722edo: Difference between revisions

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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 ===

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 edo 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 &amp; 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 ===