The reason you perceive four different "E" notes between the high and low E strings on a guitar, despite them being only two octaves apart, is due to the phenomenon of pitch. In music theory, pitch refers to the perceived frequency of a sound. While the fundamental frequency of each E note on the guitar is indeed related to the same fundamental frequency, other factors contribute to the perception of different pitches.
When you play an E note on the guitar, you not only hear the fundamental frequency but also a series of harmonics or overtones. Harmonics are multiples of the fundamental frequency that vibrate together to create the overall sound. Each harmonic has a different amplitude or strength, which gives it a unique timbre or tonal quality.
The specific combination of harmonics and their relative amplitudes in each string determines the overall sound you hear when playing an E note. Although the fundamental frequency is the same, the presence and distribution of harmonics make each string sound slightly different, resulting in distinct pitches.
Additionally, the physical characteristics of the strings themselves contribute to the variation in pitch. Different gauges, materials, tension, and lengths of the strings can affect their harmonic content and, consequently, the perceived pitch.
Moreover, when you play the same note on different strings, the string length and tension also come into play. Strings with different lengths and tensions produce different harmonic series, further contributing to the variation in pitch.
Therefore, even though the high and low E strings on a guitar are two octaves apart in terms of their fundamental frequencies, the combination of harmonic content, string characteristics, and playing technique gives rise to the perception of different pitches for each E note.