518edo - Revision history

Eliora: oops, I meant 4459/4455, not 4496/4495. Thats the right one

2026-07-30T23:30:58Z

oops, I meant 4459/4455, not 4496/4495. Thats the right one

← Older revision		Revision as of 23:30, 30 July 2026
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	In the 5-limit, it tempers out the [[counterschisma]] ({{monzo\| -69 45 -1 }}), and is a strong tuning for the [[counterschismic]] temperament hence. In the 7-limit, it tempers out [[235298/234375]], [[420175/419904]], 1959552/1953125, and 5250987/5242880 (mitonisma). In the 11-limit, it tempers out [[5632/5625]], [[9801/9800]], as well as being a tuning for [[loki]].		In the 5-limit, it tempers out the [[counterschisma]] ({{monzo\| -69 45 -1 }}), and is a strong tuning for the [[counterschismic]] temperament hence. In the 7-limit, it tempers out [[235298/234375]], [[420175/419904]], 1959552/1953125, and 5250987/5242880 (mitonisma). In the 11-limit, it tempers out [[5632/5625]], [[9801/9800]], as well as being a tuning for [[loki]].

	In the 13-limit, 518edo tempers out [[1001/1000]], [[4096/4095]], and it is a strong tuning for the 14th-octave [[silicon]] temperament.		In the 13-limit, 518edo tempers out [[1001/1000]], [[4096/4095]], [[4459/4455]], and it is a strong tuning for the 14th-octave [[silicon]] temperament.

	The 518c val, {{val\| 518 821 '''1202''' 1454 1792 }}, though less accurate, is of theoretical interest as well because it tunes [[quintilipyth]] and [[compass]].		The 518c val, {{val\| 518 821 '''1202''' 1454 1792 }}, though less accurate, is of theoretical interest as well because it tunes [[quintilipyth]] and [[compass]].

FloraC: Correct math (typo?). Misc. cleanup

2026-07-30T09:39:56Z

Correct math (typo?). Misc. cleanup

← Older revision		Revision as of 09:39, 30 July 2026
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	{{ED intro}}		{{ED intro}}

	518edo is [[Consistency limit\|consistent]] in the [[15-odd-limit]] and is an exceptionally strong 2.3.11 subgroup tuning, where it tempers out the [[frameshift comma]] as well as the [[37-11-comma]].		518edo is [[Consistency limit\|consistent]] in the [[15-odd-limit]] and is an exceptionally strong [[2.3.11 subgroup\|2.3.11-subgroup]] tuning, where it tempers out the [[frameshift comma]] as well as the [[37-11-comma]].

	In the 5-limit, it tempers out the [[counterschisma]], {{monzo\| -69 45 -1 }}, and is a strong tuning for the [[counterschismic]] temperament hence. In the 7-limit, it tempers out ~~1959552/1953125,~~ [[235298/234375]], [[420175/419904]] and 5250987/5242880 (mitonisma). In the 11-limit, it tempers out [[5632/5625]], [[9801/9800]], as well as being a tuning for [[loki]].		In the 5-limit, it tempers out the [[counterschisma]] ({{monzo\| -69 45 -1 }}), and is a strong tuning for the [[counterschismic]] temperament hence. In the 7-limit, it tempers out [[235298/234375]], [[420175/419904]], 1959552/1953125, and 5250987/5242880 (mitonisma). In the 11-limit, it tempers out [[5632/5625]], [[9801/9800]], as well as being a tuning for [[loki]].

	In the 13-limit, 518edo tempers out [[1001/1000]], [[4096/4095]]~~, 4496/4495~~, and it is a strong tuning for the 14th-octave [[silicon]] temperament.		In the 13-limit, 518edo tempers out [[1001/1000]], [[4096/4095]], and it is a strong tuning for the 14th-octave [[silicon]] temperament.

	The 518c val, {{val\| 518 821 '''1202''' 1454 1792 }}, though less accurate, is of theoretical interest as well because it tunes [[quintilipyth]] and [[compass]].		The 518c val, {{val\| 518 821 '''1202''' 1454 1792 }}, though less accurate, is of theoretical interest as well because it tunes [[quintilipyth]] and [[compass]].

	=== Prime harmonics ===		=== Prime harmonics ===

	{{Harmonics in equal\|518}}		{{Harmonics in equal\|518}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
			Since 518 factors into primes as {{nowrap\| 2 × 7 × 37 }}, 518edo has subsets edos {{EDOs\| 2, 7, 14, 37, 74, 259 }}.
	Since 518 factors as {{~~Factorization~~\|~~518~~}}, 518edo has subsets {{EDOs\|1, 2, 7, 14, 37, 74, 259}}.

Eliora at 21:34, 29 July 2026

2026-07-29T21:34:33Z

← Older revision		Revision as of 21:34, 29 July 2026
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	{{ED intro}}		{{ED intro}}

	518edo is [[Consistency limit\|consistent]] in the [[15-odd-limit]] and is an exceptionally strong 2.3.11 subgroup tuning, where it tempers out the [[frameshift comma]].		518edo is [[Consistency limit\|consistent]] in the [[15-odd-limit]] and is an exceptionally strong 2.3.11 subgroup tuning, where it tempers out the [[frameshift comma]] as well as the [[37-11-comma]].

	In the 5-limit, it tempers out the [[counterschisma]], {{monzo\| -69 45 -1 }}, and is a strong tuning for the [[counterschismic]] temperament hence. In the 7-limit, it tempers out 1959552/1953125, [[235298/234375]], [[420175/419904]] and 5250987/5242880 (mitonisma). In the 11-limit, it tempers out [[5632/5625]], [[9801/9800]], as well as being a tuning for [[loki]].		In the 5-limit, it tempers out the [[counterschisma]], {{monzo\| -69 45 -1 }}, and is a strong tuning for the [[counterschismic]] temperament hence. In the 7-limit, it tempers out 1959552/1953125, [[235298/234375]], [[420175/419904]] and 5250987/5242880 (mitonisma). In the 11-limit, it tempers out [[5632/5625]], [[9801/9800]], as well as being a tuning for [[loki]].

Eliora: Expand, use information from lower limits not the idiosyncratic 296 & 518

2026-07-29T21:34:08Z

Expand, use information from lower limits not the idiosyncratic 296 & 518

@@ Line 2: / Line 2: @@
 {{ED intro}}
-This tuning may be of interest to those who compose in larger edos as it is [[Consistency limit|consistent]] in the [[15-odd-limit]] and supports the [[Rank-2 temperament|rank-2]] [[74th-octave temperaments|74th-octave]] [[296edo|296]] & 518 temperament. This means it tempers out commas including [[9801/9800]] and 5250987/5242880, the [[Mitonisma|mitonisma]].
+edo is [[Consistency limit|consistent]] in the [[15-odd-limit]] and is an exceptionally strong 2.3.11 subgroup tuning, where it tempers out the [[frameshift comma]].
 {{Harmonics in equal|518}}

Tristanbay: Added page for 518edo

2025-06-26T03:41:41Z

Added page for 518edo

New page

{{Infobox ET}}
{{ED intro}}

This tuning may be of interest to those who compose in larger edos as it is [[Consistency limit|consistent]] in the [[15-odd-limit]] and supports the [[Rank-2 temperament|rank-2]] [[74th-octave temperaments|74th-octave]] [[296edo|296]] & 518 temperament. This means it tempers out commas including [[9801/9800]] and 5250987/5242880, the [[Mitonisma|mitonisma]].
{{Harmonics in equal|518}}