I’ve been trying to represent 494EDO in Sagittal, but I don’t know how to make it work. I’ve read somewhere on this forum that the Promethean level was specifically designed for 494, but there are some inconsistencies I can’t figure out.

First of all, the Athenian subset works perfectly, with consistent flag arithmetic and everything, and with symbols spaced by either 2 or 3 degrees of 494:

2, 4, 6, 9, 11, 14, 16, 18, 20, 22, 25, 27

But once extended to Promethean, there are a few problems. (99/98) maps to 7 degrees, which doesn’t have an exact half, and (513/512) maps to 1 degree, which is inconsistent with and . Do I need to start using schisma accents here, or is Promethean enough?

## 494EDO and Promethean accidentals

### Re: 494EDO and Promethean accidentals

I did come up with a consistent mapping, but at the expense of breaking the Athenian symbol , and switching its ordering with , so I’m not sure how useful this is.

= 1°

= 2°

= 3° (2+1)

= 4°

= 5° (1+4)

= 6° (4+2)

= 7°

= 8° (4+4), also (1+7)

= 9°

= 10° (1+9)

= 11°

= 12° (1+11)

= 13°

= 14°

= 15° (4+11)

= 16° (14+2), also (9+7)

= 17° (4+13)

= 18° (9+9)

= 19° (1+9+9)

= 20° (9+11)

= 21° (14+7)

= 22° (9+13)

= 23° (14+9), also (1+9+13)

= 24° (13+11)

= 25° (14+11)

= 26° (13+13)

= 27° (14+13), also (1+13+13)

= 1°

= 2°

= 3° (2+1)

= 4°

= 5° (1+4)

= 6° (4+2)

= 7°

= 8° (4+4), also (1+7)

= 9°

= 10° (1+9)

= 11°

= 12° (1+11)

= 13°

= 14°

= 15° (4+11)

= 16° (14+2), also (9+7)

= 17° (4+13)

= 18° (9+9)

= 19° (1+9+9)

= 20° (9+11)

= 21° (14+7)

= 22° (9+13)

= 23° (14+9), also (1+9+13)

= 24° (13+11)

= 25° (14+11)

= 26° (13+13)

= 27° (14+13), also (1+13+13)

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### Re: 494EDO and Promethean accidentals

Hi Ash. Welcome to the forum. You're certainly on the bleeding edge in wanting to notate 494-edo. It isn't quite correct to say that Promethean was designed

*for*494-edo. It's more that 494-edo (really 47-eda [equal division of the apotome {chromatic semitone}]) was used to help decide where to close Promethean, i.e. where to stop generating what might otherwise have been an almost endless series of arrow-like symbols involving every possible combination of flags, many of which would have been very close in size to one another.

But that certainly does suggest that we ought to be able to make a notation for 494-edo using only Promethean symbols. However I could not find, in searching through emails, anywhere that George or I proposed such a notation, let alone agreed on it. Good on you for having a go.

For other readers, Promethean can be seen here: http://sagittal.org/SagittalJI.gif, where you'll notice that it actually notates 52 ratios to the apotome, because you can count 26 symbols to the half-apotome (56.8c). So there are 5 symbols (3 single-shaft) in Promethean that are outside any 47-eda set.

I can confirm that the above are all correct, based on the primary comma role for every symbol.First of all, the Athenian subset works perfectly, with consistent flag arithmetic and everything, and with symbols spaced by either 2 or 3 degrees of 494:

2, 4, 6, 9, 11, 14, 16, 18, 20, 22, 25, 27

I did find email from George that mentioned that and were additional to 47-eda, but are required to complete the Olympian level. Fortunately, we don't need to use for 7 degrees because we have , the 23-comma (736/729), for 7 degrees. Also, both and map to 16 degrees, so if one of them breaks the flag arithmetic, we can ditch that one.But once extended to Promethean, there are a few problems. (99/98) maps to 7 degrees, which doesn’t have an exact half, and (513/512) maps to 1 degree, which is inconsistent with and . Do I need to start using schisma accents here, or is Promethean enough?

The other thing to be aware of is that while 494-edo is 17-odd-limit consistent (and possibly {1, 3, 5, 7, 9, 11, 13, 15, 17, 23}-consistent), it is not 19-odd-limit consistent, so you have two choices for how to map prime 19, which relates to the mapping of and other symbols containing that flag (left scroll or rai).

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**Posts:**366**Joined:**Tue Sep 01, 2015 2:59 pm**Location:**Brisbane, Queensland, Australia-
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### Re: 494EDO and Promethean accidentals

Good work on that proposed notation above.

I just figured out that 494-edo is not a very good approximation of 47-eda. Here's how Promethean notates 47-eda, from the file sag_ji2.par that we made for Scala. The offset symbols with the red text are not part of 47-edo. Note that we have allowed flag arithmetic to break rather than apply to the wrong degree.

For 494-edo, it might be preferable to use only Athenian cores, with schisma accents. In this post I wrote:

I just figured out that 494-edo is not a very good approximation of 47-eda. Here's how Promethean notates 47-eda, from the file sag_ji2.par that we made for Scala. The offset symbols with the red text are not part of 47-edo. Note that we have allowed flag arithmetic to break rather than apply to the wrong degree.

Symbol Comma Degree of 47-eda -------------------------------- 513/512 1 5120/5103 2 2187/2176 3 896/891 4 144/143 5 4131/4096 6 736/729 7 99/98 7.5 19683/19456 8 81/80 9 41553/40960 10 64/63 11 57/56 12 55/54 13 45927/45056 14 49/48 15 46/45 16 45/44 16.3 16767/16384 17 6561/6400 18 416/405 19 36/35 20 176/171 21 33/32 22 4096/3969 23 405/392 23.5 8680203/8388608 24 729/704 25 373977/360448 26 8505/8192 27 885735/851968 28

For 494-edo, it might be preferable to use only Athenian cores, with schisma accents. In this post I wrote:

George and I aren't so sure the Promethean [JI notation] level was a good idea (a bit like the Greek gods not thinking Prometheus' gift of fire to the mortals was a good idea ). You may find, somewhat paradoxically, that you actually need more core symbols in Promethean than you do in Olympian. That's because the most common ratios all have Olympian notations that use Athenian cores. I think that cryptic comment in George's brilliant JI notation spreadsheet, "The herculean & olympian levels are highly recommended", should actually read, "The promethean level is deprecated". After all, there's nothing wrong with Athenian. But the Promethean symbols have to exist, to be used for less common commas in Herculean and Olympian

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### Re: 494EDO and Promethean accidentals

If we simply adopt the above 47-eda notation as a notation for 494-edo, we could justify the use of for 3°494 by interpreting it as with its 5-schisma accent dropped. You can see in the JI Notation Spreadsheet, that represents the 5×17-kleisma (256/255).

To justify the use of as 23°494, we have to interpret it as :n: with its mina accent dropped, where :n: represents the 31-medium-diesis (32/31). And similarly its apotome-complement can be 24°494 as the 31-large-diesis (67797/65536).

To justify the use of as 23°494, we have to interpret it as :n: with its mina accent dropped, where :n: represents the 31-medium-diesis (32/31). And similarly its apotome-complement can be 24°494 as the 31-large-diesis (67797/65536).

### Re: 494EDO and Promethean accidentals

All of that makes sense, although I'd personally like to preserve flag arithmetic as much as possible.

I still have a few questions though.

Are 494edo and 47eda different enough for it to be useful to use different notations for them? In particular for 494, would you recommend using only Athenian symbols with schisma accents, the full Promethean notation, or some compromise? And if a compromise is feasible, are there tiers to the Promethean level, with some symbols being safer or more commonly used than others?

I still have a few questions though.

Are 494edo and 47eda different enough for it to be useful to use different notations for them? In particular for 494, would you recommend using only Athenian symbols with schisma accents, the full Promethean notation, or some compromise? And if a compromise is feasible, are there tiers to the Promethean level, with some symbols being safer or more commonly used than others?

- Dave Keenan
- Site Admin
**Posts:**366**Joined:**Tue Sep 01, 2015 2:59 pm**Location:**Brisbane, Queensland, Australia-
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### Re: 494EDO and Promethean accidentals

Fair enough.

Yes.I still have a few questions though.

Are 494edo and 47eda different enough for it to be useful to use different notations for them?

I think, only Athenian with schisma accents. It would be nice if the unaccented symbols could be regularly-spaced, but since 47 is prime, that's impossible. But if you had a particular temperament, and hence a particular generator, in mind for producing useful subsets of 494-edo, that might inform which alterations should have unaccented symbols, which might require using some non-Athenian Prometheans.In particular for 494, would you recommend using only Athenian symbols with schisma accents, the full Promethean notation, or some compromise? And if a compromise is feasible, are there tiers to the Promethean level, with some symbols being safer or more commonly used than others?

A good rule of thumb is that you can determine if one symbol is more common than another by summing the prime factors above 3 in its comma ratio, irrespective of whether they are in the numerator or denominator. The symbol with the lowest sum will be more common. See the table at the end of this post, viewtopic.php?p=299#p299, and the paragraph preceding the table.