Kedves Kazi!

A lyra hangolasa egy gyonyoruseges gyotrelem. Raadasul megcsak nem is fakulcsot, hanem csomokat tekegetsz. Nehez harmoniaba hozni, annal konnyebb a lehangolas. A szelore, a homersekletvaltozasra is erzekeny a mimoza lelke. Es a meleg a jo neki, akkor feszul a bor memranja. Ezert csatakos, lucskos eszaki telekre nem valo. Azt mondjak, ilyen a vilag, anarchikus, szethuzasara, szetesesere hajlik, nehez rendbe, egyensulyba hozni. A rend, taxisz, nem jon hazhoz, rendelesre, meg kell erte szenvedni. Az ataxia, az anarhia a normal allapot, a harmonia a pillanate, es minden alkalommal ra kell ujra hangolodni. Irigyellek, hogy milyen otthonosan mozogsz a geometrikus zenesemak, az analogiak, nekem sajnos meg kaotikus birodalmaban. Remelem egyszer, segitsegeddel majd orulhetek egy elegans levezetesnek, ami most meg megizzaszt. Idemasolom Barker Greek Musical Writrings cimu konyvebol,a
legutobb oly szepen altalad ideszerkeszetett Helikon tovabbfejlesztett valtozatanak leirasat.
Ezek az abrak, ha hinni lehet, kiserleti zeneszerszamok voltak. Erdekes lenne "megzengetni" oket a szamitokeppel.
"{Concerning the use of the kanon in connection with the instrument called the helicon}
The differences between tetrahords correspoding to the genera have thus been established for us by these methods, through the assesment and comparison of notes of unecual pitch. It is possible to use the eight-stringed kanon of the octave in a different way too, in conjunction with the instrument called the helikonm which has been made by students of mathematics to display the rations in the concords, in thefollowing sort of way.
They construct a square, ABCD, and after dividing AB and Bd in half at E and Z, they join up AZ and BHC, and draw parallel to AC the line EFK through E, and the line LHM through H. It follows from this that AC is doubleeach of BZ and ZD, and each of these is double EF, since AB is also double AE, so that it is also the case that AC is four times EF, and is the epitritic of the remainder FK. It is also shown that MH is double HL, since as is DC to CM, so is DB to HM, and as is BA to AL, so is BZ to LH. And for this reason,as is BD to HM, so is BZ to LH, and conversely as is BD to BZ, so is MH to LH. Then AC is the hemiolic [3:1] of HM and triple HL; so that when four strings of equal pitch are arranged in the same positions as those of the straight lines AC,EK,LM and BD, and when a kanonion is placed under them in the position of AFHZ, and when the following numbers are assigned to them, 12 to AC, 9 to FK, 8 to HM, and 6 to each of BZ and ZD, then there are produced all the concords and the tone, that of the fourth, according to the epitritic ratio,being konstitued by AC and FK and by HM and ZD and by LH and FE, that of the fifth, in hemiolic ratio, by AC and HM and by FK and ZD and BZ and LH, that of the octave, according to the duple ratio, by AC and ZD and by HM and LH and BZ and FE, that of the octave and fourth, in the ratio of 8 to 3, by HM and FE, that of the octave and fifth, according to the triple ratio, by AC and LH, that of the double octave, according to the quadruple ratio, By AC and EF, and finally the tone, according to the epogdoic ratio, by FK and HM.
Next to this instrument, supose that we draw up a rectangle ABCD, and think of AB and CD as determining the vibrating lengths of the strings, and AC and BD as the extreme notes of the octave. Then we add, equal to and extending CD, and cut the side CD, by the application of rulers [kanonia], in the ratios proper to the genera, making E the limit of high pitch. Through the resulting points of division on it we stretch strings parallel to AC and equal to one another in pitch, and when this is done we place under them what will be the bridge common to the strings in the position, AZE, that joins the points A and E. In this way we shall make all the lengths of the strings in the same ratios [ as those mamarked on CD], so that it makes possible the assessment of the ratios that have been assigned to the genera. For as the lines taken from E along CD stand to one another, so will those drawn from the limits of these parallel to AC and as far as AZ stand to one another: for instance, as is EC to ED, so is CA to DZ. Hence these lines will make the octave, since their ratio is the duple.
Suppose that we cut off from CD, once again, the line CH, as a fourth part of EC, and CF as third of the same line, and locate strings throught H and F, HKL and FMN, equal in pitch to the first ones, so that AC becomes the epitritic of HK and the hemiolic of FM, and again FM becomes the epitritic of DZ and HK its hemiolic, and again HK is to FM in the ratio 9:8. Then these will make in relation to each other the concords that go with these ratios, and the equivalent result will follow for the divisions in the interior of the tetrachords, taken in the rations appropriate to those that are being assessed.
The first method is easier to apply than this in that is not necessary to alter the distances between the strings, but this one is easier than the other in that it has a common bridge, which is single and has a single position, and further in that is possible to move the bridge down, pivoting on E, to the position of XOE, and so to make the whole tonos [ pitch or key] higher, while the special character of the genus remains unchanged. For as CA, for instance, is to ZOD, so is XC to OD, and similary for the Others. Again, let us repeat, the former method is at disadvantage by comparison with this one, in that there one has to move several small bridges [hypagogidia] to accomodate each attunement, while this one is at a disadvantage by comparison with the other in that here one has to move the strings to completely new positions, and the changes is the points of contact are brought about no longer with equal distances between strings, but often at distances that differ by a large amount."
s.