Notation for Oneirotonic 8 nominal scale

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well_temperedfox
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Notation for Oneirotonic 8 nominal scale

Post by well_temperedfox »

Has anyone considered devising a variant that allows for 8 nominals instead of just 7 for scales like father[8] or "oneirotonic". My keyboard currently is set up for 18 EDO and it's rather frustrating to try to write the white notes with accidentals. How would this work in sagittal?

I realize 8 notes could be written with accidentals but it seems very hard to read, maybe someone can explain to me how it works. It says 18 is a subset of 36 on the sagittal periodic table.
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herman.miller
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Re: Notation for Oneirotonic 8 nominal scale

Post by herman.miller »

I'm not familiar with "oneirotonic", but I experimented with using an 8-nominal notation for one of my songs that I wrote in the "Fibonacci" tuning (page 22 of Erv Wilson's "Golden Horograms of the Scale Tree" paper, http://www.anaphoria.com/hrgm.pdf). Dorico doesn't support 8-nominal scales, but you can use Finale, or just draw the notes on paper the old-fashioned way by hand. I find those sorts of notation to be more confusing than they're worth for the most part, so I usually limit myself to no more than 7 nominals (not always based on a chain of fifths). If you want to notate 8 nominals with 7 staff positions, one way to do that is to reserve one sagittal to represent the interval between the closest two nominals in your basic scale. But I'd need some basic information about your oneirotonic 8 nominal scale to make any more specific suggestions.
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Dave Keenan
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Re: Notation for Oneirotonic 8 nominal scale

Post by Dave Keenan »

Sagittal is primarily a universal set of accidentals. We've always said they can be used with notations having other than 7 nominals, but we've never got into how best to do that on a staff. So we can't help you with the latter, but we can suggest a suitable accidental to use in extending the chain of generators beyond the initial 8.

I found info about oneirotonic scales (LLsLLsLs) here: https://en.xen.wiki/w/5L_3s

Like the term "diatonic" it covers multiple rank-2 temperaments.

The oneirotonic temperament that includes 18edo (7/18-octave generator, 1-octave period) is called A-Team and has a mapping for the factors 2, 5, 9, 21 of [⟨1 0 2 4], ⟨0 6 3 1]].

This is equivalent to a 2, 3, 5, 7 mapping of [⟨1 1 0 3], ⟨0 1.5 6 -0.5]].

The 8-generator chroma is 8×7 mod 18 = 2 steps of 18-edo or 133 cents.

The simplest sagittal for that chroma is probably :|||): which represents 243/224 = [5 -5 -1⟩ and has an untempered size of 141 cents. And of course its downward counterpart :!!!): .

It might be possible to find an 8-generator accidental that is valid for more than one of the four oneirotonic temperaments.
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Dave Keenan
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Re: Notation for Oneirotonic 8 nominal scale

Post by Dave Keenan »

So a chain of 7/18-octave generators would be notated Q:!!!): L:!!!): O:!!!): J:!!!): M:!!!): P:!!!): K:!!!): N:!!!): Q L O J M P K N Q:(|||: L:(|||: O:(|||: J:(|||: M:(|||: P:(|||: K:(|||: N:(|||: . Of course, that's 24 notes. You only need the middle 18 to notate 18edo.

In pitch order, 18edo could be J K:!!!): J:|||): K L M:!!!): L:|||): M N:!!!): M:|||): N O P:!!!): O:|||): P Q J:!!!): Q:|||): (J).

But you'd probably prefer a notation that has the nominals being monotonic with pitch. That requires a symbol to go from J to K:!!!): which means -5 generators. -5×7 mod 18 = 1 step of 18edo or 67 cents. The simplest sagittal for that job would be :(|\: in a secondary role as 28/27.

Then 18edo can be J J:(|\: K:(!/: K L L:(|\: M:(!/: M M:(|\: N:(!/: N O O:(|\: P:(!/: P Q Q:(|\: J:(!/: (J).
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yahya.abdal-aziz
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Re: Notation for Oneirotonic 8 nominal scale

Post by yahya.abdal-aziz »

So, Dave, your basic "oneirotonic scale (LLsLLsLs)" would be J K L M N O P Q (J), with 3 "third-tone" steps in an 8-nominal oneirotonic scale, roughly corresponding to the 2 semitone steps of a 7-nominal diatonic? And the smallest EDOs for these two cases are 18-edo and 12-edo resp.

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Yahya
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Dave Keenan
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Re: Notation for Oneirotonic 8 nominal scale

Post by Dave Keenan »

Almost correct. As described in the notation section of the xen wiki article, JKLMNOPQ(J) is the mode LsLLsLsL. And as with the diatonic, the smallest oneirotonic EDO must be the one that sets L=2 and s=1, namely 5×2 + 3×1 = 13edo. 18edo has L=3, s=1.
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Re: Notation for Oneirotonic 8 nominal scale

Post by Dave Keenan »

well_temperedfox wrote: Thu Mar 11, 2021 7:32 am I realize 8 notes could be written with accidentals but it seems very hard to read, maybe someone can explain to me how it works. It says 18 is a subset of 36 on the sagittal periodic table.
You can read off the table, that 36edo is notated with CD=DE=FG=GA=AB=6, EF=BC=3, #=3, :|): =1.

Centering on D for symmetry, 36edo can be notated in the Evo flavour as:

D D:|): E:b::!): E:b: E:b::|): E:!): E E:!): F:!): F F:|): F:#::!): F:#: F:#::|): G:!): G G:|): G:#::!): G:#: G:#::|): A:!): A A:|): B:b::!): B:b: B:b::|): B:!): B B:!): C:!): C C:|): C:#::!): C:#: C:#::|): D:!): (D)

Or in the Revo flavour as:

D D:|): E:!!!): E:\!!/: E:!!): E:!): E E:!): F:!): F F:|): F:||): F:/||\: F:|||): G:!): G G:|): G:||): G:/||\: G:|||): A:!): A A:|): B:!!!): B:\!!/: B:!!): B:!): B B:!): C:!): C C:|): C:||): C:/||\: C:|||): D:!): (D)

Of course alternative spellings are possible. e.g. G:#: could be A:b: and G:|||): could be A:!!):.

The periodic table suggests that 18edo be notated as a subset of 36edo, which means simply taking every second note of the above. i.e.

D E:b::!): E:b::|): E F:!): F:|): F:#: G:!): G:|): G:#: A:!): A:|): B:b: B:!): B:!): C C:#::!): C:#::|): (D)

or

D E:!!!): E:!!): E F:!): F:|): F:/||\: G:!): G:|): G:/||\: A:!): A:|): B:\!!/: B:!): B:!): C C:||): C:|||): (D)

So yeah, compared to a MOS-nominals notation, it's Accidental City!
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Re: Notation for Oneirotonic 8 nominal scale

Post by yahya.abdal-aziz »

Dave, thanks for that link, and the gentle corrections. ("Almost correct" is "wrong", methinks!).

But shouldn't the N@ represent a "minor oneirofourth (aka major fourth, rising fourth)" rather than a "minor oneirofifth (aka major fourth, rising fourth)"?

Regards,
Yahya
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Dave Keenan
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Re: Notation for Oneirotonic 8 nominal scale

Post by Dave Keenan »

J(KLM)N is an oneirotonic "fifth" in the same way that A(BCD)E is a diatonic fifth. i.e. by counting the nominals.
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