### A proposal to simplify the notation of EDOs with bad fifths

Posted:

**Tue Nov 08, 2016 3:19 pm**for support and discussion of the Sagittal microtonal notation system

http://forum.sagittal.org/

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Posted: **Tue Nov 08, 2016 3:19 pm**

Posted: **Tue Nov 08, 2016 7:59 pm**

An immediate benefit of the above is that we obtain simple consistent notations for all 5n edos that have the same fifth size, and for all 7n edos that have the same fifth size, in a manner similar to the 12n stack shown in figure 10 on page 19 of , as follows:

Use the horizontal scroll bar below to see the rest of the accidentals.

Use the horizontal scroll bar below to see the rest of the accidentals.

Posted: **Tue Nov 08, 2016 8:57 pm**

All suggestions, questions and criticism of the above will be gratefully received.

Here are the proposed limma-fraction notations for 9, 16 and 23-edo.

I note that this does not constitute a single Mavila-temperament notation like the one given in figure 8 on page 16 of .

Here are the proposed limma-fraction notations for 9, 16 and 23-edo.

I note that this does not constitute a single Mavila-temperament notation like the one given in figure 8 on page 16 of .

Posted: **Tue Nov 15, 2016 11:34 am**

Here are all of the proposed apotome-fraction notations. These are the EDOs whose best fifths are wider than those of 22-edo (> 709.5 c). Those on the same row have the same number of steps per apotome, and differ only in the spacing of their nominals. This spacing can be obtained from the chart at the start of this thread. Those with a zero or negative number of steps per limma should only use the 5 nominals ACDEG. Mixed Sagittal is shown. The equivalent pure Sagittal symbols can also be used.

Here are all of the proposed limma-fraction notations. These are the EDOs whose best fifths are narrower than those of 19-edo (< 694.5 c). Those on the same row have the same number of steps per limma, and differ only in the spacing of their 7 nominals. This spacing can be obtained from the chart at the start of this thread. Pure Sagittal is shown. The equivalent mixed Sagittal symbols cannot be used for these notations, as # and b have no meaning as limma-fractions.

Here are all of the proposed limma-fraction notations. These are the EDOs whose best fifths are narrower than those of 19-edo (< 694.5 c). Those on the same row have the same number of steps per limma, and differ only in the spacing of their 7 nominals. This spacing can be obtained from the chart at the start of this thread. Pure Sagittal is shown. The equivalent mixed Sagittal symbols cannot be used for these notations, as # and b have no meaning as limma-fractions.

Posted: **Tue Nov 15, 2016 11:52 am**

Posted: **Tue Jan 03, 2017 2:04 pm**

Posted: **Tue Jan 03, 2017 6:15 pm**

That's great stuff George. Thanks. To help folks evaluate it (OK, to help me), I have a couple of requests.

1. Could you please give a table showing all the symbols you have used, in size order, and which apotome and limma fractions they correspond to. Similar to the one of mine that you quoted.

2. Could you please edit your existing tables to show where a symbol is not valid as the tempered version of its primary comma. Or putting it another way, to show where the comma you are using would have accent marks if it was notated in Olympian. Perhaps you could use asterisks for these and double-asterisks where you currently have asterisks.

1. Could you please give a table showing all the symbols you have used, in size order, and which apotome and limma fractions they correspond to. Similar to the one of mine that you quoted.

2. Could you please edit your existing tables to show where a symbol is not valid as the tempered version of its primary comma. Or putting it another way, to show where the comma you are using would have accent marks if it was notated in Olympian. Perhaps you could use asterisks for these and double-asterisks where you currently have asterisks.

Posted: **Thu Jan 05, 2017 9:06 am**

Posted: **Fri Jan 06, 2017 12:02 am**

For the benefit of other readers, I note that if I used asterisks in the way George has done, in my proposal, I think every symbol would have an asterisk, most would have two.

I agree that where a spartan is valid in its primary comma role we should use it there, as you have done with pai and tai , so I no longer support my previous proposal. However, although your current proposal unifies very-narrow-fifth notations, and separately wide-fifth-notations, it doesn't really simplify them, as it requires the learning of 7 non-spartan single-shaft symbols, most of which aren't even athenian but are from the rarely-used promethean set.

I remind you of an of mine that used prometheans, but they were all recognisable as spartans with an added left scroll.

I see no point in using non-spartans for these bad-fifth EDOs if the non-spartan doesn't even represent its primary comma. But rai slai and kai may be worth using.

And I don't have a problem with using Spartans where they are not valid. I note that this is different from not using them where they are valid. I agree we should use them where they are valid, but shouldn't shy away from also using them where they are not, if it simplifies the notations.

So I need to go back to the drawing board and come up with a new proposal that hopefully preserves what I see as the best of both our proposals so far. Please feel free to do the same.

I agree that where a spartan is valid in its primary comma role we should use it there, as you have done with pai and tai , so I no longer support my previous proposal. However, although your current proposal unifies very-narrow-fifth notations, and separately wide-fifth-notations, it doesn't really simplify them, as it requires the learning of 7 non-spartan single-shaft symbols, most of which aren't even athenian but are from the rarely-used promethean set.

I remind you of an of mine that used prometheans, but they were all recognisable as spartans with an added left scroll.

I see no point in using non-spartans for these bad-fifth EDOs if the non-spartan doesn't even represent its primary comma. But rai slai and kai may be worth using.

And I don't have a problem with using Spartans where they are not valid. I note that this is different from not using them where they are valid. I agree we should use them where they are valid, but shouldn't shy away from also using them where they are not, if it simplifies the notations.

So I need to go back to the drawing board and come up with a new proposal that hopefully preserves what I see as the best of both our proposals so far. Please feel free to do the same.

Posted: **Sun Jan 08, 2017 11:51 pm**