Single-pitch tuning: Difference between revisions

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Degeneracy
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{{Infobox ET|0edo}}
{{Infobox ET|0edo}}


Single-pitch tuning can be specified as '''0 equal divisions of the octave''' ('''0edo'''), or 0 equal divisions of anything.  
Single-pitch tuning can be specified as '''0 equal divisions of the octave''' ('''0edo'''), or 0 equal divisions of any finite interval.  


The way to approach the idea of 0edo that leads to single-pitch tuning is to see what happens as ''n'' gets smaller in ''n''-edo. At 1-edo you have one note per octave. At 0.5-edo you have 1/0.5 which is one note every two octaves. As ''n'' gets smaller, steps become sparser, and in the limit, the steps go to infinity and only one pitch is left. It is thus a degenerate case.  
The way to approach the idea of 0edo that leads to single-pitch tuning is to see what happens as ''n'' gets smaller in ''n''-edo. At 1-edo you have one note per octave. At 0.5-edo you have 1/0.5 which is one note every two octaves. As ''n'' gets smaller, steps become sparser, and in the limit, the steps go to infinity and only one pitch is left. It is thus a degenerate case.