639edo: Difference between revisions

Theory: + second harmonics table
m Theory: - typos
 
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639edo is [[consistency|distinctly consistent]] in the [[17-odd-limit]]. It has a sharp tendency, with [[harmonic]]s 3 to 17 all tuned sharp. The 639h [[val]] gives a reasonable approximation of [[19/1|harmonic 19]], in which the edo is almost consistent up to the [[25-odd-limit]], with the exception of [[19/16]] and [[25/16]] themselves and their [[octave complement]]s.  
639edo is [[consistency|distinctly consistent]] in the [[17-odd-limit]]. It has a sharp tendency, with [[harmonic]]s 3 to 17 all tuned sharp. The 639h [[val]] gives a reasonable approximation of [[19/1|harmonic 19]], in which the edo is almost consistent up to the [[25-odd-limit]], with the exception of [[19/16]] and [[25/16]] themselves and their [[octave complement]]s.  


Using this val, the equal temperament [[tempering out|tempers out]] {{monzo| 1 27 -18 }} ([[ennealimma]]) and {{monzo| 55 -1 -23 }} ([[counterwürschmidt comma]]) in the [[5-limit]]; [[2401/2400]] and [[4375/4374]] in the [[7-limit]]]; [[5632/5625]] and [[19712/19683]] in the [[11-limit]]; [[2080/2079]] and [[4459/4455]] in the [[13-limit]]; [[1156/1155]], [[2058/2057]], and [[2601/2600]] in the [[17-limit]]; [[1216/1215]], [[1445/1444]], [[1540/1539]], [[2376/2375]], and [[2926/2925]] in the [[19-limit]]; and [[1288/1287]], [[1496/1495]], among others in the [[23-limit]]. It [[support]]s [[ennealimmal]] and its 13-limit extension enneabiotic.  
Using this val, the equal temperament [[tempering out|tempers out]] {{monzo| 1 27 -18 }} ([[ennealimma]]) and {{monzo| 55 -1 -23 }} ([[counterwürschmidt comma]]) in the [[5-limit]]; [[2401/2400]] and [[4375/4374]] in the [[7-limit]]; [[5632/5625]] and [[19712/19683]] in the [[11-limit]]; [[2080/2079]] and [[4459/4455]] in the [[13-limit]]; [[1156/1155]], [[2058/2057]], and [[2601/2600]] in the [[17-limit]]; [[1216/1215]], [[1445/1444]], [[1540/1539]], [[2376/2375]], and [[2926/2925]] in the [[19-limit]]; and [[1288/1287]], [[1496/1495]] among others in the [[23-limit]]. It [[support]]s [[ennealimmal]] and its 13-limit extension enneabiotic.  


=== Prime harmonics ===
=== Prime harmonics ===