Barbershop Tag Intonation Comparison "It's My Song"

0:00 12-tone equal temperament
0:15 5-limit tuning (Eb- major is the key, Db note is a 9/5)
0:32 5-limit tuning ( Eb- major Db note in the bass part is a "Pythagorean" 16/9 and the one in the tenor part remains a 9/5)
0:49 7-limit tuning (only difference from the previous tuning is both Db's are septimal, 7/4 to the Eb-)
1:05 True Intonation aka "Pythagorean tuning" Same starting notes as the previous 4 iterations of the tag, but note Eb- is just called Eb, no more need for an extraneous minus accidental.
A=432 Hz in all examples.
I made this video to show that yes, indeed even in barbershop quartet music, Pythagorean tuning is ideal, though 5 and 7 limit seems to be the tradition. I included two 5 limit examples because for that first Db in the bass there is an option for tuning it to either a 9/5 (a 5 limit interval) or to a 16/9 (a Pythagorean interval). Amongst proponents of 5 limit both tunings are used, one for a more "stable" minor 7th (9/5) and the other for a more dominant 7th sound (16/9).
To me hearing these makes it all the more clear. When listening holistically both vertically and horizontally BOTH at once, ONLY the last iteration is in tune and worthy to be called True Intonation.
I would encourage any in a barbershop quartet to aim for the true "Pythagorean" intervals. Share this video with other barbershop people so others can see and hear as well.
God bless.
The Gospel of God, and how to be saved :
1 Corinthians 15:1-8 KJV
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[@theoriemeister]

So the tuning of the Db is the only real difference?
Can you post an example of the tag using just intonation?

[@RememberGodHolyBible]

The term "just intonation" means many things to many people. What you are probably meaning as just intonation is 5 limit tuning. Which can be heard in this video, the second and third iterations. Traditionally barbershop music often employs 7 limit tuning as well, which can be heard in the 4th example.
Technically all of the examples after the first are just intonation because the frequencies are all in whole number ratios to the fundamental, in this case, the Eb.
Contrary to what the world teaches though, 5 limit tuning is not the true just intonation, nor 7 limit, I would say that it is what the world calls Pythagorean tuning. The world falsely claims Pythagorean tuning to be out of tune and only suited for melodies but not chords, this could not be more false. As you can hear in the last example in this video, it sounds quite nice, and in my opinion, it is the only one that actually sound rightly in tune. That is why I call it true intonation.
The reason there are 2 different 5 limit tuning examples is because in 5 limit there are sometimes options for tuning certain notes. In this case the Db in the bass could be tuned to the Pythagorean 16/9 or the 5 limit 9/5, since every limit composes all of the notes of the previous limit tuning. So in certain circumstances I could see some 5 limit proponents objecting to me choosing one over the other, so I included both options in this video.
For the 7 limit just intonation example. The only note that is different from the 5 limit ones is again with the Db, now both of them being tuned to a 7/4 ratio to the Eb, it's 7th harmonic. All the other notes in the 7 limit are the same as the 5 limit examples.
With the True intonation/Pythagorean/3-limit example, the last one in the video, all of the notes are different from the previous 3 examples, except for the Eb, Ab, and Bb. The G, F, Cb, Gb ... all the others are unique. The Pythagorean Db in the last example can also be heard in the third example in the bass part like I said before.
I and currently only very few others have come to the conclusion after years of study in intonation and tuning, that extended Pythagorean tuning is the True Intonation. The reason I say extended Pythagorean is because it is not limited to only 12 notes per octave, it goes as far out as is needed to tune properly. It is the ONLY just intonation that is reflected in our music notation system. A system of 7 notes that are modified up and down by sharps and flats. All other so called just intonations must invent myriad accidentals to notate properly, none of which are practical and legible on the page.