Erac - Revision history

Inthar: Redirected page to Straddle primes

2026-03-06T16:02:55Z

← Older revision		Revision as of 16:02, 6 March 2026
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	'''Eracs''', short for error accidentals, are symbols that indicate how much a tempered interval is flat or sharp relative to others in a subgroup. They act as variables representing small pitch differences and have no set size. They are the standard notation for subgroups involving [[Straddle primes]].		#redirect [[Straddle primes]]

	Eracs provide a more complete picture of error cancelation than the standard notation of non-prime intervals. For example, 11edo almost perfectly misses primes 3 and 5 present 22edo, which still allows them to cancel out for an accurate 5/3 and 15. 11edo's [[JI group]] might be 2.5/3.15.7.11 in standard notation, which is a subgroup of the erac group 2.x3.x5.7.11. This becomes even more important in edos like 23 or 29, where several low primes are critically inaccurate and representing all of the error cancelation in standard notation creates a very long JI group.

	~~Example erac groups for edos can be found in [[EDO#List of Edos]].~~

	~~== Symbols ==~~

	~~{\| class="wikitable"~~
	~~\|+Erac Meanings (intervals represented by an underscore)~~
	\|-
	~~\|<_~~
	~~\|Flat by a set arbitrary amount.~~
	\|-
	~~\|>_~~
	~~\|Sharp by a set arbitrary amount.~~
	\|-
	~~\|x_~~
	~~\|Critically flat/sharp. Shorthand for <_.>_.~~
	\|-
	~~\|<x_ and >x_~~
	~~\|Shorthand for <<_.>_ and <_.>>_ respectively.~~
	\|-
	~~\|{ and }~~
	~~\|Partial eracs, indicating error that may be ignored.~~
	\|-
	~~\|~_~~
	~~\|Approximate, tempered equivalent. A widely accepted symbol used in this context to indicate that no eracs apply.~~
	\|}

	Eracs are placed before their respective numbers by default (although they may be placed after as well) This is for readability and to remove ambiguity with the denominator, as eracs on the denominator have an inverse effect on the size of a tempered ratio. For example, >5/3 is sharp or 5/3, but 5/>3 is flat.

	~~== Erac temperaments ==~~
	Temperament optimization algorithms can be built around eracs to create optimal error cancelation, such as [https://spoogly.website/tools/gto.html GTO]. Erac temperaments have the potential to replace exotemperaments by properly representing the large error in approximating certain primes, providing less misleading mappings with systematic accuracy.

	~~== Erac-derived temperaments ==~~

	~~These were a concept derived by [[User:2^67-1\|Cole]] to be able to quickly create temperaments.~~

	~~His procedure:~~

	* For a flat harmonic and a sharp harmonic:
	** take the flat harmonic and take it to the power of how many eracs the sharp harmonic has
	** take the sharp harmonic and take it to the power of how many eracs the flat harmonic has
	** multiply them together
	** take it to the power of how many steps there are in an EDO
	** octave-reduce (if the interval is greater than 600c octave reduced, take the inverse)

	~~{{Cat\|Atypical ratios~~
	~~Notation}}~~

Vector: pretty sure eracs are widely used enough at least in xenref; people in beginner-help are asking about em so

2026-03-06T06:19:20Z

pretty sure eracs are widely used enough at least in xenref; people in beginner-help are asking about em so

← Older revision		Revision as of 06:19, 6 March 2026
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	~~{{Proposed}}~~
	'''Eracs''', short for error accidentals, are symbols that indicate how much a tempered interval is flat or sharp relative to others in a subgroup. They act as variables representing small pitch differences and have no set size. They are the standard notation for subgroups involving [[Straddle primes]].		'''Eracs''', short for error accidentals, are symbols that indicate how much a tempered interval is flat or sharp relative to others in a subgroup. They act as variables representing small pitch differences and have no set size. They are the standard notation for subgroups involving [[Straddle primes]].

Inthar at 05:36, 29 January 2026

2026-01-29T05:36:43Z

← Older revision		Revision as of 05:36, 29 January 2026
Line 2:		Line 2:
	'''Eracs''', short for error accidentals, are symbols that indicate how much a tempered interval is flat or sharp relative to others in a subgroup. They act as variables representing small pitch differences and have no set size. They are the standard notation for subgroups involving [[Straddle primes]].		'''Eracs''', short for error accidentals, are symbols that indicate how much a tempered interval is flat or sharp relative to others in a subgroup. They act as variables representing small pitch differences and have no set size. They are the standard notation for subgroups involving [[Straddle primes]].

	Eracs provide a more complete picture of error cancelation than the standard notation of non-prime intervals. For example, 11edo almost perfectly misses primes 3 and 5 present 22edo, which still allows them to cancel out for an accurate 5/3 and 15. 11edo's JI group might be 2.5/3.15.7.11 in standard notation, which is a subgroup of the erac group 2.x3.x5.7.11. This becomes even more important in edos like 23 or 29, where several low primes are critically inaccurate and representing all of the error cancelation in standard notation creates a very long JI group.		Eracs provide a more complete picture of error cancelation than the standard notation of non-prime intervals. For example, 11edo almost perfectly misses primes 3 and 5 present 22edo, which still allows them to cancel out for an accurate 5/3 and 15. 11edo's [[JI group]] might be 2.5/3.15.7.11 in standard notation, which is a subgroup of the erac group 2.x3.x5.7.11. This becomes even more important in edos like 23 or 29, where several low primes are critically inaccurate and representing all of the error cancelation in standard notation creates a very long JI group.

	Example erac groups for edos can be found in [[EDO#List of Edos]].		Example erac groups for edos can be found in [[EDO#List of Edos]].

Inthar at 05:36, 29 January 2026

2026-01-29T05:36:09Z

← Older revision		Revision as of 05:36, 29 January 2026
Line 2:		Line 2:
	'''Eracs''', short for error accidentals, are symbols that indicate how much a tempered interval is flat or sharp relative to others in a subgroup. They act as variables representing small pitch differences and have no set size. They are the standard notation for subgroups involving [[Straddle primes]].		'''Eracs''', short for error accidentals, are symbols that indicate how much a tempered interval is flat or sharp relative to others in a subgroup. They act as variables representing small pitch differences and have no set size. They are the standard notation for subgroups involving [[Straddle primes]].

	Eracs provide a more complete picture of error cancelation than the standard notation of non-prime intervals. For example, 11edo almost perfectly misses primes 3 and 5 present 22edo, which still allows them to cancel out for an accurate 5/3 and 15. 11edo's JI group might be 2.5/3.15.7.11 in standard notation, or 2.x3.x5.7.11 ~~in erac notation~~. This becomes even more important in edos like 23 or 29, where several low primes are critically inaccurate and representing all of the error cancelation in standard notation creates a very long JI group.		Eracs provide a more complete picture of error cancelation than the standard notation of non-prime intervals. For example, 11edo almost perfectly misses primes 3 and 5 present 22edo, which still allows them to cancel out for an accurate 5/3 and 15. 11edo's JI group might be 2.5/3.15.7.11 in standard notation, which is a subgroup of the erac group 2.x3.x5.7.11. This becomes even more important in edos like 23 or 29, where several low primes are critically inaccurate and representing all of the error cancelation in standard notation creates a very long JI group.

	Example erac groups for edos can be found in [[EDO#List of Edos]].		Example erac groups for edos can be found in [[EDO#List of Edos]].

Inthar at 05:33, 29 January 2026

2026-01-29T05:33:01Z

← Older revision		Revision as of 05:33, 29 January 2026
Line 2:		Line 2:
	'''Eracs''', short for error accidentals, are symbols that indicate how much a tempered interval is flat or sharp relative to others in a subgroup. They act as variables representing small pitch differences and have no set size. They are the standard notation for subgroups involving [[Straddle primes]].		'''Eracs''', short for error accidentals, are symbols that indicate how much a tempered interval is flat or sharp relative to others in a subgroup. They act as variables representing small pitch differences and have no set size. They are the standard notation for subgroups involving [[Straddle primes]].

	Eracs provide a more complete picture of error cancelation than the standard notation of non-prime intervals. For example, 11edo almost perfectly misses primes 3 and 5 present 22edo, which still allows them to cancel out for an accurate 5/3 and 15. 11edo's ~~subgroup~~ might be 2.5/3.15.7.11 in standard notation, or 2.x3.x5.7.11 in erac notation. This becomes even more important in edos like 23 or 29, where several low primes are critically inaccurate and representing all of the error cancelation in standard notation creates a very long ~~subgroup~~.		Eracs provide a more complete picture of error cancelation than the standard notation of non-prime intervals. For example, 11edo almost perfectly misses primes 3 and 5 present 22edo, which still allows them to cancel out for an accurate 5/3 and 15. 11edo's JI group might be 2.5/3.15.7.11 in standard notation, or 2.x3.x5.7.11 in erac notation. This becomes even more important in edos like 23 or 29, where several low primes are critically inaccurate and representing all of the error cancelation in standard notation creates a very long JI group.

	Example erac ~~subgroups~~ for edos can be found in [[EDO#List of Edos]].		Example erac groups for edos can be found in [[EDO#List of Edos]].

	== Symbols ==		== Symbols ==

Inthar at 01:05, 8 January 2026

2026-01-08T01:05:59Z

← Older revision		Revision as of 01:05, 8 January 2026
Line 1:		Line 1:
			{{Proposed}}
	'''Eracs''', short for error accidentals, are symbols that indicate how much a tempered interval is flat or sharp relative to others in a subgroup. They act as variables representing small pitch differences and have no set size. They are the standard notation for subgroups involving [[Straddle primes]].		'''Eracs''', short for error accidentals, are symbols that indicate how much a tempered interval is flat or sharp relative to others in a subgroup. They act as variables representing small pitch differences and have no set size. They are the standard notation for subgroups involving [[Straddle primes]].

2^67-1: /* Erac-derived temperaments */

2026-01-07T01:30:54Z

Erac-derived temperaments

← Older revision		Revision as of 01:30, 7 January 2026
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	** take the flat harmonic and take it to the power of how many eracs the sharp harmonic has		** take the flat harmonic and take it to the power of how many eracs the sharp harmonic has
	** take the sharp harmonic and take it to the power of how many eracs the flat harmonic has		** take the sharp harmonic and take it to the power of how many eracs the flat harmonic has
	** multiply them ~~togethertake~~ it to the power of how many steps there are in an EDO		** multiply them together
			** take it to the power of how many steps there are in an EDO
	** octave-reduce (if the interval is greater than 600c octave reduced, take the inverse)		** octave-reduce (if the interval is greater than 600c octave reduced, take the inverse)

	{{Cat\|Atypical ratios		{{Cat\|Atypical ratios
	Notation}}		Notation}}

2^67-1 at 01:39, 6 January 2026

2026-01-06T01:39:45Z

@@ Line 33: / Line 33: @@
 == Erac temperaments ==
 Temperament optimization algorithms can be built around eracs to create optimal error cancelation, such as [https://spoogly.website/tools/gto.html GTO]. Erac temperaments have the potential to replace exotemperaments by properly representing the large error in approximating certain primes, providing less misleading mappings with systematic accuracy.
 {{Cat|Atypical ratios
 Notation}}

Ground at 07:16, 29 December 2025

2025-12-29T07:16:35Z

← Older revision		Revision as of 07:16, 29 December 2025
Line 24:		Line 24:
	\|{ and }		\|{ and }
	\|Partial eracs, indicating error that may be ignored.		\|Partial eracs, indicating error that may be ignored.
			\|-
			\|~_
			\|Approximate, tempered equivalent. A widely accepted symbol used in this context to indicate that no eracs apply.
	\|}		\|}

Inthar: /* Erac Temperaments */

2025-12-25T04:13:25Z

Erac Temperaments

← Older revision		Revision as of 04:13, 25 December 2025
Line 28:		Line 28:
	Eracs are placed before their respective numbers by default (although they may be placed after as well) This is for readability and to remove ambiguity with the denominator, as eracs on the denominator have an inverse effect on the size of a tempered ratio. For example, >5/3 is sharp or 5/3, but 5/>3 is flat.		Eracs are placed before their respective numbers by default (although they may be placed after as well) This is for readability and to remove ambiguity with the denominator, as eracs on the denominator have an inverse effect on the size of a tempered ratio. For example, >5/3 is sharp or 5/3, but 5/>3 is flat.

	== Erac ~~Temperaments~~ ==		== Erac temperaments ==

	Temperament optimization algorithms can be built around eracs to create optimal error cancelation, such as [https://spoogly.website/tools/gto.html GTO]. Erac temperaments have the potential to replace exotemperaments by properly representing the large error in approximating certain primes, providing less misleading mappings with systematic accuracy.		Temperament optimization algorithms can be built around eracs to create optimal error cancelation, such as [https://spoogly.website/tools/gto.html GTO]. Erac temperaments have the potential to replace exotemperaments by properly representing the large error in approximating certain primes, providing less misleading mappings with systematic accuracy.

	{{Cat\|Atypical ratios		{{Cat\|Atypical ratios
	Notation}}		Notation}}