align=center|Septimal major second |align=center|3 |align=center|233.90 |align=center|8:7 |align=center|231.17 |align=center|−2.72 |
| 770015982 | 2017-03-12T23:09:05Z | Hyacinth | #s |
| 770014127 | 2017-03-12T22:55:02Z | Hyacinth | {| class="wikitable" |align=center bgcolor="#ffffb4"|interval name |align=center bgcolor="#ffffb4"|size (steps) |align=center bgcolor="#ffffb4"|size (cents) |align=center bgcolor="#ffffb4"|just ratio |align=center bgcolor="#ffffb4"|just (cents) |align=cen |
| 734250046 | 2016-08-13T01:36:50Z | Trivialist | {{Wendy Carlos}} |
| 580074403 | 2013-11-03T23:10:26Z | Hyacinth | [[Category:Wendy Carlos]] |
| 574670150 | 2013-09-26T23:12:23Z | ArmbrustBot | /* Sources */re-categorisation per [[WP:CFDS|CFDS]], replaced: Category:Non-octave-repeating scales → Category:Non–octave-repeating scales using [[Project:AWB|AWB]] |
| 528137440 | 2012-12-15T10:14:42Z | Hyacinth | /* Sources */ {{Microtonal music}} |
| 525319672 | 2012-11-28T12:22:45Z | Hyacinth | -[[Category:Microtonality]], supercat |
| 525319046 | 2012-11-28T12:18:48Z | Hyacinth | [[Category:Non-octave-repeating scales]] |
| 476941027 | 2012-02-15T02:50:46Z | 108.16.168.115 | |
| 470928269 | 2012-01-12T06:55:44Z | Hyacinth | [[major third|5:4]] |
| 470928213 | 2012-01-12T06:55:05Z | Hyacinth | br |
| 470928014 | 2012-01-12T06:52:06Z | Hyacinth | At 78 cents per step, this totals approximately 15.385 steps per [[octave]]. |
| 470927613 | 2012-01-12T06:47:05Z | Hyacinth | Minor third (just: 315.64 cents {{audio|Just minor third on C.mid|Play}}, 12-tet: 300 cents {{audio|Minor third on C.mid|Play}} |
| 470927103 | 2012-01-12T06:40:41Z | Hyacinth | <ref name="Liner"/> |
| 470458759 | 2012-01-09T16:38:49Z | Hyacinth | move audio |
| 470457966 | 2012-01-09T16:33:21Z | Hyacinth | <ref name="Milano">Milano, Dominic (November 1986). [http://www.wendycarlos.com/other/PDF-Files/Kbd86Tunings*.pdf "A Many-Colored Jungle of Exotic Tunings"], ''Keyboard''.</ref> |
| 470352050 | 2012-01-09T00:35:43Z | Hyacinth | [[perfect fifth]] |
| 470324125 | 2012-01-08T21:19:32Z | Michael Tiemann | Reference information from [[Equal temperament]] page |
| 470294957 | 2012-01-08T18:19:42Z | Michael Tiemann | /* See also */ Added beta scale and re-alpabetized according to Greek alphabet |
| 468364698 | 2011-12-30T00:31:16Z | Hyacinth | [[Category:Microtonality]] |
| 462799305 | 2011-11-27T21:44:03Z | Hyacinth | {{audio|Alpha scale harmonic seventh chord on C.mid|Play}} |
| 462794732 | 2011-11-27T21:13:27Z | Hyacinth | /* Sources */ -*Carlos, Wendy (1989–96). [http://www.wendycarlos.com/resources/pitch.html "Three Asymmetric Divisions of the Octave"], ''WendyCarlos.com''. |
| 425461243 | 2011-04-23T07:03:56Z | Hyacinth | {{Musical tuning}} |
| 425299792 | 2011-04-22T07:42:12Z | Yobot | [[WP:CHECKWIKI]] error 61 fixes + [[WP:GENFIXES|general fixes]], References after punctuation per [[WP:REFPUNC]] and [[WP:PAIC]] using [[Project:AWB|AWB]] (7679) |
| 424799470 | 2011-04-19T03:52:52Z | RenamedUser01302013 | Reverted edits by [[Special:Contributions/119.127.124.134|119.127.124.134]] ([[User talk:119.127.124.134|talk]]) to last revision by Sailsbystars ([[WP:HG|HG]]) |
| 424799442 | 2011-04-19T03:52:36Z | 119.127.124.134 | /* See also */ |
| 424798841 | 2011-04-19T03:45:59Z | Sailsbystars | Reverted edits by [[Special:Contributions/119.127.124.134|119.127.124.134]] to last version by Mephistophelian ([[User:Ale_jrb/Scripts/igloo|GLOO]]) |
| 424798791 | 2011-04-19T03:45:28Z | 119.127.124.134 | |
| 424796878 | 2011-04-19T03:27:07Z | RenamedUser01302013 | Reverted edits by [[Special:Contributions/119.127.124.134|119.127.124.134]] ([[User talk:119.127.124.134|talk]]) to last revision by Philg88 ([[WP:HG|HG]]) |
| 424796651 | 2011-04-19T03:25:13Z | 119.127.124.134 | /* See also */ |
| 424795193 | 2011-04-19T03:11:28Z | Philg88 | Reverted edits by [[Special:Contributions/119.127.124.134|119.127.124.134]] to last version by Hyacinth ([[User:Ale_jrb/Scripts/igloo|GLOO]]) |
| 424794930 | 2011-04-19T03:09:04Z | 119.127.124.134 | |
| 424793382 | 2011-04-19T02:54:46Z | 119.127.124.134 | /* See also */ |
| 423788848 | 2011-04-13T02:04:07Z | Hyacinth | [[septimal whole tone|8/7]] |
| 423651056 | 2011-04-12T08:15:43Z | Hyacinth | However, the alpha scale has, "excellent harmonic seventh chords...using the inversion of 7/4, i.e., 8/7."<ref>Carlos, Wendy (1989–96). [http://www.wendycarlos.com/resources/pitch.html "Three Asymmetric Divisions of the Octave"], ''WendyCarlos.com' |
| 423648168 | 2011-04-12T07:40:47Z | Hyacinth | /* See also */ *[[Delta scale]] |
| 423646423 | 2011-04-12T07:17:55Z | Hyacinth | -s |
| 423646375 | 2011-04-12T07:17:27Z | Hyacinth | ({{audio|Alpha scale major triad on C.mid|Play major}} and {{audio|Alpha scale minor triad on C.mid|minor triads}}) |
| 415554416 | 2011-02-23T18:57:46Z | RjwilmsiBot | Per [[WP:ISBN]] formatted 2 ISBNs using [[Project:AWB|AWB]] (7609) |
| 408115384 | 2011-01-16T00:18:50Z | Ninly | extraneous word |
| 404024489 | 2010-12-24T13:07:36Z | Yobot | /* External links */[[WP:CHECKWIKI]] error 61 fixes + [[WP:GENFIXES|general fixes]] using [[Project:AWB|AWB]] (7500) |
| 379109026 | 2010-08-15T21:27:14Z | 173.206.40.200 | added missing hyphen |
| 376685174 | 2010-08-02T01:50:38Z | Hyacinth | Undid revision 376503678 by [[Special:Contributions/98.101.136.218|98.101.136.218]] ([[User talk:98.101.136.218|talk]]), in article body |
| 376503678 | 2010-07-31T23:31:18Z | 98.101.136.218 | /* See also */ |
| 367810302 | 2010-06-13T18:31:19Z | Hyacinth | <ref>Sethares, William (2004). ''Tuning, Timbre, Spectrum, Scale'', p.60. ISBN 1852337974. Scale step of 78 cents.</ref>. |
| 367770661 | 2010-06-13T13:37:23Z | Hyacinth | [[beta scale]] |
| 367770597 | 2010-06-13T13:36:46Z | Hyacinth | The alpha scale produces, "wonderful [[triad (music)|triads]]," and beta has similar properties but the [[Harmonic seventh|sevenths]] are more in tune<ref>Milano, Dominic (November 1986). [http://www. |
| 367768164 | 2010-06-13T13:13:42Z | Hyacinth | ==External links== *Carlos, Wendy (1989-96). [http://www.wendycarlos.com/resources/pitch.html "Three Asymmetric Divisions of the Octave"], ''WendyCarlos.com''. |
| 367767436 | 2010-06-13T13:06:12Z | Hyacinth | [[Category:Equal temperaments]] |
| 367760177 | 2010-06-13T11:50:32Z | Hyacinth | It may be derived from using 9:5 {{audio|Greater just minor seventh on C.mid|Play}} to approximate the interval 3:2/5:4<ref name="Benson"/>, which equals 6:5 {{audio|Just minor third on C.mid|Play}}. |
| 367758912 | 2010-06-13T11:35:44Z | Hyacinth | α |
| 367743496 | 2010-06-13T09:00:21Z | Hyacinth | It was used invented by [[Wendy Carlos]] and used on her album ''[[Beauty in the Beast]]'' (1986). |
| 367741737 | 2010-06-13T08:41:01Z | Hyacinth | The '''Alpha scale''' is a non-octave repeating [[musical scale]] which splits the [[minor third]] (just: 315.64 cents {{audio|Just minor third on C.mid|Play}}, 12-tet: 300 cents {{audio|Minor third o |
