Search found 37 matches

by herman.miller
Sat Mar 20, 2021 11:09 am
Forum: Linear Temperament notations
Topic: 5-limit ripple (12p&23p) notation
Replies: 3
Views: 3670

5-limit ripple (12p&23p) notation

I've been trying to work out Sagittal notations for each of the temperaments in Paul's Middle Path paper. 5-limit ripple, with the generator mapping [<1 2 3] <0 -5 -8]>, presents an interesting quirk. It's possible to notate it using the 5-limit Sagittals, but watch out! The comma symbols appear to ...
by herman.miller
Sat Mar 20, 2021 9:59 am
Forum: Linear Temperament notations
Topic: general methods for linear temperament notation
Replies: 31
Views: 17547

Re: general methods for linear temperament notation

I think the easiest way to explain how to calculate wedge products by hand is to explicitly write out the basis vectors (you might call them e1, e2, e3, e4 for a 7-limit temperament ... or maybe e2, e3, e5, e7 would be preferable). Take 7-limit meantone as an example. [<1 2 4 7] <0 -1 -4 -10]> We wa...
by herman.miller
Sat Mar 20, 2021 9:33 am
Forum: Linear Temperament notations
Topic: general methods for linear temperament notation
Replies: 31
Views: 17547

Re: general methods for linear temperament notation

There's basically two things that I find wedgies / wedge products useful for. One is to calculate the TOP tuning of a temperament, taking three elements at a time to find commas, and calculating the TOP tuning for each of those commas. In most cases, one of those will be the TOP tuning for the tempe...
by herman.miller
Fri Mar 19, 2021 10:32 am
Forum: Linear Temperament notations
Topic: general methods for linear temperament notation
Replies: 31
Views: 17547

Re: general methods for linear temperament notation

Wedgies are useful for some things, but you can easily calculate them from mappings if that's what you have. At least for rank 2 temperaments the wedge product is straightforward to calculate, and for higher ranks I think there's a way to do it with determinants of matrices. The wedgie is just a sor...
by herman.miller
Thu Mar 11, 2021 11:27 am
Forum: Equal Division notations
Topic: Notation for Oneirotonic 8 nominal scale
Replies: 8
Views: 5361

Re: Notation for Oneirotonic 8 nominal scale

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 su...
by herman.miller
Mon Mar 08, 2021 1:07 pm
Forum: Linear Temperament notations
Topic: Quadritikleismic (68&72 13-limit)
Replies: 3
Views: 3517

Re: Quadritikleismic (68&72 13-limit)

One thing to note if you're wanting to notate quadritikleismic is that :|): (64/63) and :|\: (55/54) are equivalent in this temperament: both work out to be [+1, -16>. This is also the case with the combinations :/|): (36/35) and :/|\: (33/32) = [+0, +3>, as well as :(|): (729/704) vs. :(|\: (8505/8...
by herman.miller
Sun Mar 07, 2021 5:38 am
Forum: Linear Temperament notations
Topic: myna temperament notation
Replies: 1
Views: 3608

myna temperament notation

Myna temperament (7-limit 4p&27p or 11-limit 31p&58p) is one that might be a good test case for different notation strategies. With the mapping [<1 -1 0 1 -3] <0 10 9 7 25]>, it's going to need many different sizes of accidentals to fill the gaps between the fifths, and it doesn't get any be...
by herman.miller
Sat Mar 06, 2021 10:06 am
Forum: Linear Temperament notations
Topic: miracle temperament
Replies: 6
Views: 4844

Re: miracle temperament

:||): for 52 is certainly a valid option, and I don't have any strong preferences. I like your reasoning that it's the apotome complement of :|): better than my suggestion of :~||(: as the sum of :/|: and :/|\: . As for the extra symbols beyond the 72-EDO notation, I like being able to name a pitch ...
by herman.miller
Fri Mar 05, 2021 11:39 am
Forum: Linear Temperament notations
Topic: miracle temperament
Replies: 6
Views: 4844

miracle temperament

I've made a chart for the proposed miracle notation. I had to come up with an accidental for +52 and there aren't many options, so I went with :~||(: [-9, 5, -1, 0, 1> based on the sum of :/|: [-4, 4, -1> and :/|\: [-5, 1, 0, 0, 1>.

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by herman.miller
Thu Mar 04, 2021 11:22 am
Forum: Linear Temperament notations
Topic: Mavila notation
Replies: 4
Views: 4055

Re: Mavila notation

Chart of the proposed mavila notation:

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