Goldis comma: Difference between revisions

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The '''goldis comma''' is the amount by which six classic augmented second intervals of [[75/64]] fall short of [[8/3]]. Its ratio is [[549755813888/533935546875]], and its [[monzo]] is {{monzo| 39 -7 -12 }}. It is the sum of the [[250/243|porcupine comma]] (a.k.a. maximal diesis) and the [[Luna family|luna comma]], the difference between the [[negri comma]] and the [[kwazy comma]], and the difference between the [[passion comma]] and the [[semicomma]]. It is also the difference between 4 [[128/125|dieses]] and a [[2187/2048|pythagorean chromatic semitone]], as well as the difference between a [[9/8|pythagorean whole tone]] and three [[negri comma|negri commas]].

"Goldis" is a contraction of "Golden diesis". The diesis part represents the fact that this comma is close to the size of a [[diesis]]. The golden part refers to that the temperament tempering out this comma has a generator which is extremely close to [[Golden ratio|logarithmic phi]], or 1200/phi cents. As a result of this property, it is mostly tempered out by edos in the Fibonacci sequence. These are [[13edo]], [[21edo]], [[34edo]], [[55edo]], and [[89edo]]. ([[144edo]] doesn't temper out this comma because [[144edo]] is contorted in the 5 limit, meaning it has the same 5 limit patent val as [[72edo]].)

"Goldis" is a contraction of "Golden diesis". The diesis part represents the fact that this comma is close to the size of a [[diesis]]. The golden part refers to that the temperament tempering out this comma has a generator which is extremely close to [[Golden ratio|logarithmic phi]], or 1200/phi cents. As a result of this property, it is mostly tempered out by edos in the Fibonacci sequence. These are [[13edo]], [[21edo]], [[34edo]], [[55edo]], and [[89edo]]. ([[144edo]] doesn't temper out this comma because [[144edo]] is [[contorted]] in the [[5-limit]], meaning it has the same 5 limit patent val as [[72edo]], though the [[warts|144c val]] supports it.)

== Temperaments ==

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 The '''goldis comma''' is the amount by which six classic augmented second intervals of [[75/64]] fall short of [[8/3]]. Its ratio is [[549755813888/533935546875]], and its [[monzo]] is {{monzo| 39 -7 -12 }}. It is the sum of the [[250/243|porcupine comma]] (a.k.a. maximal diesis) and the [[Luna family|luna comma]], the difference between the [[negri comma]] and the [[kwazy comma]], and the difference between the [[passion comma]] and the [[semicomma]]. It is also the difference between 4 [[128/125|dieses]] and a [[2187/2048|pythagorean chromatic semitone]], as well as the difference between a [[9/8|pythagorean whole tone]] and three [[negri comma|negri commas]].
-"Goldis" is a contraction of "Golden diesis". The diesis part represents the fact that this comma is close to the size of a [[diesis]]. The golden part refers to that the temperament tempering out this comma has a generator which is extremely close to [[Golden ratio|logarithmic phi]], or 1200/phi cents. As a result of this property, it is mostly tempered out by edos in the Fibonacci sequence. These are [[13edo]], [[21edo]], [[34edo]], [[55edo]], and [[89edo]]. ([[144edo]] doesn't temper out this comma because [[144edo]] is contorted in the 5 limit, meaning it has the same 5 limit patent val as [[72edo]].)
+"Goldis" is a contraction of "Golden diesis". The diesis part represents the fact that this comma is close to the size of a [[diesis]]. The golden part refers to that the temperament tempering out this comma has a generator which is extremely close to [[Golden ratio|logarithmic phi]], or 1200/phi cents. As a result of this property, it is mostly tempered out by edos in the Fibonacci sequence. These are [[13edo]], [[21edo]], [[34edo]], [[55edo]], and [[89edo]]. ([[144edo]] doesn't temper out this comma because [[144edo]] is [[contorted]] in the [[5-limit]], meaning it has the same 5 limit patent val as [[72edo]], though the [[warts|144c val]] supports it.)
 == Temperaments ==