User:Userminusone/Goldis comma: Difference between revisions

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The "goldis comma", or the golden diesis, is a 5 limit comma that is approximately 50.55 cents in size. Its ratio is 549755813888/533935546875, and its monzo is {{monzo| 39 -7 -12 }}. It is the sum of the porcupine comma and the luna comma, the difference between the negri comma and the kwazy comma, and the difference between the passion comma and the semicomma.

The "goldis comma", or the golden diesis, is a 5 limit comma that is approximately 50.55 cents in size, which 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]] and the [[Luna family|luna comma]], the difference between the [[negri comma]] and the [[Very high accuracy temperaments|kwazy comma]], and the difference between the [[Passion|passion comma]] and the [[semicomma]].

==Notes on naming==

"Goldis" is a contraction of "Golden diesis". The diesis part represents the fact that this comma is close to the size of other diesis. The golden part represents the fact that the temperament tempering out this comma has a generator which is extremely close to logarithmic phi, or 1200/phi cents. As a result of this property, it is mostly tempered out by EDOs in the Fibonacci sequence. These EDOs 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 other diesis. The golden part represents the fact 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 EDOs 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]])

==Temperaments==

The 5 limit parent temperament, Goldis, has a generator of approximately 458 cents. The major third is 7 generators down, and the perfect fifth is 12 generators up, making this a rather complex temperament. It should be noted that there is an alternate major third 21 generators up which is the most accurate major third whenever the generator is between 458.6314 cents and 458.8235 cents (or 13 steps of 34edo). Generators in this range generate Tetracot (which is contorted by order 3) rather than Goldis.

The 5 limit parent temperament, Goldis, has a generator of approximately 458 cents. The major third is 7 generators down, and the perfect fifth is 12 generators up, making this a rather complex temperament. It should be noted that there is an alternate major third 21 generators up which is the most accurate major third whenever the generator is between 458.6314 cents and 458.8235 cents (or 13 steps of [[34edo]]). Generators in this range generate Tetracot (which is contorted by order 3) rather than Goldis.

Goldis pure fifths generator - 458.496250072 cents

Perhaps the most accurate 7 limit extension of this temperament, which I call semigoldis, splits the generator in half and maps one step to 8/7. Semigoldis tempers out the breedsma in addition to the goldis comma. The only downside is that this drastically increases the complexity. This temperament is supported by 21edo, 68edo, 89edo, 136edo, and 157edo.

Perhaps the most accurate 7 limit extension of this temperament, which I call semigoldis, splits the generator in half and maps one step to 8/7. Semigoldis tempers out the [[breedsma]] in addition to the goldis comma. The only downside is that this drastically increases the complexity. This temperament is supported by [[21edo]], [[68edo]], [[89edo]], [[136edo]], and [[157edo]].

Semigoldis pure fifths generator - 229.248125036 cents

[http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B39%2C-7%2C-12%3E&page=2&limit=5 temperament finder]

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-The "goldis comma", or the golden diesis, is a 5 limit comma that is approximately 50.55 cents in size. Its ratio is 549755813888/533935546875, and its monzo is {{monzo| 39 -7 -12 }}. It is the sum of the porcupine comma and the luna comma, the difference between the negri comma and the kwazy comma, and the difference between the passion comma and the semicomma.
+The "goldis comma", or the golden diesis, is a 5 limit comma that is approximately 50.55 cents in size, which 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]] and the [[Luna family|luna comma]], the difference between the [[negri comma]] and the [[Very high accuracy temperaments|kwazy comma]], and the difference between the [[Passion|passion comma]] and the [[semicomma]].
 ==Notes on naming==
-"Goldis" is a contraction of "Golden diesis". The diesis part represents the fact that this comma is close to the size of other diesis. The golden part represents the fact that the temperament tempering out this comma has a generator which is extremely close to logarithmic phi, or 1200/phi cents. As a result of this property, it is mostly tempered out by EDOs in the Fibonacci sequence. These EDOs 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 other diesis. The golden part represents the fact 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 EDOs 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]])
 ==Temperaments==
-The 5 limit parent temperament, Goldis, has a generator of approximately 458 cents. The major third is 7 generators down, and the perfect fifth is 12 generators up, making this a rather complex temperament. It should be noted that there is an alternate major third 21 generators up which is the most accurate major third whenever the generator is between 458.6314 cents and 458.8235 cents (or 13 steps of 34edo). Generators in this range generate Tetracot (which is contorted by order 3) rather than Goldis.
+The 5 limit parent temperament, Goldis, has a generator of approximately 458 cents. The major third is 7 generators down, and the perfect fifth is 12 generators up, making this a rather complex temperament. It should be noted that there is an alternate major third 21 generators up which is the most accurate major third whenever the generator is between 458.6314 cents and 458.8235 cents (or 13 steps of [[34edo]]). Generators in this range generate Tetracot (which is contorted by order 3) rather than Goldis.
 Goldis pure fifths generator - 458.496250072 cents
-Perhaps the most accurate 7 limit extension of this temperament, which I call semigoldis, splits the generator in half and maps one step to 8/7. Semigoldis tempers out the breedsma in addition to the goldis comma. The only downside is that this drastically increases the complexity. This temperament is supported by 21edo, 68edo, 89edo, 136edo, and 157edo.
+Perhaps the most accurate 7 limit extension of this temperament, which I call semigoldis, splits the generator in half and maps one step to 8/7. Semigoldis tempers out the [[breedsma]] in addition to the goldis comma. The only downside is that this drastically increases the complexity. This temperament is supported by [[21edo]], [[68edo]], [[89edo]], [[136edo]], and [[157edo]].
 Semigoldis pure fifths generator - 229.248125036 cents
 [http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B39%2C-7%2C-12%3E&page=2&limit=5 temperament finder]