Bruce Olsen wrote: >What is the keynote? > >E natural with flatted 3rd is in the description, not the >specification, since the notation doesn't change if we drop that. >However, since the keynote isn't obvious that would be valuable >supplementary information, if it is correct, but maybe it isn't. >Let's see. > >In the table following the 2nd row is the % of total time spent >on the note indicated above it. We put a 1 in the 3rd row when >note is in the tune, otherwise 0. > >For keynote E we have: >E F F#/Gb G G#/Ab A A#/Bb B C C#/Db D D#/Eb >23.44 0 6.77 7.81 0 8.85 0 17.19 0 1.56 34.38 0 >(1) 0 1 1 0 1 0 1 0 1 1 0 > 0 1 2 4 8 16 32 64 128 256 512 1024 = >mult. last 2 rows together, column by column, and add >Mode#=0 +2 +4 +0 +16 +0 +64 +0 +256 +512 +0 = 854
I find it easier to look at these things as histograms: Note useage % Histogram E ************************* F F# ******* G ******* G# A ********** A# B ****************** C C# * D ******************************** D# >854 = Dorian mode, which fits with the 2 sharps on the key >signature, which is what Jack said, but the tune spends >1.47 times longer on D than on E, so let's rearrange to >start with D and see what we get. > >[Phil Taylor's % time ordering scheme fits beautifully with my >mode numbering system. Once you have his pattern starting with >the most common note you don't have to search for a match, you >can just calculate the mode number for any mode that you can >score in 12TET, no matter how many different notes you have. [If >the mode number you get doesn't match one in the file >MODETABL.TXT on my website, I would greatly appreciate a copy of >the tune, so I can add another 'real' mode to my data base.] > > D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B C C#/Db >34.38 0 23.44 0 6.77 7.81 0 8.85 0 17.19 0 1.56 > (1) 0 1 0 1 1 0 1 0 1 0 1 > 0 1 2 4 8 16 32 64 128 256 512 1024 >Mode#= 0 + 2 +0 +8 +16 +0 +64 +0 +256 +0 +1024 = 1370 Here's the histogram rearranged: Note useage % Histogram D ******************************** D# E ************************* F F# ******* G ******* G# A ********** A# B ****************** C C# * >1370 is Ionian/major mode, So Gow's tune looks more like it might >be D major instead of E Dorian. What is it? Apart from the strong D, the first histogram is very typical of a dorian mode tune. The second histogram would be very atypical for a major-key tune - the second (E) is much too strong, and the fifth (G) is very weak. E Dorian is a much better fit here, and indeed you can accompany the tune using Em, G and D chords, but not using D, G and A. The tune does end on a D chord though. <snip> >When looking for the 'final' of a tune you have to ignore any >flare of short-time notes at the very end. If we ignore that >B/A/G/F/ at the end here, we get that (d)D as the keynote. Yes, the final here is definitely D, but I think the tune as a whole is in E dor. Phil Taylor To subscribe/unsubscribe, point your browser to: http://www.tullochgorm.com/lists.html
