Breedsmic temperaments: Difference between revisions
Note on temperaments not discussed in this page |
m Note on decimal and quadrimage |
||
| Line 3: | Line 3: | ||
It is also the amount by which four stacked 10/7 intervals exceed 25/6: 10000/2401 * 2401/2400 = 10000/2400 = 25/6, which is two octaves above the chromatic semitone, 25/24. We might note also that 49/40 * 10/7 = 7/4 and 49/40 * (10/7)^2 = 5/2, relationships which will be significant in any breedsmic temperament. As a consequence of these facts, the 49/40+60/49 neutral third and the 7/5 and 10/7 intervals tend to have relatively low complexity in a breedsmic system. | It is also the amount by which four stacked 10/7 intervals exceed 25/6: 10000/2401 * 2401/2400 = 10000/2400 = 25/6, which is two octaves above the chromatic semitone, 25/24. We might note also that 49/40 * 10/7 = 7/4 and 49/40 * (10/7)^2 = 5/2, relationships which will be significant in any breedsmic temperament. As a consequence of these facts, the 49/40+60/49 neutral third and the 7/5 and 10/7 intervals tend to have relatively low complexity in a breedsmic system. | ||
Temperaments not discussed here include [[Meantone family #Squares|squares]], [[Archytas clan #Beatles|beatles]], [[Gamelismic clan #Miracle|miracle]], [[Starling temperaments #Myna|myna]], [[Tetracot family #Octacot|octacot]], [[Kleismic family #Quadritikleismic|quadritikleismic]], [[Schismatic family #Sesquiquartififths|sesquiquartififths]], [[Würschmidt family #Hemiwürschmidt|hemiwürschmidt]], [[Ragismic microtemperaments #Ennealimmal|ennealimmal]], and [[Gammic family #Neptune|neptune]]. | Temperaments not discussed here include [[Meantone family #Squares|squares]], [[Archytas clan #Beatles|beatles]], [[Dicot family #Decimal|decimal]], [[Gamelismic clan #Miracle|miracle]], [[Starling temperaments #Myna|myna]], [[Magic family #Quadrimage|quadrimage]], [[Tetracot family #Octacot|octacot]], [[Kleismic family #Quadritikleismic|quadritikleismic]], [[Schismatic family #Sesquiquartififths|sesquiquartififths]], [[Würschmidt family #Hemiwürschmidt|hemiwürschmidt]], [[Ragismic microtemperaments #Ennealimmal|ennealimmal]], and [[Gammic family #Neptune|neptune]]. | ||
=Hemififths= | =Hemififths= | ||