Enharmonic difference and Pythagorean just intonation

[JustIntonation]

Hi all,

I made a few videos demonstrating enharmonic difference (as opposed to enharmonic equivalence) and Pythagorean tuning and thought it would be nice to share them here.

Enharmonic difference:

Here you can hear the difference between an Ab and a G#, while both are tuned at the same pitch height (are the same key) in 12-tone equal temperament, they are actually two completely different tones and this is reflected in the above demonstration (where the Pythgorean version is in tune, and the others are "colorings")
Sorry for the bad piano timbre though.

And here a video with a good piano timbre playing a piece by Fauré in Pythagorean just intonation:

The interesting thing is that if you listen closely you can hear the "function" of intervals reflected in the tuning much more so than with standard 12-tone equal temperament.
The high leading tones for instance have more audible tension and really want to resolve. And the whole piece becomes more dynamic, colorful and expressive.
And another interesting thing which is audible here is that at certain points one chord uses an A# and the chord right after a Bb, here you can hear the change in tuning (also known as a comma shift, similar to the enharmonic difference demo video). This occurs at 55 seconds and 3min50sec.
Score is here: http://imslp.org/wiki/Special:ImagefromIndex/00529

And here 2 older videos that demonstrate the difference between 1/4 comma meantone (the old tuning system of the Renaissance and Baroque periods), 12-tone equal temperament (current western fixed pitch instrument tuning system), Pythagorean just intonation (pure tuning according to the function of intervals), and 17-tone equal temperament (a tuning system with extra wide fifths).


Though I made these demos with a not so great sampled piano so be careful not to confuse timbre qualities with tuning. Some tunings will tend to hide / modify the timbre making many thing sound "sweeter", like 1/4 comma meantone, while Pythagorean will not color the timbre in this way. Try not to listen only to this effect tuning has on timbre in chords, but also to how well the tuning of the melodies etc matches your internal representation /expectation of the pitch height of the tones.

Hope these videos are of interest to some of you. And perhaps make certain concepts in music theory more clear.