Negri temperament

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herman.miller
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Negri temperament

Post by herman.miller »

Negri divides the perfect fourth into four equal parts, so we really only need names for the three notes between A and D, D and G, etc. In 19-EDO it goes A B:b: B:#:/C:b: C:#: D; 29-EDO has A B:!!/: B:/|:/C:\!: C:||\: D. It makes sense to use the :||\: for -9 negri generators, but we'll need :/|: for -19 so that we can spell the minor third as D : F:/|: . So for +10 generators, I think it makes more sense to use :)||(: . So we could notate the 9-note scale from A to G as A B:!!/: B:)||(:/C:)!!(: C:||\: D E:!!/: E:)||(:/F:)!!(: F:||\: G. Here's a list of suggestions for other intervals:

-19 :/|:
+10 :)||(:
-9 :||\:
+1 :|||(:
-18 :|||):
+11 :(|||~:
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Dave Keenan
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Re: Negri temperament

Post by Dave Keenan »

Good to hear from you, Herman.

I agree those are valid, except I get -18g, not +11g, for :(|||~: . One different suggestion I have is to use :/|\: for +10g, based on extending the mapping of the 124 to 126 cent generator to 0 -4 3 -2 14]. :/|\: is used in 48edo which supports Negri temperament. This mapping of prime 11 also allows :/|||\: for -18g. I'm not sure what use you see for +1g and +11g, but the prime 11 mapping allows :|||\: for +1g. But I don't have any unaccented symbol for +11g, or even a good symbol to drop the accents from.

Chain of fifths
gens	symbol
---------------
-4	C:G etc
-8	C:D etc
+20	B:C E:F
-28	:#: or :/||\:
-19	:/|:	≡ 1 mod 4
+10	:/|\:	≡ 2 mod 4
-9	:||\:	≡ 3 mod 4

9-MOS nominals
gens	symbol
---------------
-9	:||\:
-18	:/|||\:
-27	:/|||\::||\:
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herman.miller
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Re: Negri temperament

Post by herman.miller »

I do like the idea of :/|\: for +10 and :|||\: for +1. I'm working on the score for my Negri piece now and I'm using the +1 to make sense of the note spelling for voice leading purposes (see the image where D :|||(: is followed by E :)||(: )

https://drive.google.com/file/d/1NO-qWj ... sp=sharing

I might not have a need for +11, but it could be used to respell B :\!: using A or F :/|: with G, if there's ever a need for that.
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herman.miller
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Re: Negri temperament

Post by herman.miller »

I found a potential use for +11 if I notate this part in E:/|\: major:

Image

Ignore the red notes: Dorico is trying to be helpful and warn me that the harp can't play these notes. If I want to notate the B:\!: in the first bar as some kind of A leading up to the B:/|\: in the next bar, it would have to be A +11. But it might be easier to just leave it as B:\!: in this case, or rewrite it in F:\!/: major. I haven't yet figured out whether the piece as a whole is better written in E:/|\: minor or F:\!/: minor.

Image

I tried the "image" and "insert image" buttons but they don't seem to be working for me. Is there another way to add images to a post?
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Dave Keenan
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Re: Negri temperament

Post by Dave Keenan »

Sorry Herman. I somehow missed your previous post until now.

The F:\!/: notation does seem simpler, at least in those few bars. But I'd hate for the decision to be forced on you by the lack of a symbol for +11g (175 ¢ when the generator is 125 ¢, i.e. in 48edo). The only suggestion I have for +11g is :X\: which is really a symbol for -37g (assuming the mapping I gave above), which is only the same as 11g in 48-edo. But if you are unlikely to ever need a symbol for -37g it could work.

Regarding attached images: We currently have turned off the option to automatically display them. Maybe this is a bad idea, and it may be reviewed in future. But in the meantime, in order to display each one, you need to obtain its URL by right-clicking on its filename in the Attachments tab (in the area below the reply-editing pane) and choosing "Copy Link". Then paste this into the editing pane and enclose it in an [img]...[/img] or [image=<width>]...[/image] BBCode, as you will see if you now edit your post.
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רועיסיני
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Re: Negri temperament

Post by רועיסיני »

I don't think it's best to use :X\: for +11 as it literally means :||\::/||\: = -9-28 = -37. I guess it's fine if the piece is explicitly in 48edo and you use other enharmonic equivalences of it (but in this case why not just notate it in 48edo...)
Anyway, I ran a search and didn't find any primary commas that interpreted in 13-limit Negril (which seems to be the logical extension of what you base your notation of) as 11 or 17 mod 28. If I try to find higher limit primary commas that given 11-limit POTE Negri's fifth of 701.136 cents temper to about the size of 11 generators and try to make up mappings for other primes so they give +11, I get that :(X~: works if we choose to represent 19 with -17 generators (although +12 gives a much better approximation, unfortunately no symbol for +11g) and :~X: works if we choose to represent 23 with -43 (although +34 gives a better approximation, however it's positive while most other primes are negative, so -43 may be acceptable).
If I search for secondary commas though I get :.::|||):, :`::|||\: and :.::/|||\:. Each of which can be used as is (I'm too tired today to think which one would be the best), but I wouldn't recommend either of those to be used with the accidental dropped, as :|||): has a really strong 7-limit connotation (that contradicts its usage as +11g), and :|||\: and :/|||\: seem to already be used, for +1 and -18 generators respectively. This makes me like :.::/|||\: the most as the literal interpretation works for it with -18+29 = 11 (because the schisma is -29 generators in negri), and is also the true meaning of this Herculean symbol.
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רועיסיני
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Re: Negri temperament

Post by רועיסיני »

When I think about it again :.::/|||\: is problematic because the accent points in the wrong direction, as the schisma is negative in most of the Negri EDOs (in particular any Negri tuning with flatter fifth, or equivalently, sharper generator, than 29), so this leaves is only with :`::|||\: where the accent points in the right direction. Another option would be to notice that the accent is actually worth +10g here, so if you can have many accidentals on the same note maybe :/|\::|||\:, or conversely, :|\::/|||\:, would be better.
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