Organteq 2 Diapason Settings

Nice post!

Yes, from my research Baroque temperaments and diapason are absolutely all over the place!  I think it's very unfortunate whenever I see it oversimplified into a one-size-fits-all solution like A415 is Baroque tuning (especially with Equal Temperament).

I really like the variety and balance they chose between presets.  For example, while the actual Frieberg organ is a modernized Silbermann 1/6 comma at A476.3 (historically A473 with a Silberman 1/6 comma before the 20th century), I like having it set to Kirnberger III (as Silbermann 1/6 is something of an acquired taste) and the A470 is really close to 473/476 (and I think the ceiling of what OTQ2 can do).  https://www.freiberger-dom.de/en/concer...rmann.html & https://www.youtube.com/watch?v=Y4VYUUlCtcQ

Versailles is an interesting case, as the original organ was A390 or A392, based on the tuning fork found at Versailles, but when it was rebuilt and restored, the builders decided to set it to A415 but the restoration kept the "Temperament Ordinaire" of the time: https://www.youtube.com/watch?v=PENR9dH_yJ8 & https://www.hpschd.nu/tech/tmp/dalembert.html

It's also fascinating how much methodology influences temperament and tuning, as the way that an instrument was tuned before computers was--as any piano technician or organ tuner will tell you--done by counting beats and increasing or decreasing intervals to minimize various wolf-tones or sour harmonics.  Pythagorean and meantone commas are very easy to tune to--which is why they were typical of Renaissance music--because no "well-tempering" was done to reduce wolf tones around infrequently used tri-tones and within more exotic key signatures like C# major, B major or F# minor (or their enharmonic counterparts--though the sharp and flat keys aren't considered equivalent in terms of historic temperament in they usually are now with equal temperament).

If scales like C major were in order, then no further adjustments or "tempering" was needed.  As music became increasingly chromatic by the end of the Baroque era, more and more well-tempered and (eventually) equal-tempered scales and tuning methodologies were developed to allow playing in the more exotic portions of the circle of fifths (or more exotic modes)--particularly during the "development" sections of fugues and the early large-scale Classical music forms.  The downside to well-temperaments is that as you, for example, narrow a third in one key or mode, you are lowering the leading tone in another or as you increase the width of a third, you're adding a leading to a mode or scale that doesn't/shouldn't have one in that place.  So, you have a trade-off between sounding better in all keys but less exceptional in some keys--which wasn't to all musicians' tastes in the mid-Baroque, which is why meantone commas (like Silbermann's 1/6) persisted for decades alongside more and more newer well-temperaments.  To many tastes--even in the late-Baroque and early-Classical, the best music was still in the mathematically precise meantone commas with key signatures that favored that precision.

I'm reminded of when I was looking through the online copies of Isaac Newton's college notebooks made available by Cambridge during his music theory classes (back when music theory was considered high mathematics), where he lists "the 12 musical modes in theire order of gratefulnesse" (you would think it was "gracefulness" but no, it's clearly "gratefulness") and the order doesn't really match what we would list with modern tastes as the modes ranked from best to worst (Lydian, Ionian, Dorian, Aeolian, Phrygian, Mixolydian, Locrian!?, and five other Greek Tonoi that we don't consider among the seven diatonic modes--though for the sake of trivia his list continues--Bb Dorian, G# Low Hypolydian/Hypoaeolian, C# Low Lydian/Aeolian, F# Low Hypophrygian/Hypoiastian, and Eb Low Mixolydian/Hyperdorian). https://cudl.lib.cam.ac.uk/view/MS-ADD-04000/233

The ultimate solution was equal temperament, but it had the major disadvantage that while, on paper (and known in Europe as early as 1585 by Simon Stevin--a year after an independent discovery of it was published in China by Zhu Zaiyu 朱載堉), it made all intervals equal, nobody could create a simple method for tuning an entire instrument like an organ to that.  Only by the time of Neidhardt's work in the early eighteenth century was a method for (fairly) easily achieving equal temperament on an actual instrument conceived and published; however, it took a very long time for any method of tuning to equal temperament to be widely adopted--near the middle and end of the nineteenth century.