Hemimean clan: Difference between revisions

Isra results from taking every other generator of [[septimal meantone]]. It is named after the Isrāʾ (''iss-RAH'') night journey in the Qur'an, because it is similar to [[luna]].  

Tutone is every other step of [[Meantone vs meanpop|undecimal meantone]].  

=== Deutone ===

{{See also| Chromatic pairs #Deutone }}

Deutone is every other step of [[meanpop]].  

[[Subgroup]]: 2.9.5.7.13

[[Comma list]]: 65/64, 81/80, 91/90

{{Mapping|legend=2| 1 0 -4 -13 10 | 0 1 2 5 -2 }}

{{Mapping|legend=3| 1 3/2 2 2 0 4 | 0 1/2 2 5 0 -2 }}

: [[gencom]]: [2 9/8; 65/64 81/80 91/90]

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 191.059

{{Optimal ET sequence|legend=1| 6, 7, 13, 19, 25e, 44de }}

[[Tp tuning #T2 tuning|RMS error]]: 2.003 cents

=== Leantone ===

{{See also| Chromatic pairs #Leantone }}

Leantone is every other step of [[meanenneadecal]].  

[[Subgroup]]: 2.9.5.7.11

[[Comma list]]: 45/44, 56/55, 81/80

{{Mapping|legend=2| 1 0 -4 -13 -6 | 0 1 2 5 3 }}

{{Mapping|legend=3| 1 3/2 2 2 3 | 0 1/2 2 5 3 }}

: [[gencom]]: [2 9/8; 45/44 56/55 81/80]

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 192.500

{{Optimal ET sequence|legend=1| 6, 7, 13, 19, 25, 31, 56, 81 }}

[[Tp tuning #T2 tuning|RMS error]]: 3.882 cents