# Jorgensen's 7+5 temperament

24 August 2013 Filed in: Tuning
Theory

After posting “JY’s Infra-Worlds” on my blog, I received the following comments:

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so I started investigating!

The scale I had used for that piece was a combination of 7EDO and 5EDO “the former on 0 cents, the latter on 100 cents to get 12 tones” in the words of John H. Chalmers (of course 7EDO is mapped to the white keys and 5EDO to the black ones of an Halberstadt keyboard).

I had then thought I could shift the starting point of 5EDO to get other combinations and tried starting it at 50 cents empirically arriving very close to “Jorgensen’s famous 7 + 5 temperament” mentioned by Paul Erlich that, I guess, is the following one:

These are the degrees of 70EDO (in cents from the root note):

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These are the degrees of 7EDO:

0., 171.429, 342.857, 514.286, 685.714, 857.143, 1028.571

If the scale starts on C, D is at 171.429 cents so Ab (that is part of 5EDO) must be at 771.429 cents if they have to be 600 cents apart “as in conventional equal temperament” as stated by Paul Erlich.

From that note you calculate the other degrees of 5EDO (starting at 51.429):

51.429, 291.429, 531.429, 771.429, 1011.429 (0., 240., 480., 720., 960.)

So, the combination of these 2 scales is:

0., 51.429, 171.429, 291.429, 342.857, 514.286, 531.429, 685.714, 771.429, 857.143, 1011.429, 1028.571

Using the following degrees of 70EDO:

0, 3, 10, 17, 20, 30, 31, 40, 45, 50, 59, 60