696edo - Revision history

FloraC at 06:45, 12 October 2025

2025-10-12T06:45:34Z

← Older revision		Revision as of 06:45, 12 October 2025
Line 2:		Line 2:
	{{ED intro}}		{{ED intro}}

	696edo is a strong 7-limit tuning, but unfortunately it is consistent only up to the [[9-odd-limit]]. In the 5-limit, it tempers out the schisma, and in the 7-limit, the landscape comma. It ~~supports~~ the [[magnesium]] temperament which divides the octave in 12, as well as [[chromium]] temperament that divides it in 24.		== Theory ==
			696edo is a strong [[7-limit]] tuning, but unfortunately it is [[consistent]] only up to the [[9-odd-limit]]. In the [[5-limit]], it tempers out the [[schisma]], and in the 7-limit, the [[landscape comma]]. It [[support]]s the [[magnesium]] temperament which divides the octave in 12, as well as [[chromium]] temperament that divides it in 24.

	Nonetheless despite inconsistency, it is a valuable xenharmonic system in higher limits. It provides the [[optimal patent val]] for the [[octant]] temperament in the 13-limit, even if its approximation of 13 is almost half a step off. Likewise, 696edo tunes [[altierran]] and [[house]] temperaments in the 11-limit. In the higher limits, it may be used as a 2.3.5.7.17.31 subgroup tuning.		Nonetheless despite inconsistency, it is a valuable xenharmonic system in higher limits. It provides the [[optimal patent val]] for the [[octant]] temperament in the 13-limit, even if its approximation of 13 is almost half a step off. Likewise, 696edo tunes [[altierran]] and [[house]] temperaments in the 11-limit. In the higher limits, it may be used as a 2.3.5.7.17.31 subgroup tuning.
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	=== Subsets and supersets ===		=== Subsets and supersets ===
			Since 696 factors as {{nowrap\| 2<sup>3</sup> × 3 × 29 }}, 696edo has subset edos {{EDOs\| 2, 3, 4, 6, 8, 12, 24, 29, 58, 87, 116, 174, 232, 348 }}.
	Since 696 factors as {{~~Factorization~~\|~~696~~}}, 696edo has subset edos {{EDOs\|1, 2, 3, 4, 6, 8, 12, 24, 29, 58, 87, 116, 174, 232, 348}}.

	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \|[[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal		! rowspan="2" \| Optimal<br>8ve stretch (¢)
	8ve stretch (¢)		! colspan="2" \| Tuning error
	! colspan="2" \|Tuning error
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.3		\| 2.3
	\|{{~~monzo~~\|-1103 696}}		\| {{Monzo\| -1103 696 }}
	\|{{~~mapping~~\|696 1103}}		\| {{Mapping\| 696 1103 }}
	\|0.072829		\| 0.072829
	\|0.073		\| 0.073
	\|4.22		\| 4.22
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|32805/32768, {{monzo\|52 80 -77}}		\| 32805/32768, {{monzo\| 52 80 -77 }}
	\|{{~~mapping~~\|696 1103 1616}}		\| {{Mapping\| 696 1103 1616 }}
	\|0.060798		\| 0.060798
	\|0.064		\| 0.064
	\|3.71		\| 3.71
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|32805/32768, 250047/250000, {{monzo\|22 10 -3 -11}}		\| 32805/32768, 250047/250000, {{monzo\| 22 10 -3 -11 }}
	\|{{~~mapping~~\|696 1103 1616 1954}}		\| {{Mapping\| 696 1103 1616 1954 }}
	\|0.072061		\| 0.072061
	\|0.035		\| 0.035
	\|2.06		\| 2.06
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|9801/9800, 32805/32768, 46656/46585, 250047/250000		\| 9801/9800, 32805/32768, 46656/46585, 250047/250000
	\|{{~~mapping~~\|696 1103 1616 1954 2408}}		\| {{Mapping\| 696 1103 1616 1954 2408 }}
	\|0.004896		\| 0.004896
	\|0.089		\| 0.089
	\|5.15		\| 5.15
	\|-		\|-
	\|2.3.5.7.11.13		\| 2.3.5.7.11.13
	\|729/728, 1575/1573, 4096/4095, 67392/67375, 250047/250000		\| 729/728, 1575/1573, 4096/4095, 67392/67375, 250047/250000
	\|{{~~mapping~~\|696 1103 1616 1954 2408 2576}}		\| {{Mapping\| 696 1103 1616 1954 2408 2576 }}
	\| -0.034283		\| -0.034283
	\|0.119		\| 0.119
	\|6.92		\| 6.92
	\|}		\|}

Eliora: /* Regular temperament properties */

2025-10-11T23:55:35Z

Regular temperament properties

← Older revision		Revision as of 23:55, 11 October 2025
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	\|-		\|-
	\|2.3.5		\|2.3.5
	\|32805/32768, 52 80 -77		\|32805/32768, {{monzo\|52 80 -77}}
	\|{{mapping\|696 1103 1616}}		\|{{mapping\|696 1103 1616}}
	\|0.060798		\|0.060798
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	\|-		\|-
	\|2.3.5.7		\|2.3.5.7
	\|32805/32768, 250047/250000, 22 10 -3 -11		\|32805/32768, 250047/250000, {{monzo\|22 10 -3 -11}}
	\|{{mapping\|696 1103 1616 1954}}		\|{{mapping\|696 1103 1616 1954}}
	\|0.072061		\|0.072061

Eliora at 23:55, 11 October 2025

2025-10-11T23:55:05Z

@@ Line 2: / Line 2: @@
 {{ED intro}}
-edo is a strong 7-limit tuning, but unfortunately it is consistent only up to the [[9-odd-limit]]. In the higher limits, it may be used as a 2.3.5.7.17.31 subgroup tuning. In the 5-limit, it supports the [[magnesium]] temperament which divides the octave in 12, as well as [[chromium]] temperament that divides it in 24.
+edo is a strong 7-limit tuning, but unfortunately it is consistent only up to the [[9-odd-limit]]. In the 5-limit, it tempers out the schisma, and in the 7-limit, the landscape comma. It supports the [[magnesium]] temperament which divides the octave in 12, as well as [[chromium]] temperament that divides it in 24.
-Nonetheless despite inconsistency, it is a valuable xenharmonic system. It provides the [[optimal patent val]] for the [[octant]] temperament in the 13-limit, even if its approximation of 13 is almost half a step off. Likewise, 696edo tunes [[altierran]] and [[house]] temperaments in the 11-limit.
+Nonetheless despite inconsistency, it is a valuable xenharmonic system in higher limits. It provides the [[optimal patent val]] for the [[octant]] temperament in the 13-limit, even if its approximation of 13 is almost half a step off. Likewise, 696edo tunes [[altierran]] and [[house]] temperaments in the 11-limit. In the higher limits, it may be used as a 2.3.5.7.17.31 subgroup tuning.
 The 696cc val is also very close to the [[POTE]] tuning for the [[witcher]] temperament, while 696f tunes [[semiterm]] and the inaccurate 696d tunes [[pontic]].
@@ Line 10: / Line 10: @@
 === Prime harmonics ===
 {{Harmonics in equal|696}}

Ganaram inukshuk at 08:33, 17 March 2025

2025-03-17T08:33:48Z

← Older revision		Revision as of 08:33, 17 March 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|696~~}}		{{ED intro}}

	696edo is a strong 7-limit tuning, but unfortunately it is consistent only up to the [[9-odd-limit]]. In the higher limits, it may be used as a 2.3.5.7.17.31 subgroup tuning. In the 5-limit, it supports the [[magnesium]] temperament which divides the octave in 12, as well as [[chromium]] temperament that divides it in 24.		696edo is a strong 7-limit tuning, but unfortunately it is consistent only up to the [[9-odd-limit]]. In the higher limits, it may be used as a 2.3.5.7.17.31 subgroup tuning. In the 5-limit, it supports the [[magnesium]] temperament which divides the octave in 12, as well as [[chromium]] temperament that divides it in 24.

Eliora: Created page with "{{Infobox ET}} {{EDO intro|696}} 696edo is a strong 7-limit tuning, but unfortunately it is consistent only up to the 9-odd-limit. In the higher limits, it may be used as..."

2025-03-14T02:06:39Z

Created page with "{{Infobox ET}} {{EDO intro|696}} 696edo is a strong 7-limit tuning, but unfortunately it is consistent only up to the 9-odd-limit. In the higher limits, it may be used as..."

New page

{{Infobox ET}}
{{EDO intro|696}}

696edo is a strong 7-limit tuning, but unfortunately it is consistent only up to the [[9-odd-limit]]. In the higher limits, it may be used as a 2.3.5.7.17.31 subgroup tuning. In the 5-limit, it supports the [[magnesium]] temperament which divides the octave in 12, as well as [[chromium]] temperament that divides it in 24.

Nonetheless despite inconsistency, it is a valuable xenharmonic system. It provides the [[optimal patent val]] for the [[octant]] temperament in the 13-limit, even if its approximation of 13 is almost half a step off. Likewise, 696edo tunes [[altierran]] and [[house]] temperaments in the 11-limit.

The 696cc val is also very close to the [[POTE]] tuning for the [[witcher]] temperament, while 696f tunes [[semiterm]] and the inaccurate 696d tunes [[pontic]].

=== Prime harmonics ===
{{Harmonics in equal|696}}