As no one has been able yet to learn its scale lengths or other dimensions, we can only deduce what’s going on from the single photo and the scant sources, given next.  The two of importance are Curt Sach’s dictionary, Real-Lexicon der Musikinstrumente (1913, Berlin) and Josef Zuth’s Handbuch der Laute und Gittarre (1926, Vienna).  We can ignore Baines’ American and European Instruments (see my blog) and Timmerman’s 2006 Ivan Padovec book chapter (as he repeats the Zuth information). I found nothing in Fritz Buek’s Die Gitarre und Ihre Meister (1926, Berlin).  A couple of other Google Book search results offer nothing so far.

Sachs is the oldest entry I know of.  He gives “Guitharfe” and describes it as a type of “Guitarrenharfe” (“harp-guitar”).  From what we can glean from the photograph, his definition appears accurate:

“Viennese mathematician Joseph Petzval named his instrument the Guitharfe. Petzval invented it, and J. Scherzer of Vienna built it in 1862. The instrument has two fingerboards, one of which has the customary six strings over a fretboard using the 31-step tone system; the other has 6 bass strings and a 12-step fretboard.” ¹

Zuth inconsistently gives “Gitarrharfe” in his Scherzer entry, then “Guitharfe” (from Sachs) and “Githarfe” (his own spelling) in his Petzval entry.  The latter may simply be an example of the eventual dropping of the “u” from the German spelling (guitarre > gitarre).  In his Guitharfe entry (again sourcing Sachs), he copies Sachs’ choice of calling it a type of harp-guitar (switching the term now to “Harfengitarre”).  In his Harfengitarre entry, Zuth seems to imply that Scherzer made multiple “Githarfen.” ² This man seems as confused as I am.

Zuth similarly fails to divulge where the name comes from (likely from Sachs).  But fortunately, he gives the description of the printed label: “Invention of Joseph Petzval, 1862, executed by J. Scherzer, Vienna.”  Zuth probably examined the instrument himself, as, along with the label text, he adds to its description that it is “twice as big as a guitar.”  I suspect that Zuth’s entries would have had a specific, consistent name had he found an actual term on the label or in the collection’s files.

Incidentally, Scherzer would have been sixty years old when he constructed this instrument.  The birth date of 1834 that has been given in every source save one is a repeated error (Erik Hofmann finally presented the true date, 1802, in 2011’s Stauffer & Co.).

Buek does not mention the Petzval instrument, but tells an interesting story about another unrelated Scherzer “Gitarfe.”  It seems that the guitar virtuoso Sokolowski had ordered from Scherzer a “Kontragitarre mit fünfzehn Bässen” (you catch that? Surely Buek meant “15 strings,” not “15 basses”…?  Perhaps, yet even though that would seem to make the most sense, a Russian guitar site [musicmaster1994.ru] says about the Zuth error that “the guitar of Sokolowski had twelve and not fifteen additional basses.” [Theoretically possible, as an 11-bass Scherzer is known]).  So, 9 or 12 basses...  Regardless, when the Russian border guards saw it, they were unable to clear it for customs, as they had never seen any instrument like it.  The only way was to give it a new name, so they came up with “Gitarfe,” as it was to them a cross between harp and guitar (what do you know - just like today’s “harp-guitar)! ³

Finally, in Alex Timmerman’s chapter in the Padovec book, he restates the Zuth information (he apparently was not able to inspect it, either), with one typo (writing “thirteen” instead of “thirty-one” frets on the main neck). ⁴

If there is any other information out there, I would love to hear of it.  Most beneficial would be to have an opportunity to actually examine, measure and study the museum specimen, something no one since Zuth seems to have done.

And so, meanwhile – back to the priceless photo.

In my view, the whole point of Petzval’s invention would seem to be the “31-stufigen Tonsystem” (31-step tone system).  I am unable to deduce exactly where these thirty-one points would lie on the complex fret pattern.  The double inlays at the halfway point occur at the traditional 12^th fret position, but that’s as far as I get!  Thoughts? 

As to scale, there are three clues: This neck’s strings are described as “gewöhnlichen” (ordinary, customary), while the other has six “Baßsaiten” (bass strings).  Finally, Zuth describes the instrument as “doppelt so groß, wie eine Gitarre” (twice as large as a guitar).  Given the many microtonal frets and the disparity between the two fretted scales, I thus postulate that the 31-step neck is “standard scale”, while the bass neck is literally that – a bass.  I.E: The 31-step neck is tuned EADGBE, and the bass neck is tuned…well, there are at least two choices: 1) to the same intervals as the neck, but down a fourth, fith, or even octave lower?  Or 2) diatonically or chromatically step-wise, as in a harp guitar, with the frets being capotasto locations.  With the resolution of the photo, I see what appears to be a standard gut set on the short neck (3 overspun, then 3 thick gut strings).  On the bass neck, the strings appear to all be copper wound, with evenly smaller diameters (the 4^th being a mismatched replacement?).  But I can’t tell if the gauges are different enough to represent standard guitar intervals or diatonic intervals.  Nor can we know if those are original strings (unlikely).  If option #1, then this was an “experimental double-neck guitar.”  If option #2, then this may have been an “experimental fretted harp guitar.”  We simply cannot (yet) know.  Either way, the Guitharfe does not appear to be a true harp guitar.  Perhaps a bigger question is why the bass neck frets are installed in such poor alignment – this is Scherzer we're talking about, creating a micro-tonal instrument for a mathematics genius...and he does sloppy frets on the "bass neck"?  And then there is that funny extra fret between the 1^st and the nut…(?).  Again, this instrument simply has to be examined by historical guitar experts!

If, for sake of discussion, we use a nominal 635mm (25 inches) for the shorter “standard” neck, this would put the bass scale at about 825mm (32-1/2”), with the instrument body dimensions at roughly 500 x 675mm (19-5/8” x 26-1/2”).  Pretty imposing!

The next question is why the two necks?  One is obviously meant to explore Petzval’s 31-step system, but what of the bass?  Beyond the two options above, was Petzval experimenting with another way to utilize the sub-bass strings of Scherzer’s typical harp guitars (which were then on their way to becoming extended range Schrammelgitarres)?  Or did Scherzer suggest including some sub-basses, with Petzval replying, “Well, OK – but only if you have frets available”…?  Note that Scherzer was never known to use six basses.

Of particular interest to me was the source (and variants) of the “Guitharfe” name, something still unanswered.  The Collection of the Gesellschaft der Musikfreunde now calls it “Gitarrenharfe.”  What feature could possibly be referring to the harp?  Did Petzval truly name his invention that?  Or was this another “assigned” name by a bewildered Sachs? ⁵

Final observations concern the shape (did Petzval request a “giant cello shape”?!), and the extra hardware.  The heavy metal bars look like later additions, don’t they?  To hold the thing together?  Likewise, the added tailpiece.

Here are a few last pieces of information on Petzval from the web:

Entry below from: The Sharpened Eye: Joseph Petzval: Light, the City and Photography, October 23, 2003 – February 22, 2004 (exhibition of the Technisches Museum Wien):

Ludwig Erményi (?): Petzval’s “Guitharfe”, signed “LE”, collodion, ca. 1910. MA 36a(?)/9

A guitar maker from Vienna got Petzval interested in acoustics. In 1859, Petzval published his “Theorie der Schwingungen gespannter Saiten” ["Theory of Vibrations of Taut Strings”]. He developed a 31-step tonal system. To test his theories, he had an instrument built to his specifications, a combination of a guitar and a harp, which he called “Guitharfe”.

Entry below from: Encyclopaedia of Tuning, © 2004 Tonalsoft Inc.
English translation ©2001 by Klaus Schmirler, webpage and MIDI-files ©2001 by Joe Monzo:

Vielleicht hätte ich hier als Ersten den nun längst verstorbenen Herrn Professor Josef Petzval nennen müssen, der sich schon in den sechziger Jahren bei seinen Vorlesungen an der Wiener Universität eines Instrumentes mit mehr als 12 Stufen bediente. Doch will es mir scheinen, als ob die Bestrebungen dieses originellen Kopfes doch mehr darauf hinausliefen, unser altes System hinsichtlich seiner Reinheit zu verbessern, als es durch neue Tonstufen zu bereichern. Denn auf seinem Klavier (übrigens auch auf seiner "Guitharfe", einem völlig neuen Instrument) konnte man ausser mit 12 auch noch mit 31 Stufen musizieren, so dass hier von *Viertel*tonmusik kaum die Rede gewesen sein dürfte. Ich selbst habe von den Arbeiten dieses musikalisch gebildeten Akustikers, der, nebenbei bemerkt, zuvor als Optiker durch Erfindung des Anastigmaten berühmt geworden war, erst im Januar 1917 gelegentlich meiner Anwesenheit in Wien durch die Herren Alfred Finger, Ing. Gerbel (Physiker), Dr. Ludwig Erményi ("Der Merker") und Ludwig Karpath ("Neues Wiener Tagblatt") Kenntnis erhalten.

Perhaps I would have had to call the now long-deceased professor Josef Petzval here as first, already in the 1860s with his lectures at Vienna University he availed himself of an instrument with more than 12 steps. But it seems to me as if the efforts of this original heading nevertheless were more towards improving our old system regarding its purity, than to enrich it with new tone steps. Because on his piano (by the way also on his "Guitharp", a completely new instrument) one could make music either with 12 or with 31 steps, so that one could hardly speak of quarter-tone music here. I have from the work of this in music educated acoustician, who notices, besides, had become famous before as an optician by the invention of anastigmatic lenses, only received knowledge in January 1917 during my occasional presence in Vienna by the gentlemen Alfred Finger, Ing. Gerbel (Physicists), Dr. Ludwig Erményi ("Der Merker" ["The Flag"]) and Ludwig Karpath ("Neues Wiener Tagblatt" ["New Viennese Daily"]).

I now encourage other scholars to help close the book on the true name, the scale & size, the tunings, the mathematics of the 31-step fingerboard, and the purpose of this strange invention!

NOTE 1: Sachs, C. Real-Lexicon der Musikinstrumente (1913, Berlin): “Guitharfe nannte der Wiener Mathematiker Jos. Petzval eine von ihm erfundene und 1862 von J. Scherzer in Wien gebaute Guitarrenharfe mit zwei Griffbrettern, von denen das eine die gewöhnlichen 6 Spielsaiten und Bünde nach dem 31-stufigen Tonsystem, das andere 6 Baßsaiten und 12-stufige Bünde enthält. Wien, Ges. d. Mf. - Z.f.I. XXVll 561.”

NOTE 2: Zuth, J. Handbuch der Laute und Gittarre (1926, Vienna): “SCHERZER, Johann Gottfried, berühmter Alt-Wiener Gitarrenmacher, geb. 1843, gest. 14. Jän. 1870, wahrscheinlich aus dem Vogtland eingewandert. Seine Werkstatt hatte er zu Wien in der Hundsturmerstraße Nr. 65, später Margarethenstraße Nr. 99; dort arbeitete "der kleine hagere Mann ohne Gehilfen und Lehrbuben" (Makarow, Selbstbiogr.) zum Teil für das Geschäft Staufers. Erstellte, wie dieser, allerlei Versuche zur Verbesserung des Gitarrbaues an, stand auch in Verbindung mit Physikern u. Gelehrten: er verfertigte Gitarren mit Doppelboden, zog Eisenstäbe im Resonanzkörper, um den Saitenzug der Baßgitarren (s. G. Ferrari) entgegenzuwirken, baute die Petzvalsche Gitarrharfe (Sammlung der Wiener Musikfreunde). In einer Baßgitarre mit 5 Freisaiten stand der Zettel: "Joh. Gottfried Scherzer, vormals Stauffer (!) in Wien, Margarethenstraße Nr. 99 anno 1859”; eine 12saitige Gitarre mit Doppelhals, eine 13saitige mit Bodenwölbung von 2•2 cm in der Längenmitte und eine 6saitige Gitarre mit einwärts geneigten Zargen (Boden kleiner als Decke) hat F. Nowy, Wien, ausgebessert.

“PETZVAL, Josef, ausgezeichneter Physiker, Mathematiker und Techniker, der sich auch mit musiktheoretischen Studien befaßte. 1862 konstruierte er eine “Guitharfe”; sie ist doppelt so groß, wie eine Gitarre, hat zwei Griffbretter, von denen das eine die 6 Griffsaiten und 31 stufige, das andre 6 Baßsaiten und 12 stufige Bünde enthält. [Sachs, »Rea1-L. der Musikinstrumente« u. Lütgendorff,  G Lm. II.] Eine solche “Githarfe” befindet sich in der Sammlung der Ges. d. Mus.-Freunde in Wien mit dem gedruckten Zettel: "Erfindung von Josef Petzval 1862, ausgeführt von J. Scherzer, Wien«.

“GUITHARFE, von dem Wiener Mathematiker Jos. Petzval erfundene, von J. Scherzer gebaute Harfengitarre mit 2 Griffbrettern, von denen das eine Bünde nach dem 31 stufigen Tonsystem für die 6 Griffsaiten, das zweite 12 stufige Bünde für die 6 Baßsaiten trugen. [Sachs, »Real-L. d. Musikinstrumente «, Berlin 1913.]

“HARFENGITARRE, eine Form von Baßgitarren, der ein säulenartiger Nebenhals, mitunter auch die Gestalt des Schallkörpers das Aussehen einer Harfe geben. Die Entstehung dieser Gitarrform weist auf England hin. Ein anonymes Buch »Compleat lnstructor for all sorts of guitars« aus dem Anfang des 19. Jhdts. schreibt: "Die neu erfundene Harfengitarre ist ein sehr beliebtes Instrument geworden, welches, wenn es mit Harfensaiten bezogen wird, einen der wirklichen Harfe sehr wenig nachstehenden Ton hervorbringt.." Nach den umständlichen Angaben a. a. 0. hatte die H.-G. 6 Griffbrett- und 2 Freisaiten aus Darm und silberumsponnener Seide der Stimmung: F (freischwebend) – B (übergreifbar), es- g- b- es¹ - g¹- b¹. Die Vermehrung der Freisaiten führte zur Form der Harfenlautengitarre, der Stimmung G-c-d-e (freischwebend), f-g-a-h (übergreifbar), c¹ -e¹ - g¹ (eigentliche Greifsaiten); tonartgemäße Umstimmungen sind vorgesehen. H.-G. von Scherzer nach Petzvals Konstruktion hießen Githarfen. Die von Schenk wurden nach dem oberen, kreisbogenförmigen Verbindungsteil der beiden Hälse auch Bogengitarren genannt. Eine Harfengitarrlaute brachte 1912 der Frankfurter O. Buß in den Handel. Hierher zählt auch die französ. Guitare mu1ticorde, eine Verbindung von Lyra, Gitarre und Harfe. - In der Form der Harfe näher kommend, der Spielpraxis nach eine Gitarre, ist die Gitarrenharfe, von der ein Stück das Heyersche Museum in Köln (Ktlg. Nr. 603) besaß.

NOTE 3: Buek, F. Die Gitarre und Ihre Meister (1926, Berlin), p.150: “Der Gitarrevirtuose Ssokolowski bestellte sich bei Scherzer eine Kontragitarre mit fünfzehn Bässen. Als dieses Instrument die russische Grenze passierte, wußten die Zollbeamten damit nichts anzufangen, da ihnen Gitarren in dieser Form und Besaitung unbekannt waren; als eine gewöhnliche Gitarre konnten sie das Instrument nicht ansprechen, so gaben sie ihm den Namen "Gitarfe" und verzollten es als Zwischending von Harfe und Gitarre.”

NOTE 4: Timmerman, A. Ivan Padovec (1800-1873) and His Time (2006, Zagreb), p.122: “In cooperation with Josef Petzval, a physicist involved with music theoretical studies, Scherzer developed the ‘Guitharfe’ in 1862. This model was about twice as large as a normal guitar. The main difference was that it had two fingerboards: the ‘usual’ one with thirteen positions (!) and an extra fingerboard with twelve positions, placed under the bass strings.”  

NOTE 5: For I am all but certain that many of the "one-off" experimental guitars that Sachs found in European museums were named by himself (in the source referenced in Note 1) just to have some sort of entry heading (See my Organology for more on this).