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# Piece: https://leibnizlegible.com/api/records/49947/text
# Catalogue record: 49947 — [für die Miscellanea Berolinensia]: G.G.L. Annotatio ad praecedens Systema Musicum
# Incipit: Cum Vir Nobilissimus C. Henflingius
# Date: 1709-04-03
# Sender: Leibniz — Addressee: (Misc.Berol.)
# Other printings: -Haase, Rudolf [Hrsg.]: Der Briefwechsel zwischen Leibniz und Conrad Henfling. Ein Beitr. zur Musiktheorie d. 17.Jh. Frankfurt a.M. 1982. S.136-141. -Bailhache, Patrice: Leibniz et la théorie des la musique. Paris 1992. S.143-148.
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=49947&katnr=37088
# The Leibniz-Archiv's transcriptions of the letters of 1709 (pre-edition): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-transkriptionen-1709
# Work: https://leibnizlegible.com/work/DE-611-HS-970559
# Title: LBr. 390 · Henfling
# Folios: Bl. 83 (from the shelfmark LBr 390 Bl. 83.86): 2 pages, canvases 171–172, page ids DE-611-HS-970559:0171 to DE-611-HS-970559:0172
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-970559&page=171
# Lines: 54 recognised on 2 of 2 pages, mean confidence 0.99
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
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# After the first blank line, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 83r — DE-611-HS-970559:0171
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 86v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-970559/jpgs/default/00000171.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 249, 2026-09-10T12:59:33Z — 25 lines, status machine
G. G. L. Annolatio ad praecedens hystema Musicum
Cum Vir Nobilissimus C. Henflingius Smi Marchionis Brandeburgici
Onolds bacensis Consiliarius Aulicus tum in aliis Matheseos partibus, tum
in Musica egregie versatus, Epistolam ad me de novo Systemate suo, Musicisque
fundementis dedisset, et in Hugemonas pariter ac nuperas demperaturas
Cl. Viri, cujus Systema Commentariis publicis Regiae Academiae Parisinae
intertum est, non nihil animadvertiset, ac post Cl. Vignolii pariter ac mea
annotata, quaedam addidisset atque explicuiset; nova ejus cogitata, scientiae
incremento occasionem non spernendam datura, ipso non invito in lucem pro–
ducenda putavi. Excogitavit etiam ex principiis suis novum Claviarii
Organi genus, a multis commoditatibus commendatum, quod actu ipso est
executus, ejusque descriptionem plenam ab eo expectamus.
Equidem constat, additiones et subtractiones intervallorum Musicorum
revera esse multiplicationes et divisiones numerorum, qui rationes sonorum
exprimunt. Unde mihi olim in mentem venit hir Logarithmos adhibere
quos etiam intervallis ascripseram, confecta Tabula sequenti, aliaque etiam
ampliore; ex quibus postea varia primo aspectu colligi poterant, quae alias
ex calculo difficulter eruerentur, verbi gratia, semitonium minus parum
admodum excedere decimam partem lvinta; differentiam semitonii majoris
et minoris non multum excedere partem trigesimam Octavae, certe minorem
esse parte ejus vigesima nona; Tonum Aminorem non multum excedere
quintam partem Sextae Majoris, aut quartam partem avintae; Tonum
Majorem non multum excedere quartam partem sextae Minoris, aut
sextam partem Octavre, aliaque id genus. Sed iisdem Logarithmis alio
ad huc modo pereleganter usus est Dn. Salvator, autor supradicti hyste

## Folio 83v — DE-611-HS-970559:0172
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 86r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-970559/jpgs/default/00000172.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 249, 2026-09-10T12:59:33Z — 29 lines, status machine
matis novi, Commentariis Parisinis inserti, qui considerans Octavae, seu
rationis 2 ad +, Logarithmum Fabularem esse 301030, contentus partibus
3010, commodum animadvertit, hunc numerum dividi posse per 70, et prodire
43. Itaque judicavit, Octavam posse dividi in partes 43, quarum quaelibet, si
major requiratur accuratio, dividatur in partes 7, ut prodeant partes
aequales 302: quod si aliquid adhuc accuratius desideretur, harum quam libet
subdividendo in partes i0 rediri ad partes aequales 3010, quae sufficiant ad
omnia intervalla Musica sensibilia designanda, et systemata quaecunque expri-
menda. Haec clavis et
fuc origo est processus Dni Salvatoris. Hu-
genius tamen, qui profunde inspicere solitus est, quae tractavit, divisionem
Otavae adhibuit in sc partes aequales, et Zartini quoque ac Salinae tempera-
mentum probavit per Avartam partem Commatis seu Rationis 81 ad 80
Sane et Loachimus Lungius, qui medio nupero seculo floruit, magni vir
acuminis, nec minoris diligentiae, in harmonicis suis posthumis etiam
temperaturam per quartam partem Commatis (ipse Avartulam vorat) sec
tus est. At Dn. Henflingius haec non satis commoda judicat, et divisi
oni in partes 31 vel 43 divisionem praefert in partes 12, vel pro majore
accuratione in partes 5o; multaque consideratione digna notat: atque
illud inter caetera, non esse spernendos exiguos errores in Octavae divi
sione, tum quia aliquoties repetitur. Octava: (ideo cavendum saltem
ut compensantitus se erroribus bene compleatur) tum quod in chorda
rum quidem divisione (tanquam linearum) eadem ratio observetur, quae
est intervallorum; sed cum intervalla ponderibus exhibentur, rationes
in nonnullis organis etiam
intervallorum duplicentur, et cae titunrguaatei
errores
triplicentur, adeoque in construendo oculis sensibiles reddantur, quanquam
ab aure non satis percipiantur.