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Autumn Leaves in Blackjack scale

[Joe Monzo]

(This page is accompanied by an mp3 loop of the beginning of Autumn Leaves in 12-EDO and Blackjack tuning.
download the mp3 here.)

In Yahoo Tuning Group message 22726, Mon May 14, 2001 7:53 am, Bob Valentine wrote:

> ... I wrote out a three voice
> triadic harmonization of 'Autumn Leaves'
> which is
> ii V I IV  full cadence to vi
> and then a three voice jazz renderring
> G  F#  F# E  E  D# E
> C  C   B  B  A  A  G
> A  D   G  C  F# B  E
> where seventh chords are generally
> consonant. However, I don't believe
> [s]eventh chords imply 7-limit in Western
> music, so this line of pursuit failed...

I made an mp3 of this, first in 12-EDO (at the beginning) and then in Blackjack 21-of-72-EDO (starting at about 13 seconds).

(You should be hearing it automatically. It may also be downloaded here: beginning of Autumn Leaves in 12-EDO and Blackjack tuning.)

The Semitone values of the The regular 12-EDO tuning are as follows, with approximate frequency proportions shown below:

 19       18       18       16       16       15      16
 12       12       11       11        9        9       7
  9        2        7        0        6       -1       4

5:6:9   4:7:10   8:10:15   8:15:20   5:6:9   4:7:10  5:6:10

The Semitone values of the Blackjack notes I chose are as follows, with approximate frequency proportions shown below:

 19       18&1/6  17&5/6   15&5/6   15&1/2   14&2/3   15&5/6
 12       12      10&5/6   10&1/2    8&1/2    8&1/2    7
  9&1/3    2&1/3   7        0        5&5/6   -1&1/6    3&5/6

12:14:21  4:7:10  8:10:15  6:11:15  12:14:21  4:7:10  5:6:10

(Blackjack is a much closer approximation to its proportions than 12-EDO is to its proportions.)

I should have used a Blackjack scale where G = 0, but I didn't realize that until after I had done it, so C = 0.

Something pretty strange is happening between the C-major-7 and F#-minor-7 chords. I tried several different Blackjack tunings for the notes in these chords, because there was a shift at the F#-minor that didn't sound good, so I tried to smooth it out by changing some of the pitches in C-major.

I settled on the ones here by ear. The C chord has almost exactly the integer proportions 6:11:15 and is a sound I like, but the microtonal movement between these two chords sounds a little off.

I don't have an instrument that can be tuned this way and did it strictly "by eye", using these graphs:

If I had a keyboard tuned to the Blackjack scale I could play around with the tune a little more and probably come up with harmonies that sound a little smoother.

But even with this defect, I still feel that the Blackjack version is much more expressive than the bland 12-EDO version, and I prefer it.


In the correct orientation, where G=0, the Semitone values of the pitches I used above would transpose into the following:

24      23&1/6  22&5/6  20&1/2  20&1/2  19&2/3  20&5/6
17      17      15&5/6  15&1/2  13&1/2  13&1/2  12
14&1/3   7&1/3  12       5      10&5/6   4&1/6   8&5/6

Note, however, that if the Blackjack scale originated on G, it would not have all of these pitches, so some of them would have to be adjusted.