There is no correct frequency for E5?

This applies for any note. For example C6, D7, A2.


The right frequency for example for E6 will depend on the key the music is written. It may be different if the bass is C helping create a C major chord. It may be different if the key is C sharp minor (Moonlight sonata played with an orchestra for example) and the bass is C sharp helping create a C# major chord. It will be different if the key is F major and the bass is F helping to create a F major 7th chord, when the bass is A helping create an A minor chord.


Why is this so?


Because a particular bass note from a particular bass instrument, for example the string of a double bass etc will create certain overtones (modes of vibration from a certain string). A good orchestra might match the particular overtones of a bass instrument to what a high flute is paying at that particular moment. Perhaps the best musicians and conductors find the best compromise in real time as music unfolds from all instruments in real time.


There are other reasons, for example the intensity of a particular note. Pitch does not only depend on frequency but on intensity too.


It seems a complicated subject but in reality all that is needed is the musicians making sure that it sounds pleasing and correct to the listener's brain. Good musicians are listeners of themselves and the room when they play.


What do electronic tuners have to do with all this.


Nothing. They are very good at measuring engineering octaves that have almost nothing to do with human brain octave or other pitch perception.


See also nearby euroelectron posts:


Reference:


Ear brain octave vs engineering octave - euroelectron


Bibliography:


Musical Acoustics - Donald Hall - Wadsworth