Bit Shifting

Bit shifting is equivalent to the process which creates the church modes: relocating the leftmost series member to the rightmost position. A seed of n bits may be shifted (n – 1) times, creating n modes. Performed on a binary seed, which is a set of neither absolute pitches (Bb, C, D, Eb,…) nor intervals (M2, M2, m2,…) but rather chromatic alteration data (1, 0, 0, 1, 0, 0, 0), bit shifting creates a set of at least (7w + 5b + wc) scales, where w is the number of ones, b is the number of zeroes, and c is the number of chromatic variants arising from the presence of black keys both a half-step above and a half-step below the keys D, G, and A.

Pan-chromatic Seventh Chord Sets

The above thumbnails link to music manuscript containing pan-chromatic 7th chord solutions. Each solution contains three 7th chords which together contain each note of the chromatic scale exactly once. The below table displays the same solutions in numeral/text format. Arabic numeral roots refer to relative position in a chromatic scale, not diatonic relationships typical of Roman numerals.

The Critique Of Pure Led Zeppelin

Thus the shriek, the caterwaul, the chainsaw gnarlgnashing, the yowl and the whizz that decapitates may be reheard by the adventurous or emotionally damaged as mellifluous bursts of unarguable affirmation.

Lester Bangs, A Reasonable Guide to Horrible Noise

On December 10th, 2007, at O2 arena, Led Zeppelin performed their only full-length concert since July 7, 1980, and I missed it. The band’s website has links to ten reviews of the concert, but those ten reviews don’t really address the music.

Mechanical Transposition

Mechanical transposition is the physical relocation of a specific order of accidentals to another root of the same state. The pitches C, D, E, F, G, A, B, and their enharmonic equivalents, all are of the state 0; the pitches Db, Eb, Gb, Ab, Bb, and their enharmonic equivalents are all of the state 1.

The Prime Seeds

The 8-bit binary scale data set comprises numbers 00000000-11111111 (hex:00-FF, dec:0-255).  Each number 8-bit number comprises two 4-bit tetrachords in the range of 0000-1111 (hex:0-F, dec. 0-15).   Applying the techniques of ones’ complement and bit shifting reduces this data set to only a few prime seeds from which the entire data set can be generated.

An Introduction To Binary Scales

Consider the notes of the 12 major scales, as played at a keyboard instrument, as orders of black and white keys, not as orders of specific pitches:

Pan-chromatic Triad Sets

The above thumbnail links to a document containing the complete pan-chromatic triad sets.  Each row of the below table contains a combination of four 3-note chords which together use each note of the chromatic scale exactly once. Roots refer to relative position in a chromatic scale and as such do not indicate diatonic relationships.