The Riemann zeta function and tuning: Difference between revisions

Line 16:

'''Zeta record edo:''' An equal tuning that sets some kind of record in regards to the zeta function compared to all smaller equal tunings.

'''Zeta peak:''' A zeta record equal tuning, evaluated by the absolute "goodness" of the edo according to the zeta function. This is a tuning which is closer to JI than any previous tuning, and is usually an EDO with compressed or stretched octaves.

'''Zeta record peak:''' A zeta record equal tuning, evaluated by the absolute "goodness" of the edo according to the zeta function. This is a tuning which is closer to JI than any previous tuning, and is usually an EDO with compressed or stretched octaves.

'''Zeta ~~peak~~ integer:''' A zeta record edo by absolute "goodness", when compared only to other edos (i.e. ignoring nonoctave tunings and stretched/compressed octaves).

'''Zeta record integer:''' A zeta record edo by absolute "goodness", when compared only to other edos (i.e. ignoring nonoctave tunings and stretched/compressed octaves).

'''Zero:''' A point where the Riemann zeta function is equal to zero, such as ~2.759edo, representing an equal tuning that does not represent JI much at all. EDOs close to zeroes are called zeta valley EDOs.

'''Zero:''' A point where the Riemann zeta function is equal to zero, such as ~2.759edo, representing an equal tuning that does not represent JI much at all. EDOs close to zeroes are called zeta valley EDOs; all known zeroes are on the "critical line" used to obtain tuning information.

'''Zeta gap:''' A zeta record edo by the size of the gap between its surrounding zeroes, adjusted for the fact that zeroes generally become more dense with larger inputs.

'''Zeta record gap:''' A zeta record edo by the size of the gap between its surrounding zeroes, adjusted for the fact that zeroes generally become more dense with larger inputs.

'''Zeta integral:''' A zeta record edo by the size of the area enclosed by the shape of the function between the edo's surrounding zeroes.

'''Zeta record integral:''' A zeta record edo by the size of the area enclosed by the shape of the function between the edo's surrounding zeroes.

== Quick info: zeta peak edos ==

@@ Line 16: / Line 16: @@
 '''Zeta record edo:''' An equal tuning that sets some kind of record in regards to the zeta function compared to all smaller equal tunings.
-'''Zeta peak:''' A zeta record equal tuning, evaluated by the absolute "goodness" of the edo according to the zeta function. This is a tuning which is closer to JI than any previous tuning, and is usually an EDO with compressed or stretched octaves.
+'''Zeta record peak:''' A zeta record equal tuning, evaluated by the absolute "goodness" of the edo according to the zeta function. This is a tuning which is closer to JI than any previous tuning, and is usually an EDO with compressed or stretched octaves.
-'''Zeta peak integer:''' A zeta record edo by absolute "goodness", when compared only to other edos (i.e. ignoring nonoctave tunings and stretched/compressed octaves).
+'''Zeta record integer:''' A zeta record edo by absolute "goodness", when compared only to other edos (i.e. ignoring nonoctave tunings and stretched/compressed octaves).
-'''Zero:''' A point where the Riemann zeta function is equal to zero, such as ~2.759edo, representing an equal tuning that does not represent JI much at all. EDOs close to zeroes are called zeta valley EDOs.
+'''Zero:''' A point where the Riemann zeta function is equal to zero, such as ~2.759edo, representing an equal tuning that does not represent JI much at all. EDOs close to zeroes are called zeta valley EDOs; all known zeroes are on the "critical line" used to obtain tuning information.
-'''Zeta gap:''' A zeta record edo by the size of the gap between its surrounding zeroes, adjusted for the fact that zeroes generally become more dense with larger inputs.
+'''Zeta record gap:''' A zeta record edo by the size of the gap between its surrounding zeroes, adjusted for the fact that zeroes generally become more dense with larger inputs.
-'''Zeta integral:''' A zeta record edo by the size of the area enclosed by the shape of the function between the edo's surrounding zeroes.
+'''Zeta record integral:''' A zeta record edo by the size of the area enclosed by the shape of the function between the edo's surrounding zeroes.
 == Quick info: zeta peak edos ==