Goldis comma - Revision history

FloraC: - duplicate info

2025-06-14T16:16:45Z

- duplicate info

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 }}
 The '''goldis comma''' ([[ratio]]: 549755813888/533935546875, {{monzo|legend=1| 39 -7 -12 }}) is a [[medium comma|medium]] [[5-limit]] [[comma]] which is the amount by which six classic augmented second intervals of [[75/64]] fall short of [[8/3]]. It is the sum of the [[250/243|porcupine comma]] (a.k.a. maximal diesis) and the [[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]].
 == Temperaments ==
-Despite being a quarter-tone in size, due to its complexity, the damage is spread out, so that simple intervals of the [[5-limit]] tend to be tuned reasonably. Of the edos aforementioned, [[34edo]] is an especially good and tone-efficient tuning (also evidenced by being the largest "golden edo" appearing in the [[optimal ET sequence]]), [[55edo]] is good for combining it with an approximation of [[1/6-comma meantone]] that closes after 55 notes so that 5/4 is slightly more in tune, and [[89edo]] is an overlooked [[nestoria]] tuning supporting it (though it's very flat for a nestoria tuning).
+[[Tempering out]] this comma leads to the [[goldis]] temperament. It is mostly [[support]]ed by [[edo]]s in the Fibonacci sequence. These are [[21edo]], [[34edo]], [[55edo]], and [[89edo]]. ([[144edo]] does not temper out this comma in the [[patent val]], though the [[warts|144c val]] supports it.)
-{{Optimal ET sequence|legend=1| 21, 47b, 68, 157 }}
+== Etymology ==
 == See also ==

FloraC: Improve intro

2025-01-18T10:10:10Z

Improve intro

← Older revision		Revision as of 10:10, 18 January 2025
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	\| Comma = yes		\| Comma = yes
	}}		}}
			The '''goldis comma''' ([[ratio]]: 549755813888/533935546875, {{monzo\|legend=1\| 39 -7 -12 }}) is a [[medium comma\|medium]] [[5-limit]] [[comma]] which is the amount by which six classic augmented second intervals of [[75/64]] fall short of [[8/3]]. It is the sum of the [[250/243\|porcupine comma]] (a.k.a. maximal diesis) and the [[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]].
	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]], though the [[warts\|144c val]] supports it.)		"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.)

BudjarnLambeth at 00:32, 4 November 2024

2024-11-04T00:32:11Z

← Older revision		Revision as of 00:32, 4 November 2024
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	* [[Golden ratio]]		* [[Golden ratio]]

	[[Category:Commas named for their ~~regular~~ temperament ~~properties~~]]		[[Category:Commas named for the generator of their temperament]]
	[[Category:Commas named after their interval size]]		[[Category:Commas named after their interval size]]

BudjarnLambeth at 00:22, 4 November 2024

2024-11-04T00:22:48Z

← Older revision		Revision as of 00:22, 4 November 2024
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	[[Category:Commas named for their regular temperament properties]]		[[Category:Commas named for their regular temperament properties]]
			[[Category:Commas named after their interval size]]

BudjarnLambeth at 08:01, 3 November 2024

2024-11-03T08:01:50Z

← Older revision		Revision as of 08:01, 3 November 2024
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	* [[Acoustic phi]]		* [[Acoustic phi]]
	* [[Golden ratio]]		* [[Golden ratio]]

			[[Category:Commas named for their regular temperament properties]]

TallKite: add color name

2024-09-24T20:39:50Z

add color name

← Older revision		Revision as of 20:39, 24 September 2024
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	{{Infobox Interval		{{Infobox Interval
	\| Name = Goldis comma		\| Name = Goldis comma
			\| Color name = Trisa-quadtrigu comma
	\| Ratio = 549755813888/533935546875		\| Ratio = 549755813888/533935546875
	\| Comma = yes		\| Comma = yes

Godtone: other small fixes

2024-08-15T23:25:22Z

other small fixes

← Older revision		Revision as of 23:25, 15 August 2024
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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]].		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 ==		== Temperaments ==

Godtone: wrong header level

2024-08-15T23:21:55Z

wrong header level

← Older revision		Revision as of 23:21, 15 August 2024
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	{{Optimal ET sequence\|legend=1\| 21, 47b, 68, 157 }}		{{Optimal ET sequence\|legend=1\| 21, 47b, 68, 157 }}

	=== See also ===		== See also ==
	* [[Logarithmic phi]]		* [[Logarithmic phi]]
	* [[Acoustic phi]]		* [[Acoustic phi]]
	* [[Golden ratio]]		* [[Golden ratio]]

Godtone: Created page with "{{Infobox Interval | Name = Goldis comma | Ratio = 549755813888/533935546875 | Comma = yes }} The '''goldis comma''' is the amount by which six classic augmented second inter..."

2024-08-15T20:46:47Z

Created page with "{{Infobox Interval | Name = Goldis comma | Ratio = 549755813888/533935546875 | Comma = yes }} The '''goldis comma''' is the amount by which six classic augmented second inter..."

New page

{{Infobox Interval
| Name = Goldis comma
| Ratio = 549755813888/533935546875
| Comma = yes
}}

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]].)

== Temperaments ==
Despite being a quarter-tone in size, due to its complexity, the damage is spread out, so that simple intervals of the [[5-limit]] tend to be tuned reasonably. Of the edos aforementioned, [[34edo]] is an especially good and tone-efficient tuning (also evidenced by being the largest "golden edo" appearing in the [[optimal ET sequence]]), [[55edo]] is good for combining it with an approximation of [[1/6-comma meantone]] that closes after 55 notes so that 5/4 is slightly more in tune, and [[89edo]] is an overlooked [[nestoria]] tuning supporting it (though it's very flat for a nestoria tuning).

=== Goldis ===
As the generator doesn't admit a plausible interpretation in the [[5-limit]], a number of extensions are possible. One possibility is to notice that the generator is close to [[49/32]], resulting in [[hemigoldis]], which splits the generator in half.

Subgroup: 2.3.5

Comma list: [[549755813888/533935546875]]

{{Mapping|legend=1| 1 9 -2 | 0 -12 7 }}

[[Optimal tuning]] ([[CWE]]): 2 = 1\1, ~131072/84375 = 741.381

{{Optimal ET sequence|legend=1| 13, 21, 34, 123, 157 }}

=== Hemigoldis ===
Though fairly complex in the [[7-limit]], hemigoldis does a lot better in badness metrics than pure 5-limit goldis, and yet again has many possible extensions to other primes. For example, two periods minus six generators yields a "tetracot 2nd" which can be interpreted as ~[[21/19]] to add prime 19 or perhaps more accurately ~[[31/28]] to add prime 7, or even simply as ~[[32/29]] to add prime 29, though the other two have the benefit of clearly connecting to the 7-limit representation. Note that again [[89edo]] is a possible tuning for combining it with flat nestoria and not appearing in the optimal ET sequence.

Subgroup: 2.3.5.7

Comma list: [[549755813888/533935546875]], [[2401/2400]]

{{Mapping|legend=1| 1 21 -9 2 | 0 -24 14 1}}

[[Optimal tuning]] ([[CWE]]): 2 = 1\1, ~7/4 = 970.690

{{Optimal ET sequence|legend=1| 21, 47b, 68, 157 }}

=== See also ===
* [[Logarithmic phi]]
* [[Acoustic phi]]
* [[Golden ratio]]