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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