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I am trying to reconstruct the tuning of the Roman water-organ (hydraulis) of Aquincum. The original instrument had 13 pipes for each of the 4 registers (three stopped pipe registers and one open pipe register), and it was possible to play one, two, three, or all four pipes corresponding to each key at the same time.

The best description I found of what could be the tuning comes from the booklet of "Apollo & Dionysus" cd (https://www.chandos.net/chanimages/Booklets/DC4188.pdf), which is based on an actual hydraulis reconstruction by Justus Willberg:

The organ is tuned to an ancient tonal system, drawing upon a range of sources, including Bellermann and Koine Hormasia (Codex Palatinus 281, et al.). The registers are assigned individual modes (Hyperlydian, Hyperiastian, Lydian and Phrygian), allowing a specific set of notes to be played in each register: proslambanómenos, hypáte hypaton, parypáte hypaton, diápemptos, hypáte, parypáte, khromatiké, diátonos, mése, parámesos, tríte, paranéte, néte. In today’s notation this corresponds approximately to the pitch series D E F G A B♭ B C' D' E' F' G' A'. The organ can also be played with all the registers switched on, which results in a characteristic timbre in which the open Hyperlydian register dominates.

What I understand with my limited musical knowledge is:

  1. the register of the open pipes (which should be the highest pitched one) was Hyperlydian;
  2. the three registers of the stopped pipes were Hyperiastian, Lydian and Phrygian;
  3. one of the registers (the highest one?) was tuned according to the scale (that I do not recognize) D E F G A B♭ B C' D' E' F' G' A'.

My question is: how was this organ tuned? What were the pitches for each register? It seems they could be played at the same time, but would they sound nice together?

Edit:
As suggested by user Owain Evans, this is the instrument:

However, it can't be the setup presented in Hagel's book since (1) Hagels himself doubts the correctness of Walker-Mayer reconstruction and (2) none of the registers in Hagel's picture (borrowed from Walker-Mayer, actually) has the range proposed by Willberg

The supposed range of the Aquincum organ from HAGEL, S. (2018). Ancient Greek music: a new technical history. Cambridge, Cambridge University Press, p365.

Albrecht Hügli
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user2227111
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    Maybe The Roman organ of Aquincum https://archive.org/embed/romanorganofaqui0000walc (need to register on archive.org). Has 119 pages, quite alot of images, tuning from a brief glance. –  Jul 25 '20 at 11:58
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    Thanks, I did not know it was accessible. However, recent scholarship (Ancient Greek Music by Hagel) seems to reject the musical reconstruction by Walcker-Mayer as wrong – user2227111 Jul 25 '20 at 12:17
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    It’s in German, but here’s a site about a reconstruction done in the 1990s: http://www.hydraulis.de/0496e29a0c08d0302/index.html Also I learned today that pairs of aulos were often stopped (with wax or metal slides) to two different (but related) diatonic modes for a single performance. That caused the burden of the performer having to be careful about certain note combinations, but also allowed flexibility in key and harmony. It could be similar with the hydraulis. – Todd Wilcox Jul 26 '20 at 05:50
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    NB: “Iastian” is another name for “Ionian”, so hyperiastian is just hyperionian. I think the alleged “modern scale” mentioned from D to A’ including a Bb should be temporarily ignored in favor of researching the ancient pitches corresponding to the modes named for each register. It does seem like the modes mentioned in facts 1 and 2 are listed in order from highest register to lowest, but of course there is much overlap (that part of the diagram at the bottom of the question seems somewhat accurate). – Todd Wilcox Jul 26 '20 at 06:51
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    As far as I can tell, Lydian goes from a modern F to a modern F with a “keynote” of F, while hyperlydian goes from a modern Bb to a modern Bb with a keynote of F also. Which suggest that the modern equivalent of the highest note of the highest set of pipes would be a Bb, not an A. I don’t quite understand why an A would be listed as the highest note of a hyperlydian tuning. – Todd Wilcox Jul 26 '20 at 06:54
  • I think your point 3 is incorrect in interpreting then quoted text. My reading is that the notes listed are the entire compass of the instrument and the highest register doesn’t start on the D. – Todd Wilcox Jul 26 '20 at 07:14
  • If you look here: https://en.wikipedia.org/wiki/Musical_system_of_ancient_Greece you’ll see ancient Phrygian started on a note that is called “D” in many modern texts. That suggests to me that the lowest register of the organ was the Phrygian register and went from the D mentioned in the quote up to probably D’. Next higher would be the Lydian register from F to F’, then the hyperionian from G to G’, and finally hyperlydian, which is where my theory breaks down. Wouldn’t it run from C to C’? What about the Bbs, are they for the Lydian and hyperlydian registers? – Todd Wilcox Jul 26 '20 at 07:25
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    @ToddWilcox, the website you linked is owned by Justus Willberg, and reports (in German) precisely what I quoted in English above: "Dabei sind den Registern einzelne Tonarten zugeordnet (hyperlydisch, hyperiastisch, lydisch und phrygisch). In jedem Register sind folgende Töne spielbar: proslambanómenos, hypáte hypaton, parypáte hypaton, diápemptos, hypáte, parypáte, khromatiké, diátonos, mése, parámesos, tríte, synemméne, néte. Das entspricht in heutigen Noten etwa der Tonreihe d e f g a b h c' d' e' f' g' a'." – user2227111 Jul 26 '20 at 17:11
  • @ToddWilcox "The Roman organ of Aquincum", p. 78, gives that d-a' sequence for the Lydian register (actually, a Lydian/Ipolydian register) – user2227111 Jul 26 '20 at 17:37
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    Warning :-) -- in the absence of some physical evidence (dug up an ancient set of pipes) or specified pipe lengths & diameters in units we trust, the best you can do is tune the correct intervals, not the exact pitches . As you no doubt know, in just the last few centuries, middle "A" has moved by at least 10% – Carl Witthoft Jul 28 '20 at 13:59
  • @ToddWilcox But do you then consider the different tuning of today’s music? Singing Bach with a period tuning as compared to a modern tuning are two quite different experiences, the latter being much more strained. Archaeological evidence should provide clues as to what the tuning of the instrument was, and to my knowledge, there is archaeological evidence giving us clues as to the tuning. Have you read https://www.mclerranjournal.com/technology-1/2018/4/14/hydraulis-the-ancient-roman-pipe-organ? Here they touch upon the reconstruction of the hydraulis found at Mt. Olympus. – Canned Man Dec 09 '20 at 19:33

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In my humble opinion, there is no answer to this question. The tubes recovered in Dion, Greece, or elsewhere, do not provide full information about the tuning system. Reproducing any music score from manuscripts requires a lot of assumptions. In my humble opinion, the sound of the instrument, its colour, its timbre, are more important than the scales. I would have tried the well tempered chromatic scale.

  • This is okay up until the last sentence. The well-tempered chromatic scale did not exist in ancient Greece. – Aaron May 18 '22 at 14:00
  • Of course! I only wanted to say that I would appreciate the sound of the instrument better over a scale that my ear and mind are well trained. –  May 18 '22 at 16:42