Diaschismic extensions: Difference between revisions
m 22 notes for 5-odd-limit? and odd 15 and 17 are reached in the same note count, but as odd 9 is added i'll leave it as 22 for more room to modulate ig but we should add 25... (btw srutal's 5-odd-limit minimax is just the pure-6/5's tuning) |
added the pergen, added the color name, added the monzo for that huge ratio with two 4-digit numbers |
||
| Line 8: | Line 8: | ||
| MOS scales = [[2L 8s]], [[10L 2s]], [[12L 10s]] | | MOS scales = [[2L 8s]], [[10L 2s]], [[12L 10s]] | ||
| Mapping = 2; 1 -2 1 | | Mapping = 2; 1 -2 1 | ||
| Pergen = (P8/2, P5) | |||
| Color name = Saguguti | |||
| Odd limit 1 = 5 | Mistuning 1 = 3.259 | Complexity 1 = 12 | | Odd limit 1 = 5 | Mistuning 1 = 3.259 | Complexity 1 = 12 | ||
| Odd limit 2 = (2.3.5.17) 25 | Mistuning 2 = ??? | Complexity 2 = 22 | | Odd limit 2 = (2.3.5.17) 25 | Mistuning 2 = ??? | Complexity 2 = 22 | ||
}} | }} | ||
'''Srutal''', known interchangeably as '''diaschismic''' in the [[5-limit]], is a [[regular temperament]] defined by [[tempering out]] the comma [[2048/2025]], the diaschisma. The octave is split into two periods, each representing [[~]][[45/32]]~[[64/45]]; and the [[generator]] can be considered to be a perfect fifth (~[[3/2]]), or a perfect fifth less a period, which is a diatonic semitone of ~[[16/15]]. Tempering out the diaschisma implies that two of these semitones are equated to [[9/8]], and therefore as [[9/8]] = ([[18/17]])([[17/16]]), ~[[16/15]] can very naturally be equated to 17/16 and 18/17 as well, producing a 2.3.5.17 [[subgroup]] extension known as '''srutal archagall''', whose commas are [[136/135]] and [[256/255]]. | '''Srutal''', known interchangeably as '''diaschismic''' in the [[5-limit]], is a [[regular temperament]] defined by [[tempering out]] the comma [[2048/2025]] = [11 -4 -2⟩, the diaschisma. The octave is split into two periods, each representing [[~]][[45/32]]~[[64/45]]; and the [[generator]] can be considered to be a perfect fifth (~[[3/2]]), or a perfect fifth less a period, which is a diatonic semitone of ~[[16/15]]. Tempering out the diaschisma implies that two of these semitones are equated to [[9/8]], and therefore as [[9/8]] = ([[18/17]])([[17/16]]), ~[[16/15]] can very naturally be equated to 17/16 and 18/17 as well, producing a 2.3.5.17 [[subgroup]] extension known as '''srutal archagall''', whose commas are [[136/135]] and [[256/255]]. | ||
{{Tdlink|Diaschismic family #Srutal aka diaschismic}} | {{Tdlink|Diaschismic family #Srutal aka diaschismic}} | ||