A proposal to simplify the notation of EDOs with bad fifths

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Dave Keenan
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Re: A proposal to simplify the notation of EDOs with bad fifths

Post by Dave Keenan » Tue Jul 24, 2018 5:53 pm

George Secor wrote:
Dave Keenan wrote:66 is 1:3:17 consistent. It is not 1:3:p consistent for any other prime p up to 19 (no higher primes were checked). So no useful JI-based notation is possible for it. But the following apotome-fraction notation is acceptable. Although :)~|: is not valid as 2 degrees, it's close.
66: :)|: :)~|: :/|: :/|): :(|\: :||\: :~||\: :(||~: :/||\: AF (same as 59)
I agree -- with one exception: according to my spreadsheet 143C :)~|: is indeed valid as 2 degrees of 66-EDO! :P
It's good that we agree on the notation, but it's strange that our spreadsheets disagree on this.

I've attached below, the spreadsheet I built last week for this purpose. It shows on a chart, how the size of each symbol's comma varies, as a fraction of the apotome, as the size of the fifth changes.

EDOs are listed under their fifth-size to the nearest cent. A table below the chart tells you how many steps-per-apotome each EDO has. You can then calculate the midpoints between steps, as decimal fractions of the apotome, and determine which symbols fall within the capture zone for each step. e.g. For an EDO with 2 steps to the apotome, a symbol must fall between 0.25 and 0.75 apotomes in order to correspond to 1 step.
comma apotome fraction vs fifth size.xlsx
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comma apotome fraction vs fifth size.gif
comma apotome fraction vs fifth size.gif (216.2 KiB) Viewed 220 times

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Dave Keenan
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Re: A proposal to simplify the notation of EDOs with bad fifths

Post by Dave Keenan » Wed Jul 25, 2018 3:21 pm

I suggest that, to reduce the total number of symbols required to cover all the EDOs up to 72, we adopt the alternative notation for 58-edo described in the note at the bottom of page 15 of the XH article. i.e.

Change it from
58: :/|: :(|(: :/|\:
to
58: :/|: :|\: :/|\:

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