(French)
Gammoid structure withFertility axiom
Harmoid structure withRegularity axiomContiguity axiomCongruity axiom
Chordoid structure onrational numbers withstandard multiplicationstandard orderfinite chordoid congruence modulo 2
It is sufficient to know at this level that any finite set of odd numbersA = <k1 k2 ... kn>generates a finite chordoid of classes modulo 2 with the matrixA\A = [aij]where the generic element isaij = kj/kiand a corresponding harmoid with the set{2xa. . . . . . . . .The tonalsoft.com website is almost entirely the work of one person: me, Joe Monzo. Please reward me for my knowledge and effort by choosing your preferred level of financial support. Thank you.
a&b temperament [a&b are numbers]55-edo (comma) (Mozart's tuning)1/1 or 1:1 (ratio)2/1 or 2:1 (ratio)a&b temperament [a&b are numbers]apotome (Greek interval)aristoxenean (temperament family)atomic (temperament family)augmented / diesic (temperament family)augmented-2nd / aug-2 / #2 (interval)augmented-4th / aug-4 / #4 (interval)augmented-5th / aug-5 / #5 (interval)augmented-6th / aug-6 / #6 (interval)augmented-9th / aug-9 / #9 (interval)blackjack (tuning)cent / ¢ (unit of interval measurement)centitone / iring (unit of interval measurement)chromatic-semitone / augmented-prime (interval)daseian (musical notation)dekamu / 10mu (MIDI-unit)diapason (Greek interval)diapente (Greek interval)diatessaron (Greek interval)diatonic semitone (minor-2nd) (interval)diesic (temperament family)diezeugmenon (Greek tetrachord)diminished-5th / dim5 / -5 / b5 (interval)diminished-7th / dim7 / o7 (interval)doamu / 2mu (MIDI-unit)dodekamu / 12mu (MIDI-unit)dominant-7th (dom-7, x7) (chord)dorian (mode)eleventh / 11th (interval)enamu / 1mu (MIDI-unit)endekamu / 11mu (MIDI-unit)enharmonic semitone (interval)ennealimmal (temperament family)enneamu / 9mu (MIDI-unit)farab (unit of interval measurement)fifth / 5th (interval)flu (unit of interval measurement)Gentle introduction to Fokker periodicity-blocks (by Paul Erlich)fourth / 4th (interval)Gentle introduction to Fokker periodicity-blocks (by Paul Erlich)grad (unit of interval measurement)hexamu / 6mu (MIDI-unit)Hurrian Hymn (Monzo reconstruction)hypate (Greek note)hypaton (Greek tetrachord)hyperbolaion / hyperboleon (Greek tetrachord)hypophrygian (Greek mode)imperfect (interval quality)iring / centitone (unit of interval measurement)1/1 or 1:1 (ratio)2/1 or 2:1 (ratio)jot (unit of interval measurement)JustMusic: A New Harmony [Monzo's book]JustMusic prime-factor notation [Monzo essay]kwazy (temperament family)leimma / limma (Greek interval)lichanos (Greek note)limma / leimma (Greek interval)locrian (mode)lydian (mode)magic (temperament family)Mahler 7th/1 [Monzo score and analysis]marvel (temperament family)meantone (temperament family)mem (unit of interval measurement)meride (unit of interval measurement)mese (Greek note)meson (Greek tetrachord)millioctave / m8ve (unit of interval measurement)mina (unit of interval measurement)minerva (temperament family)miracle (temperament family)mixolydian (mode)monzo (prime-exponent vector)Monzo, Joe (music-theorist)morion / moria (unit of interval measurement)mutt (temperament family)mystery (temperament family)octamu / oktamu / 8mu (MIDI-unit)octave (interval)oktamu / octamu / 8mu (MIDI-unit)orwell (temperament family)p4, perfect 4th, perfect fourth (interval)p5, perfect 5th, perfect fifth (interval)pantonality of Schoenberg [Monzo essay]paramese (Greek note)paranete (Greek note)parhypate (Greek note)pentamu / 5mu (MIDI-unit)prime-factor notation (JustMusic) [Monzo essay]proslambanomenos (Greek note)savart (unit of interval measurement)schismic / skhismic (temperament family)Schoenberg's pantonality [Monzo essay]second / 2nd (interval)semisixths (temperament family)semitone (unit of interval measurement)seventh / 7th (interval)sixth / 6th (interval)sk (unit of interval measurement)skhismic / schismic (temperament family)sruti tuning [Monzo essay]studloco (tuning)subminor 3rd (interval)Sumerian tuning [speculations by Monzo]synemmenon (Greek tetrachord)temperament-unit / tu (unit of interval measurement)tenth / 10th (interval)tetrachord-theory tutorial [by Monzo]tetradekamu / 14mu (MIDI-unit)tetramu / 4mu (MIDI-unit)third / 3rd (interval)thirteenth / 13th (interval)tina (unit of interval measurement)tone (interval, and other definitions)tredek (unit of interval measurement)triamu / 3mu (MIDI-unit)tridekamu / 13mu (MIDI-unit)trihemitone (Greek interval)trite (Greek note)tu / temperament-unit (unit of interval measurement)Türk sent (unit of interval measurement)twelfth / 12th (interval)whole-tone (interval)woolhouse-unit (unit of interval measurement)