Search found 37 matches
- 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 ...
- 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...
- 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...
- 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...
- 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...
- 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...
- 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...
- 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 ...
- 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>.
- 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: