Diaschismic: Difference between revisions

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{{Infobox Regtemp

| Title = Diaschismic; srutal archagall

| Subgroups = 2.3.5, 2.3.5.17

| Comma basis = [[2048/2025]] (2.3.5); <br /> [[136/135]], [[256/255]] (2.3.5.17)

| Edo join 1 = 12 | Edo join 2 = 22

| Generator = 16/15 | Generator tuning = 104.898 | Optimization method = POTE

| MOS scales = [[2L 8s]], [[10L 2s]], [[12L 10s]]

| 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 2 = (2.3.5.17) 25 | Mistuning 2 = ??? | Complexity 2 = 22

}}

'''Diaschismic''', sometimes known as [[srutal vs diaschismic|srutal]] in the [[5-limit]], is a half-octave [[regular temperament|temperament]] [[generator|generated]] by a [[3/2|perfect fifth]] or that minus a half-octave [[period]], which is a semitone representing [[16/15]]. Two of these semitones give a whole tone of [[9/8]], so the diaschisma, [[2048/2025]], is [[tempering out|tempered out]]. We also have a whole tone plus a period represent [[8/5]], and in the canonical [[extension]] to the [[7-limit]], the fifth is tuned a little sharp such that eight of them octave reduced (an augmented fifth) minus a period approximate [[8/7]], tempering out the starling comma, [[126/125]].

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+{{Infobox Regtemp
+| Title = Diaschismic; srutal archagall
+| Subgroups = 2.3.5, 2.3.5.17
+| Comma basis = [[2048/2025]] (2.3.5); <br /> [[136/135]], [[256/255]] (2.3.5.17)
+| Edo join 1 = 12 | Edo join 2 = 22
+| Generator = 16/15 | Generator tuning = 104.898 | Optimization method = POTE
+| MOS scales = [[2L 8s]], [[10L 2s]], [[12L 10s]]
+| 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 2 = (2.3.5.17) 25 | Mistuning 2 = ??? | Complexity 2 = 22
+}}
 '''Diaschismic''', sometimes known as [[srutal vs diaschismic|srutal]] in the [[5-limit]], is a half-octave [[regular temperament|temperament]] [[generator|generated]] by a [[3/2|perfect fifth]] or that minus a half-octave [[period]], which is a semitone representing [[16/15]]. Two of these semitones give a whole tone of [[9/8]], so the diaschisma, [[2048/2025]], is [[tempering out|tempered out]]. We also have a whole tone plus a period represent [[8/5]], and in the canonical [[extension]] to the [[7-limit]], the fifth is tuned a little sharp such that eight of them octave reduced (an augmented fifth) minus a period approximate [[8/7]], tempering out the starling comma, [[126/125]].