7th-octave temperaments

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

Fractional-octave temperaments

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← 6th-octave • 7th-octave • 8th-octave →

A 7th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 7. The most notable 7th-octave family is the whitewood family – tempering out 2187/2048 and associating 4\7 to 3/2.

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 → Porwell temperaments

Nitrogen

Nitrogen may be described as the 140 & 1407 temperament in the 7-limit. It was named after the 7th element for having a 7th-octave period 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 the 7th harmonic 7 generators down.

Subgroup: 2.3.5.7

Comma list: 3955078125/3954653486, [47 -7 -7 -7⟩

Mapping: [⟨7 10 17 20], ⟨0 22 -15 -7]]

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

Optimal tunings:

• WE: ~1157625/1048576 = 171.4278 ¢, ~1029/1024 = 8.5308 ¢

error map: ⟨-0.005 +0.001 -0.002 +0.015]

• CWE: ~1157625/1048576 = 171.4286 ¢, ~1029/1024 = 8.5308 ¢

error map: ⟨0.000 +0.008 +0.010 +0.030]

Optimal ET sequence: 140, 847, 987, 1127, 1267, 1407, 1547, 2954

Badness (Sintel): 1.50