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- Bohlen–Pierce_scale abstract "The Bohlen–Pierce scale (BP scale) is a musical tuning and scale, first described in the 1970s, that offers an alternative to the octave-repeating scales typical in Western and other musics, specifically the equal tempered diatonic scale. The interval 3:1 (often called by a new name, tritave) serves as the fundamental harmonic ratio, replacing the diatonic scale's 2:1 (the octave). For any pitch that is part of the BP scale, all pitches one or more tritaves higher or lower are part of the system as well, and are considered equivalent.The BP scale divides the tritave into 13 steps, either equal tempered (the most popular form), or in a justly tuned version. Compared with octave-repeating scales, the BP scale's intervals are more consonant with certain types of acoustic spectra. The scale was independently described by Heinz Bohlen, Kees van Prooijen and John R. Pierce. Pierce, who, with Max Mathews and others, published his discovery in 1984, renamed the Pierce 3579b scale and its chromatic variant the Bohlen–Pierce scale after learning of Bohlen's earlier publication. Bohlen had proposed the same scale based on consideration of the influence of combination tones on the Gestalt impression of intervals and chords.The intervals between BP scale pitch classes are based on odd integer frequency ratios, in contrast with the intervals in diatonic scales, which employ both odd and even ratios found in the harmonic series. Specifically, the BP scale steps are based on ratios of integers whose factors are 3, 5, and 7. Thus the scale contains consonant harmonies based on the odd harmonic overtones 3/5/7/9 (About this sound play ). The chord formed by the ratio 3:5:7 (About this sound play ) serves much the same role as the 4:5:6 chord (a major triad About this sound play ) does in diatonic scales (3:5:7 = 1:1.66:2.33 and 4:5:6 = 2:2.5:3 = 1:1.25:1.5).".
- Bohlen–Pierce_scale thumbnail BP_chord_357_just.png?width=300.
- Bohlen–Pierce_scale wikiPageExternalLink bohlen-pierce-conference.org.
- Bohlen–Pierce_scale wikiPageExternalLink ppPdesc.html.
- Bohlen–Pierce_scale wikiPageExternalLink bpsite.
- Bohlen–Pierce_scale wikiPageExternalLink scale13.html.
- Bohlen–Pierce_scale wikiPageExternalLink BP_sale.htm.
- Bohlen–Pierce_scale wikiPageExternalLink playlist?list=PLE4AEC5BC4B7AA4F1&feature=plcp.
- Bohlen–Pierce_scale wikiPageExternalLink 17tppp4_Walker_Love_Song.mp3.
- Bohlen–Pierce_scale wikiPageExternalLink BP.
- Bohlen–Pierce_scale wikiPageID "321868".
- Bohlen–Pierce_scale wikiPageLength "29030".
- Bohlen–Pierce_scale wikiPageOutDegree "92".
- Bohlen–Pierce_scale wikiPageRevisionID "682659728".
- Bohlen–Pierce_scale wikiPageWikiLink 41_equal_temperament.
- Bohlen–Pierce_scale wikiPageWikiLink 5-limit_limma.
- Bohlen–Pierce_scale wikiPageWikiLink 7-tet.
- Bohlen–Pierce_scale wikiPageWikiLink 833_cents_scale.
- Bohlen–Pierce_scale wikiPageWikiLink A12_scale.
- Bohlen–Pierce_scale wikiPageWikiLink Aesthetics_of_music.
- Bohlen–Pierce_scale wikiPageWikiLink Alpha_scale.
- Bohlen–Pierce_scale wikiPageWikiLink Berklee_College_of_Music.
- Bohlen–Pierce_scale wikiPageWikiLink Beta_scale.
- Bohlen–Pierce_scale wikiPageWikiLink Bohlen–Pierce_scale.
- Bohlen–Pierce_scale wikiPageWikiLink Boston_Microtonal_Society.
- Bohlen–Pierce_scale wikiPageWikiLink Category:Just_tuning_and_intervals.
- Bohlen–Pierce_scale wikiPageWikiLink Category:Musical_temperaments.
- Bohlen–Pierce_scale wikiPageWikiLink Category:Non–octave-repeating_scales.
- Bohlen–Pierce_scale wikiPageWikiLink Cent_(music).
- Bohlen–Pierce_scale wikiPageWikiLink Chalumeau.
- Bohlen–Pierce_scale wikiPageWikiLink Chord_progression.
- Bohlen–Pierce_scale wikiPageWikiLink Chromatic_scale.
- Bohlen–Pierce_scale wikiPageWikiLink Clarinet.
- Bohlen–Pierce_scale wikiPageWikiLink Classical_music.
- Bohlen–Pierce_scale wikiPageWikiLink Combination_tone.
- Bohlen–Pierce_scale wikiPageWikiLink Consonance_and_dissonance.
- Bohlen–Pierce_scale wikiPageWikiLink Curtis_Roads.
- Bohlen–Pierce_scale wikiPageWikiLink Degree_(music).
- Bohlen–Pierce_scale wikiPageWikiLink Delta_scale.
- Bohlen–Pierce_scale wikiPageWikiLink Diatonic_function.
- Bohlen–Pierce_scale wikiPageWikiLink Diatonic_scale.
- Bohlen–Pierce_scale wikiPageWikiLink Diesis.
- Bohlen–Pierce_scale wikiPageWikiLink Dominant_(music).
- Bohlen–Pierce_scale wikiPageWikiLink Elaine_Walker_(composer).
- Bohlen–Pierce_scale wikiPageWikiLink Equal_temperament.
- Bohlen–Pierce_scale wikiPageWikiLink Fibonacci_number.
- Bohlen–Pierce_scale wikiPageWikiLink Fibonacci_sequence.
- Bohlen–Pierce_scale wikiPageWikiLink Frequency.
- Bohlen–Pierce_scale wikiPageWikiLink Frequency_spectrum.
- Bohlen–Pierce_scale wikiPageWikiLink Gamma_scale.
- Bohlen–Pierce_scale wikiPageWikiLink Generated_collection.
- Bohlen–Pierce_scale wikiPageWikiLink Georg_Hajdu.
- Bohlen–Pierce_scale wikiPageWikiLink Gestalt_psychology.
- Bohlen–Pierce_scale wikiPageWikiLink Goethe-Institut.
- Bohlen–Pierce_scale wikiPageWikiLink Goethe_Institut.
- Bohlen–Pierce_scale wikiPageWikiLink Golden_Ratio.
- Bohlen–Pierce_scale wikiPageWikiLink Golden_ratio.
- Bohlen–Pierce_scale wikiPageWikiLink Harmonic.
- Bohlen–Pierce_scale wikiPageWikiLink Harmonic_series_(music).
- Bohlen–Pierce_scale wikiPageWikiLink Heinz_Bohlen.
- Bohlen–Pierce_scale wikiPageWikiLink Hochschule_für_Musik_und_Theater_Hamburg.
- Bohlen–Pierce_scale wikiPageWikiLink Integer.
- Bohlen–Pierce_scale wikiPageWikiLink Interval_(music).
- Bohlen–Pierce_scale wikiPageWikiLink Intonation_(music).
- Bohlen–Pierce_scale wikiPageWikiLink Joe_Maneri.
- Bohlen–Pierce_scale wikiPageWikiLink John_R._Pierce.
- Bohlen–Pierce_scale wikiPageWikiLink Jon_Appleton.
- Bohlen–Pierce_scale wikiPageWikiLink Just_chromatic_semitone.
- Bohlen–Pierce_scale wikiPageWikiLink Just_intonation.
- Bohlen–Pierce_scale wikiPageWikiLink Just_minor_second.
- Bohlen–Pierce_scale wikiPageWikiLink Kees_van_Prooijen.
- Bohlen–Pierce_scale wikiPageWikiLink Major_sixth.
- Bohlen–Pierce_scale wikiPageWikiLink Max_Mathews.
- Bohlen–Pierce_scale wikiPageWikiLink Minor_second.
- Bohlen–Pierce_scale wikiPageWikiLink Minor_seventh.
- Bohlen–Pierce_scale wikiPageWikiLink Musical_temperament.
- Bohlen–Pierce_scale wikiPageWikiLink Musical_tuning.
- Bohlen–Pierce_scale wikiPageWikiLink New_England_Conservatory.
- Bohlen–Pierce_scale wikiPageWikiLink New_England_Conservatory_of_Music.
- Bohlen–Pierce_scale wikiPageWikiLink Octave.
- Bohlen–Pierce_scale wikiPageWikiLink Octave_equivalency.
- Bohlen–Pierce_scale wikiPageWikiLink Paul_Erlich.
- Bohlen–Pierce_scale wikiPageWikiLink Perfect_fifth.
- Bohlen–Pierce_scale wikiPageWikiLink Pitch_class.
- Bohlen–Pierce_scale wikiPageWikiLink Pseudo-octave.
- Bohlen–Pierce_scale wikiPageWikiLink Pseudooctave.
- Bohlen–Pierce_scale wikiPageWikiLink Regular_temperament.
- Bohlen–Pierce_scale wikiPageWikiLink Richard_Boulanger.
- Bohlen–Pierce_scale wikiPageWikiLink Ron_Sword.
- Bohlen–Pierce_scale wikiPageWikiLink Scale_(music).
- Bohlen–Pierce_scale wikiPageWikiLink Semitone.
- Bohlen–Pierce_scale wikiPageWikiLink Semitone_maximus.
- Bohlen–Pierce_scale wikiPageWikiLink Septimal_diatonic_semitone.
- Bohlen–Pierce_scale wikiPageWikiLink Septimal_major_third.
- Bohlen–Pierce_scale wikiPageWikiLink Septimal_minor_third.
- Bohlen–Pierce_scale wikiPageWikiLink Social_conditioning.
- Bohlen–Pierce_scale wikiPageWikiLink Spectral_density.
- Bohlen–Pierce_scale wikiPageWikiLink Stephen_Fox_(clarinet_maker).
- Bohlen–Pierce_scale wikiPageWikiLink Subdominant.
- Bohlen–Pierce_scale wikiPageWikiLink Syntonic_comma.