Chris, I think you have the problem nailed, polyphony had a great influence in the development of the scale. I realize that I neglected the hexachord scale in my previous message, as I neglected the tetrachord scale. But my statement of the "octave" was correct. The doubling or halving of a frequency will result in a perfect harmony as all the overtones will be the same (just higher or lower).
But I don't understand your saying that gamut is a contrivance. As I understand it gamut is just the name for the lowest note in the medieval hexachord scales which ran from G to e''. That low G was designated by the capital Greek gamma, and therefore was the gamma ut. The next ut was the "la" of that scale (c), and so forth. Ah so, now I think I see where Mathias hears the ascending and descending (I am looking at a layout of a seven hexachord scale that is reputed to be the real thing). The "fa" in the 3rd hexachord and the 6th hexachord is a Bb, whereas the "mi" in the 4th and 7th is a B #. So my question to Mathias was wrong. I was assuming the change was a matter of the notorious comma and temperament. But it still comes to the matter of where the mutation is made. It would seem that the forms were in transition as polyphony came into fashion, and that there may have been some contrivances in wording, but not in the music. This is of interest, and I have to go to my book on early composition and follow up. In the meantime I beg the list to accept these first views with an open mind. I have a lot of facsimiles of early vocal staff notation - as vocal is where I started. Most of these seem to be in octave format, and some are quite early. I'd be curious to know why the hexachord scale ever existed. The Greek tetrachord was a perfect fourth (with the intervening second and third a bit undefined as to exact pitch. Understandable, the string range wouldn't have been great and the instruments were basically a "chorus" behind the story teller. But once an instrument could have a greater range (and the voi ce always had that) why would one stop the scale on the sixth (la) when Pythagorous had investigated string vibrations and sound over a millenium before. My best guess is that because the music was sacred the church set traditions, and then musicians bent the traditions to the church. I doubt that the harpists and pipers of the towns had such theoretical scales, note the unique scale of the Scots pipes (not unique, just limited). With the indulgence of you all I'd like to continue in this thread, you have forced me to my bookshelves and have made this senior citizen's mind have to work a bit (and learn a lot). Best, Jon To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
