Bisect — Bisection is the general activity of dividing something into two parts.Bisect may mean:*bisection, in geometry, dividing something into two equal parts * bisection of earthworms to study regeneration *bisect (philately), the use of postage stamp… … Wikipedia
Diatonic set theory — is a subdivision or application of musical set theory which applies the techniques and insights of discrete mathematics to properties of the diatonic collection such as maximal evenness, Myhill s property, well formedness, the deep scale property … Wikipedia
Generated collection — In diatonic set theory, a generated collection is a collection or scale formed by repeatedly adding a constant interval in integer notation, the generator, also known as an interval cycle, around the chromatic circle until a complete collection… … Wikipedia
Diatonic scale — Qualities Number of pitch classes 7 Maximal evenness Well formed generated collection Myhill s property Deep scale property Cardinality equals variety Struc … Wikipedia
Golden ratio — For the Ace of Base album, see The Golden Ratio (album). Not to be confused with Golden number. The golden section is a line segment divided according to the golden ratio: The total length a + b is to the length of the longer segment a as the… … Wikipedia
Greek arithmetic, geometry and harmonics: Thales to Plato — Ian Mueller INTRODUCTION: PROCLUS’ HISTORY OF GEOMETRY In a famous passage in Book VII of the Republic starting at Socrates proposes to inquire about the studies (mathēmata) needed to train the young people who will become leaders of the ideal… … History of philosophy
Maximal evenness — The major scale is maximally even. For example, for every generic interval of a second there are only two possible specific intervals: 1 semitone (a minor second) or 2 semitones (a major second) … Wikipedia
Mathematics and art — have a long historical relationship. The ancient Egyptians and ancient Greeks knew about the golden ratio, regarded as an aesthetically pleasing ratio, and incorporated it into the design of monuments including the Great Pyramid,[1] the Parthenon … Wikipedia
Common tone — C is a common tone betwee the C and G major scales, as are D, E, G, A, and B. In music a common tone is a pitch class that is a member of, or common to, a musical scale and a transposition of that scale, as in modulation (Johnson 2003, p.42). Six … Wikipedia
Myhill's property — The major scale is maximally even. For example, for every generic interval of a second there are only two possible specific intervals: 1 semitone (a minor second) or 2 semitones (a major second). In diatonic set theory Myhill s property is the… … Wikipedia
