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Euler's Tonnetz. The Tonnetz originally appeared in Leonhard Euler's 1739 Tentamen novae theoriae musicae ex certissismis harmoniae principiis dilucide expositae.Euler's Tonnetz, pictured at left, shows the triadic relationships of the perfect fifth and the major third: at the top of the image is the note F, and to the left underneath is C (a perfect fifth above F), and to the right is A (a ...
For the ordinary diatonic scales described here, the T-s are tones and the s-s are semitones which are half, or approximately half the size of the tone.But in the more general regular diatonic tunings, the two steps can be of any relation within the range between T = 171.43 ¢ (for s = T at the high extreme) and T = 240 ¢ (for s = 0 at the low extreme) in musical cents (fifth, p5, between 685 ...
Harmonic Materials of Modern Music is a book on musical set theory by American composer Howard Hanson that overlaps significantly with composer Elliott Carter's Harmony Book and theorist Allen Forte's subsequent Structure of Atonal Music.
Claudius Ptolemy of Alexandria described several 7-limit tuning systems for the diatonic and chromatic genera. He describes several "soft" (μαλακός) diatonic tunings which all use 7-limit intervals. [7]
31 EDO on the regular diatonic tuning continuum at p5 = 696.77 cents [1]. In music, 31 equal temperament, 31 ET, which can also be abbreviated 31 TET (31 tone ET) or 31 EDO (equal division of the octave), also known as tricesimoprimal, is the tempered scale derived by dividing the octave into 31 equally-proportioned steps (equal frequency ratios).
Assuming the equal-tempered scale, one considers twelve chroma values represented by the set {C, C ♯, D, D ♯, E, F, F ♯, G, G ♯, A, A ♯, B} that consists of the twelve pitch spelling attributes as used in Western music notation. Note that in the equal-tempered scale different pitch spellings such C ♯ and D ♭ refer to the
The Quadrangularis Reversum, an instrument constructed by Harry Partch based on the 11-limit tonality diamond. In music theory and tuning, a tonality diamond is a two-dimensional diagram of ratios in which one dimension is the Otonality and one the Utonality. [1]
[2] [3] The other, older, scale commonly used is called slendro. Pelog has seven notes, but many gamelan ensembles only have keys for five of the pitches. Even in ensembles that have all seven notes, many pieces only use a subset of five notes, sometimes the additional 4th tone is also used in a piece like western accidentals.