La Monte Young - Magic opening chord: E♭, E, F, A, B♭, C, D, E♭, E, F, G, A, B♭ = 2:3:7:9:21:63:567:189:567. The opening chord (left), E, F, A, B♭, D, E, G, and A, and the magic chord (right), E♭, B♭, C, E♭, F, B♭.
5 7 9 chord on E, eight steps in the octave. Other non-octave tunings investigated by Bohlen besides the Bohlen-Pierce scale include eight steps in the octave, based on 5:7:9 and of which only the just version would be used. Traditional notation: E B♭ D.
Author: Created by Hyacinth (talk) 06:34, 25 November 2010 using Sibelius 5.
7-tone equal tempered scale represented in traditional notation. + and - indicates approximate distance above and below notated pitch. Pitch bend matches intervals.
Author: Created by Hyacinth (talk) 23:38, 12 October 2010 using Sibelius 5.
Diatonic scale in 19-et on C. MIDI pitch bend matches intervals. Steps: 0, 3, 6, 8, 11, 14, 17, and 19. Cents: 0, 189.473684210526315789, 378.947368421052631578, 505.263157894736842105, 694.736842105263157894, 884.210526315789473684, 1073.684210526315789473, and 1200 cents. Created in Sibelius with midi pitch bend on 8 (6) different instruments.
Regular diatonic tuning 72-tone. A regular diatonic tuning is five "whole tones", T, and two half tones, S, arranged in any rotation of TTSTTTS. In 12-tone, T=200 cents and S=100 cents. In 72-tone, T=233.3 cents and S=16.6. This is that scale: C = 0 D = 233.3 E# = 466.6 F# = 483.3 G = 716.6 A = 950 B# = 1183.3 C = 1200
Chord from just Bohlen–Pierce scale: C-G-A Title refers to harmonics (fundamental=1:3:9:etc.)., tuned to harmonics 3, 5, and 7. "BP" above the clefs indicates Bohlen–Pierce notation.
Author: Created by Hyacinth (talk) in Sibelius with midi pitch bend on 4 different instruments.
Beta scale dominant seventh chord on C. Created by Hyacinth (talk) 07:35, 12 April 2011 (UTC) using Sibelius 5 with midi pitch bend. Pitch bend appears to match intervals.
Miracle scale, derived from the secor (s = 116.72 cents), plus the difference between 10 secors and a perfect octave (q = 32.84 cents). MIDI pitch bend appears to match intervals. The Miracle scale is 0 1 2 3 4 5 6 7 8 9 0' s s s s s s s s s s+q The difference between s and q (r) is used in the File:Blackjack scale.mid.
Blackjack scale, derived from the secor (s = 116.72 cents), the difference between 10 secors and a perfect octave (q = 32.84 cents), and the difference between that and a secor (r = s-q = 83.88 cents). MIDI pitch bend appears to match intervals. If the Miracle scale is 0 1 2 3 4 5 6 7 8 9 0' s s s s s s s s s s +q q +r q +r q +r q +r q +r q +r q +r q +r q +r q +r +q then the Blackjack scale is 0 >0 1 >1 2 >2 3 >3 4 >4 5 >5 6 >6 7 >7 8 >8 9 >9 <0 0' q r q r q r q r q r q r q r q r q r q r q
*Augmented octave and diminished unison on C = C♯. Equal-tempered: 21/12:1 = 100 cents. MIDI pitch bend: none Note how the diminished unison is essentially equivalent to the augmented unison.
5 25 {\displaystyle {\sqrt[{25}]{5}}} = 5:11/25 = 111.45 cents. Interval used in Stockhausen's Studie II, a compound just major third (5/1) divided into 25 equal parts.