Pleiades Equal Temperament

It is still equal temperament but attempts to make all octaves sound correct to our brain rather than being integer multiples of frequency.


Historically temperament means tuning a centre octave ie 12 notes.


The tuning of the rest of the keyboard is dictated by the instrument, by listening to beats and tuning. Or by listening to our brain for satisfactory octaves.


The 2 do not nessasarily coincide. They usually coincide to state of the art instruments that took centuries of evolution, like a good Steinway or Pleyel piano etc.


For example if a note has a frequency of 220Hz, 440Hz does not sound a perfect octave to our brain . It sounds a bit flat. As frequency rises the effect increases. 880Hz sounds an even worse double octave of 220Hz.


For the same reason individual notes may or may not sound satisfying to our brain. A string that has a fundamental frequency of 220Hz also has a mode of vibration near 440Hz, 880Hz, what are called overtones or harmonics.


But harmony means to our brain not to our computer. For example 441Hz and 882.3Hz may be harmony to our brain.


On world class instruments the tension of the string is arranged to be so large that the correct to our brain "inharmonisity" is achieved. Or better stated the correct harmony to our brain is achieved.


Then when tuning octaves they sound correct and without beats too.


And the Pythagoras (uncompleted in frequency circle of faiths) can be solved as the frequency of that large interval is stretched by our brain requirement.


An idea by eBay user light_bearer_11 is to have a plugin that does the conversion of equal temperament to the Pleiades equal temperament.


So that for example midi notes can be stretched by the correct amount.


Or a midi to midi file converter etc.


Great musicians on our planet get away with this problem by using their ears and brain.


For example if we try to add a very high pitch part on a synthesizer that uses standard equal,temperament it sounds ridiculously low at those high notes. At very high notes our brain may perceive a whole semitone flat. This is very easy to demonstrate. Just play a very low C and then a very high C. The very high C sounds a very high B!


They get away with it by using the master tuning knob on the synthesizer that adds the high part. For example Vangelis, Air, Brian Eno etc may do this by turning the tuning knob on a Solina String Ensemble clockwise until the notes sound correct to their brain.


Or a rock band will tune the electric bass much lower in frequency while listening to an organ until it sounds correct to the brain.


The same for a good quality orchestra and conductor when they are using their ear and brain.


They may not know they are further decreasing the low frequencies and further increasing the high ones.


But who cares.


It is their brain and the brain of even untrained listener's that cares.


And it is the end result that matters.


Acknowledgment to the piano tuner Alber Ketenzian who took time to explain all this. References:


Sound and Hearing - SS Stevens


Pleiades tuning for DX7ii and Korg Triton - Euroelectron blogspot


Octave Strech - Ernst Terhardt