7th-octave temperaments

7th octave temperament occurs through temperament merging any two edos whose greatest common divisor is 7. A comma that frequently appears in 7th-octave temps is akjaysma, which sets 105/64 to be equal to 5\7.

Temperaments discussed elsewhere include:

• Septant → Schismatic family
• Brahmagupta → Ragismic microtemperaments
• Absurdity → Syntonic chromatic equivalence continuum

Nitrogen

Described as 140 & 1407 temperament in the 7-limit, named after the 7th element for being period-7 and also because 140 and 1407 only contain numbers 7 and 14, atomic number and atomic weight of nitrogen respectively. On top of this connection to the number 7, it also reaches 7th harmonic 7 generators down.

Subgroup: 2.3.5.7

Comma list: 3955078125/3954653486, 140737488355328/140710042265625

Mapping: 7 10 17 20, 0 22 -15 -7

Mapping generators: ~1157625/1048576, ~1029/1024

Optimal tuning (CTE): ~1157625/1048576 = 1\7, ~1029/1024 = 8.531

Vals: 140, 1407, 1547, ...