722edo - Revision history

ArrowHead294 at 12:45, 21 February 2025

2025-02-21T12:45:54Z

← Older revision		Revision as of 12:45, 21 February 2025
Line 4:		Line 4:
	722edo is a strong 2.7.19.23 subgroup tuning, with 179\722 being a semiconvergent to the log<sub>2</sub>(19/16). Despite having a strong approximation of 7, it is only consistent upwards to the 5-limit.		722edo is a strong 2.7.19.23 subgroup tuning, with 179\722 being a semiconvergent to the log<sub>2</sub>(19/16). Despite having a strong approximation of 7, it is only consistent upwards to the 5-limit.

	Using the 421\722 fifth, it supports a variant of fifth-stacked tuning that divides 38th harmonic into 9 parts, meaning that ~~C - D#~~ in this system is equal to [[19/16]], the otonal minor third. This creates a peculiar violation of Western theory which would require spelling this minor triad involving 19/16 as ~~C-D#-G~~ instead of ~~C-Eb-G~~. This can be realized as 355 & 722 2.17.19.23 temperament from a regular temperament theory ~~perspective - it~~ should be noted that the fifth is not mapped to [[3/2]] but is slightly flatter.		Using the 421\722 fifth, it supports a variant of fifth-stacked tuning that divides 38th harmonic into 9 parts, meaning that C−D♯ in this system is equal to [[19/16]], the otonal minor third. This creates a peculiar violation of Western theory which would require spelling this minor triad involving 19/16 as C–D♯–G instead of C–E♭–G. This can be realized as {{nowrap\|355 & 722}} 2.17.19.23 temperament from a regular temperament theory perspective—it should be noted that the fifth is not mapped to [[3/2]] but is slightly flatter.

	Aside from this, 722bc val tempers out the [[hemifamity comma]] and is a tuning for the [[undecental]] temperament. Since 722 is divisible by 19, the 722dg val is a tuning for the [[kalium]] temperament in the 19-limit.		Aside from this, the 722bc val tempers out the [[hemifamity comma]] and is a tuning for the [[undecental]] temperament. Since 722 is divisible by 19, the 722dg val is a tuning for the [[kalium]] temperament in the 19-limit.

	=== Odd harmonics ===		=== Odd harmonics ===

Francium: changed EDO intro to ED intro

2025-02-21T06:02:41Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:02, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|722~~}}		{{ED intro}}

	722edo is a strong 2.7.19.23 subgroup tuning, with 179\722 being a semiconvergent to the log<sub>2</sub>(19/16). Despite having a strong approximation of 7, it is only consistent upwards to the 5-limit.		722edo is a strong 2.7.19.23 subgroup tuning, with 179\722 being a semiconvergent to the log<sub>2</sub>(19/16). Despite having a strong approximation of 7, it is only consistent upwards to the 5-limit.

Eliora at 14:12, 14 May 2023

2023-05-14T14:12:27Z

← Older revision		Revision as of 14:12, 14 May 2023
Line 4:		Line 4:
	722edo is a strong 2.7.19.23 subgroup tuning, with 179\722 being a semiconvergent to the log<sub>2</sub>(19/16). Despite having a strong approximation of 7, it is only consistent upwards to the 5-limit.		722edo is a strong 2.7.19.23 subgroup tuning, with 179\722 being a semiconvergent to the log<sub>2</sub>(19/16). Despite having a strong approximation of 7, it is only consistent upwards to the 5-limit.

	Using the 421\722 fifth, it supports a variant of fifth-stacked tuning that divides 38th harmonic into 9 parts, meaning that C - D# in this system is equal to [[19/16]], the otonal minor third. This creates a peculiar violation of Western theory which would require spelling this minor triad involving 19/16 as C-D#-G instead of C-Eb-G. This can be realized as 355 & 722 2~~.3.5~~.17.19.23 temperament from a regular temperament theory perspective - it should be noted that the fifth is not mapped to [[3/2]] but is slightly flatter.		Using the 421\722 fifth, it supports a variant of fifth-stacked tuning that divides 38th harmonic into 9 parts, meaning that C - D# in this system is equal to [[19/16]], the otonal minor third. This creates a peculiar violation of Western theory which would require spelling this minor triad involving 19/16 as C-D#-G instead of C-Eb-G. This can be realized as 355 & 722 2.17.19.23 temperament from a regular temperament theory perspective - it should be noted that the fifth is not mapped to [[3/2]] but is slightly flatter.

	Aside from this, 722bc val tempers out the [[hemifamity comma]] and is a tuning for the [[undecental]] temperament. Since 722 is divisible by 19, the 722dg val is a tuning for the [[kalium]] temperament in the 19-limit.		Aside from this, 722bc val tempers out the [[hemifamity comma]] and is a tuning for the [[undecental]] temperament. Since 722 is divisible by 19, the 722dg val is a tuning for the [[kalium]] temperament in the 19-limit.

Eliora: slightly reword and elaborate

2023-05-09T12:04:21Z

slightly reword and elaborate

← Older revision		Revision as of 12:04, 9 May 2023
Line 4:		Line 4:
	722edo is a strong 2.7.19.23 subgroup tuning, with 179\722 being a semiconvergent to the log<sub>2</sub>(19/16). Despite having a strong approximation of 7, it is only consistent upwards to the 5-limit.		722edo is a strong 2.7.19.23 subgroup tuning, with 179\722 being a semiconvergent to the log<sub>2</sub>(19/16). Despite having a strong approximation of 7, it is only consistent upwards to the 5-limit.

	Using the 421\722 fifth, it supports a variant of fifth-stacked tuning that divides 38th harmonic into 9 parts, meaning that C - D# in this system is equal to [[19/16]], ~~creating~~ a peculiar violation of Western ~~harmony~~ which would require spelling ~~the~~ minor triad as C-D#-G instead of C-Eb-G.		Using the 421\722 fifth, it supports a variant of fifth-stacked tuning that divides 38th harmonic into 9 parts, meaning that C - D# in this system is equal to [[19/16]], the otonal minor third. This creates a peculiar violation of Western theory which would require spelling this minor triad involving 19/16 as C-D#-G instead of C-Eb-G. This can be realized as 355 & 722 2.3.5.17.19.23 temperament from a regular temperament theory perspective - it should be noted that the fifth is not mapped to [[3/2]] but is slightly flatter.

	Aside from this, 722bc val tempers out the [[hemifamity comma]] and is a tuning for the [[undecental]] temperament. Since 722 is divisible by 19, the 722dg val is a tuning for the [[kalium]] temperament in the 19-limit.		Aside from this, 722bc val tempers out the [[hemifamity comma]] and is a tuning for the [[undecental]] temperament. Since 722 is divisible by 19, the 722dg val is a tuning for the [[kalium]] temperament in the 19-limit.

Eliora: Created page with "{{Infobox ET}} {{EDO intro|722}} 722edo is a strong 2.7.19.23 subgroup tuning, with 179\722 being a semiconvergent to the log₂(19/16). Despite having a strong appr..."

2023-05-09T11:56:08Z

Created page with "{{Infobox ET}} {{EDO intro|722}} 722edo is a strong 2.7.19.23 subgroup tuning, with 179\722 being a semiconvergent to the log<sub>2</sub>(19/16). Despite having a strong appr..."

New page

{{Infobox ET}}
{{EDO intro|722}}

722edo is a strong 2.7.19.23 subgroup tuning, with 179\722 being a semiconvergent to the log<sub>2</sub>(19/16). Despite having a strong approximation of 7, it is only consistent upwards to the 5-limit.

Using the 421\722 fifth, it supports a variant of fifth-stacked tuning that divides 38th harmonic into 9 parts, meaning that C - D# in this system is equal to [[19/16]], creating a peculiar violation of Western harmony which would require spelling the minor triad as C-D#-G instead of C-Eb-G.

Aside from this, 722bc val tempers out the [[hemifamity comma]] and is a tuning for the [[undecental]] temperament. Since 722 is divisible by 19, the 722dg val is a tuning for the [[kalium]] temperament in the 19-limit.

=== Odd harmonics ===
{{harmonics in equal|722}}

=== Subsets and supersets ===
722edo has subset edos {{EDOs|1, 2, 19, 38, 361}}.

722edo - Revision history

ArrowHead294 at 12:45, 21 February 2025

Francium: changed EDO intro to ED intro

Eliora at 14:12, 14 May 2023

Eliora: slightly reword and elaborate

Eliora: Created page with "{{Infobox ET}} {{EDO intro|722}} 722edo is a strong 2.7.19.23 subgroup tuning, with 179\722 being a semiconvergent to the log2(19/16). Despite having a strong appr..."

Eliora: Created page with "{{Infobox ET}} {{EDO intro|722}} 722edo is a strong 2.7.19.23 subgroup tuning, with 179\722 being a semiconvergent to the log₂(19/16). Despite having a strong appr..."