The six symmetries of music
- The six symmetries of music
The six symmetries of music refers to a set of transformations that can be applied to music while leaving a fundamental essence of the music unchanged. The six symmetries are: pitch translation invariance, time scaling invariance, octave translation invariance, time translation invariance, amplitude scaling invariance, and pitch reflection invariance.
Pitch translation invariance
When the key is changed the tune remains the same
Time scaling invariance
When the tempo is changed the rhythm remains the same
Octave translation invariance
Similar to Pitch Translation Invariance however it can be applied to more things, whole chords can be moved up or down an octave without affecting the musical "quality", for example.
Time translation invariance
Not specific to just music this refers to the fact that music is the same today as it was yesterday.
Amplitude scaling invariance
Music remains the same no matter what volume it is played. This isn't quite true as loudness or quietness may effect the emotional impact of a piece. However most music is unaffected by volume changes.
Pitch reflection invariance
"This applies specifically to the consonance relation between notes. For example, the degree of consonance between A and C is the same as the degree of consonance between C and A. This symmetry does not imply that music can be played "upside down", no doubt because there are aspects of melody perception that are more than just a function of consonance relationships between notes. However, there is an apparent "upside-downness" in the preferred choices of home chord in the diatonic scale (consisting of the notes A, B, C, D, E, F and G). The two preferred choices are A minor and C major, which are indeed mirror images of each other within the scale, reflected about the note D." [Philip Dorrell. The 6 Symmetries of Music. 26 August 2005. http://www.1729.com/lists/SymmetriesOfMusic.html ]
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