Beta scale (original) (raw)
The β (beta) scale is a non-octave-repeating musical scale invented by Wendy Carlos and first used on her album Beauty in the Beast (1986). It is derived from approximating just intervals using multiples of a single interval without, as is standard in equal temperaments, requiring an octave (2:1). It may be approximated by splitting the perfect fifth (3:2) into eleven equal parts [(3:2)1⁄11 ≈ 63.8 cents]. It may be approximated by splitting the perfect fourth (4:3) into two equal parts [(4:3)1⁄2], or eight equal parts [(4:3)1⁄8 = 64 cents], totaling approximately 18.8 steps per octave. and
| Property | Value |
|---|---|
| dbo:abstract | The β (beta) scale is a non-octave-repeating musical scale invented by Wendy Carlos and first used on her album Beauty in the Beast (1986). It is derived from approximating just intervals using multiples of a single interval without, as is standard in equal temperaments, requiring an octave (2:1). It may be approximated by splitting the perfect fifth (3:2) into eleven equal parts [(3:2)1⁄11 ≈ 63.8 cents]. It may be approximated by splitting the perfect fourth (4:3) into two equal parts [(4:3)1⁄2], or eight equal parts [(4:3)1⁄8 = 64 cents], totaling approximately 18.8 steps per octave. The scale step may also precisely be derived from using 11:6 (B↑♭-, 1049.36 cents, ) to approximate the interval 3:2⁄5:4, which equals 6:5 . In order to make the approximation as good as possible we minimize the mean square deviation. ... We choose a value of the scale degree so that eleven of them approximate a 3:2 perfect fifth, six of them approximate a 5:4 major third, and five of them approximate a 6:5 minor third. and Although neither has an octave, one advantage to the beta scale over the alpha scale is that 15 steps, 957.494 cents, is a reasonable approximation to the seventh harmonic (7:4, 968.826 cents) though both have nice triads . "According to Carlos, beta has almost the same properties as the alpha scale, except that the sevenths are slightly more in tune." The delta scale may be regarded as the beta scale's reciprocal since it is "as far 'down' the (0 3 6 9) circle from α as β is 'up'." (en) |
| dbo:thumbnail | wiki-commons:Special:FilePath/Perfect_fourth_on_C.png?width=300 |
| dbo:wikiPageExternalLink | http://www.wendycarlos.com/resources/pitch.html |
| dbo:wikiPageID | 27697100 (xsd:integer) |
| dbo:wikiPageLength | 5183 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 1081785855 (xsd:integer) |
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| dbp:caption | Twelve-tone equal temperament vs. just (en) Comparing the beta scale's approximations with the just values (en) |
| dbp:direction | vertical (en) |
| dbp:header | dbr:Chromatic_circle |
| dbp:image | 12 (xsd:integer) Beta scale chromatic circle.png (en) |
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| dcterms:subject | dbc:Equal_temperaments dbc:Non–octave-repeating_scales dbc:Wendy_Carlos |
| gold:hypernym | dbr:Scale |
| rdf:type | yago:WikicatNon–octave-repeatingScales yago:Abstraction100002137 yago:Act100030358 yago:Activity100407535 yago:Adjustment100999787 yago:Calibration100999245 yago:EqualTemperament101000610 yago:Event100029378 yago:Measure100033615 yago:PsychologicalFeature100023100 yago:YagoPermanentlyLocatedEntity dbo:Aircraft yago:Scale113850304 yago:Standard107260623 yago:SystemOfMeasurement113577171 yago:Temperament101000411 yago:WikicatEqualTemperaments |
| rdfs:comment | The β (beta) scale is a non-octave-repeating musical scale invented by Wendy Carlos and first used on her album Beauty in the Beast (1986). It is derived from approximating just intervals using multiples of a single interval without, as is standard in equal temperaments, requiring an octave (2:1). It may be approximated by splitting the perfect fifth (3:2) into eleven equal parts [(3:2)1⁄11 ≈ 63.8 cents]. It may be approximated by splitting the perfect fourth (4:3) into two equal parts [(4:3)1⁄2], or eight equal parts [(4:3)1⁄8 = 64 cents], totaling approximately 18.8 steps per octave. and (en) |
| rdfs:label | Beta scale (en) |
| owl:sameAs | freebase:Beta scale yago-res:Beta scale wikidata:Beta scale https://global.dbpedia.org/id/4Xko5 |
| prov:wasDerivedFrom | wikipedia-en:Beta_scale?oldid=1081785855&ns=0 |
| foaf:depiction | wiki-commons:Special:FilePath/Perfect_fourth_on_C.png wiki-commons:Special:FilePath/12-tet_scale_chromati...comparison_with_alpha_scale_et_al.png wiki-commons:Special:FilePath/Beta_scale_chromatic_circle.png |
| foaf:isPrimaryTopicOf | wikipedia-en:Beta_scale |
| is dbo:wikiPageWikiLink of | dbr:Beauty_in_the_Beast dbr:List_of_pitch_intervals dbr:Index_of_music_articles dbr:List_of_musical_scales_and_modes dbr:Equal_temperament dbr:Gamma_scale dbr:Bohlen–Pierce_scale dbr:Delta_scale dbr:Tone_cluster dbr:Twelfth_root_of_two dbr:Wendy_Carlos dbr:Alpha_scale dbr:19_equal_temperament dbr:Musical_tuning dbr:Octatonic_scale |
| is foaf:primaryTopic of | wikipedia-en:Beta_scale |
