Mutt: Difference between revisions

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The other remarkable property explains its name: it is supported by the standard val for [[768edo]]. Since dividing the octave into 768 = 12 × 64 parts is what some systems use for defining pitch (using the coarse, but not the fine, conceptual "pitch wheel" of [[MIDI]]), mutt is a temperament which accords to this kind of MIDI unit, hence the acronym "MIDI unit tempered tuning", or "mutt", as was named by [[Gene Ward Smith]] in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_53634.html#53850 Yahoo! Tuning Group | ''Retuning using midi to produce beatless music - You gotta be kidding!'']</ref>.

The fact that the smallest mos is 84 and the generator is about the 14-cent difference between the 400-cent third of equal temperament and a just third of 386 cents limits the applicability of mutt. If we tune 84 notes in 768edo to mutt, we divide 400 cents by a step of 9 repeated 27 times, followed by a step of 13. If we now use this to tune seven rows, each of which divides the octave into twelve parts, we have rows with the pattern [63 63 63 67 63 63 63 67 63 63 63 67], a modified version of [[12edo]].

The fact that the smallest proper mos is 84 and the generator is about the 14-cent difference between the 400-cent third of equal temperament and a just third of 386 cents limits the applicability of mutt. If we tune 84 notes in 768edo to mutt, we divide 400 cents by a step of 9 repeated 27 times, followed by a step of 13. If we now use this to tune seven rows, each of which divides the octave into twelve parts, we have rows with the pattern [63 63 63 67 63 63 63 67 63 63 63 67], a modified version of [[12edo]].

See [[Horwell temperaments]] for technical data.

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 The other remarkable property explains its name: it is supported by the standard val for [[768edo]]. Since dividing the octave into 768 = 12 × 64 parts is what some systems use for defining pitch (using the coarse, but not the fine, conceptual "pitch wheel" of [[MIDI]]), mutt is a temperament which accords to this kind of MIDI unit, hence the acronym "MIDI unit tempered tuning", or "mutt", as was named by [[Gene Ward Smith]] in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_53634.html#53850 Yahoo! Tuning Group | ''Retuning using midi to produce beatless music - You gotta be kidding!'']</ref>.
-The fact that the smallest mos is 84 and the generator is about the 14-cent difference between the 400-cent third of equal temperament and a just third of 386 cents limits the applicability of mutt. If we tune 84 notes in 768edo to mutt, we divide 400 cents by a step of 9 repeated 27 times, followed by a step of 13. If we now use this to tune seven rows, each of which divides the octave into twelve parts, we have rows with the pattern [63 63 63 67 63 63 63 67 63 63 63 67], a modified version of [[12edo]].
+The fact that the smallest proper mos is 84 and the generator is about the 14-cent difference between the 400-cent third of equal temperament and a just third of 386 cents limits the applicability of mutt. If we tune 84 notes in 768edo to mutt, we divide 400 cents by a step of 9 repeated 27 times, followed by a step of 13. If we now use this to tune seven rows, each of which divides the octave into twelve parts, we have rows with the pattern [63 63 63 67 63 63 63 67 63 63 63 67], a modified version of [[12edo]].
 See [[Horwell temperaments]] for technical data.