Disputatio:Pentagrammum (musica)

De "pentagrammata (-ae, f.) "

(1) Why is this term feminine? The attestation, "utemur binis pentagrammatis ordinariis, quorum alterum discanti, alterum bassi clave est instructum," seems thrice to be implying the neuter pentagrammatum (a hapax legomenon?). (2) Or, since bina, -orum can serve as a substantive, maybe Euler is conceiving the phrase to be 'a staff's ordinary pair', in which case the noun is pentagramma (in its genitive singular form), not pentagrammatum (in its ablative plural form). (3) Given the three (or four) cited attestations of pentagramma, why (as said in the editbox) is pentagrammum "the most accurate" term? IacobusAmor (disputatio) 11:14, 30 Iunii 2023 (UTC)

I think you are right (my bad). Here you can see all the attestations of pentagrammat-* in Chapter XI, and Euler actually uses pentagrammatum (e.g. “binis pentagrammatis ordinariis”, “inter haec pentagrammata contineantur”, “inter pentagrammata vero gradum”, “opus erat tribus pentagrammatis”, “duo reliqua pentagrammata”, etc.). As for why pentagrammum instead of pentagramma, as you can see from the page history, I first moved the page to “pentagramma” and then I moved it back to “pentagrammum”; the reason is that apparently the word comes from Gr. “pentagrammon”, which is a substantive adjective of “pentagrammos, -e, -on”. But I don't have a Greek dictionary at hand right now, and I will be more than happy to be proved wrong. --Grufo (disputatio) 12:06, 30 Iunii 2023 (UTC)

The ancient Greek noun is indeed "pentagrammon": I don't see evidence of an adjective "pentagrammos", though Onions, Oxford dict. of English etymology, makes the same claim as Grufo about this. The form of the noun is, I suppose, defensible, even though, speaking generally, -gramma (neuter, plural -grammata) is much more commonly seen in Greek compounds (see Onions again s.v. "-gram"). "Pentagrammon", apparently a hapax, was perhaps consciously invented by Lucian in his dialogue Lexiphanes which is all about the misuse of strange words. I don't have time to pursue the implications -- could take all afternoon -- but what I can see right now suggests to me that Euler might have had good reason for avoiding Lucian's neologism and choosing pentagramma. Andrew Dalby (disputatio) 12:45, 30 Iunii 2023 (UTC)

Thank you for the insight, Andrew. I am all for moving the page to pentagramma. No matter what we decide however, we will have a few incoherent titles to deal with, such as

• Hexagramma unicursale
• Hexagrammum mysticum
• Pentagrammum et Pentagrammum (discretiva)
• (probably other pages that I am missing)

--Grufo (disputatio) 12:50, 30 Iunii 2023 (UTC)

[Added meanwhile:] I think "vel aliquando pentagrammatum[5] (-i, n.)," is a mistake. The form "pentagrammatis" used by Euler in the cited text is a genitive singular of "pentagramma", neatly placed between two dative plurals in "-is" to trick the unwary. Andrew Dalby (disputatio) 12:53, 30 Iunii 2023 (UTC)

You would also have to justify “Ad haec autem distincte exprimenda opus erat tribus pentagrammatis” (p.174)… and that would make two streches and not just one. Consider that the word pentagrammaton exists as well, and that might be the source of pentagrammatum and the confusion.

Going back to the main title independently of Euler… Interestingly, modern Greek uses pentagramma, -atos, n. for our “Pentagrammum” (see el:Πεντάγραμμα_(γεωμετρία), i.e. d:Q182186), but pentagrammo, -ou, n. (which is the modern version of pentagrammon, -ou, n.) for our “Pentagrammum (musica)” (see el:Μουσικό πεντάγραμμο, i.e. d:Q192193). My idea is that the musical pentagram ended up in modern Greek through modern Latin via pentagrammum. Nevertheless, Lat. pentagramma -atis, n. for indicating music staves is attested, and the fact that πεντάγραμμα exists is one more reason to move this page back to “Pentagramma (musica)”. --Grufo (disputatio) 13:14, 30 Iunii 2023 (UTC)

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Andrew, about this edit, you still haven't explained how you would interpret this passage (emphasis mine):

Ad haec autem distincte exprimenda opus erat tribus pentagrammatis, in quorum infimo solae bassi notae cum numeris suprascriptis, uti in basso continuo seu generali fieri solet, repraesentantur; duo reliqua pentagrammata vero continent integram consonantiam, qua numeri basso adscripti commodissime et suavissime exprimuntur. Scala hic quidem usi sumus vacua, sed facile erit per transpositionem huius tabulae usum ad quamvis aliam scalam sonosque alios accommodare. Distinguimus ut ante gradus suavitatis atque etiam species, ad quam quaeque consonantia pertinet, notavimus. Duabus denique haec tabula quoque constat partibus, in quarum priore consonantiae usque ad speciem decimam, in posteriore vero duarum reliquarum specierum consonantiae sunt enumeratae.

– Eulerus, Leonhardus (1739). Tentamen novae theoriae musicae, p. 174

which gets translated by Ian Bruce as follows:

But for this to be expressed distinctly there was a need for three sets of five lined staves, in the lowest of which the bass notes alone may be represented with superscribed numbers, as is accustomed to be done with the bass continuo, or in the general bass ; the two remaining staves truly contain whole consonances, by which the numbers ascribed to the bass may be expressed most conveniently and pleasantly. Here indeed we have made use of an empty scale, but it will be easy by the transposition of this table used to be adapted to any other scale and other tones. As before we may distinguish the order of the agreeability and also we have noted the species, to which each consonance pertains. Finally this table consists of two parts, in the first of which the consonances are enumerated as far as to the tenth kind, in the latter of the two remaining the kinds of consonances have been enumerated.

– Ian Bruce's translation

It might well be that *pentagrammatus, -a, -um is actually a participle from *pentagrammare. --Grufo (disputatio) 21:01, 30 Iunii 2023 (UTC)

I aimed to save your citation. If you doubt that it supports "pentagramma", remove it from the footnote, which already has your other citations in support of "pentagramma". Don't add "pentagrammatum" to the lemmas, it's a useless variant even if you could prove it valid. Sorry, no more time. Andrew Dalby (disputatio) 09:10, 1 Iulii 2023 (UTC)

OK, I tried to find a compromise by splitting the notes. --Grufo (disputatio) 14:13, 1 Iulii 2023 (UTC)