Search found 33 matches

by herman.miller
Thu Mar 25, 2021 11:38 am
Forum: Linear Temperament notations
Topic: 5-limit misty (12p&51p) notation
Replies: 9
Views: 140

Re: 5-limit misty (12p&51p) notation

That works reasonably well for 5-limit misty, although 7-limit misty [<3 5 6 6] <0 -1 4 10]> would map :~|): as (-5, +21), but that differs from (+3, -12) by only 0.06 cents which is negligible. Now if we take :|~: as the 23-comma 736/729, we can use a 2.3.5.23-limit temperament with 23 mapped to (+...
by herman.miller
Wed Mar 24, 2021 11:35 am
Forum: Linear Temperament notations
Topic: 5-limit misty (12p&51p) notation
Replies: 9
Views: 140

Re: 5-limit misty (12p&51p) notation

You could use :/|: and :\!: up to a point. If you want to notate the full 99-note MOS, you'll need triple sharps and triple flats for some of the notes, since E:\!: is 4 generators above C, which is 4 generators above E. Here's what that would look like with single and double sharps. You could alway...
by herman.miller
Tue Mar 23, 2021 1:23 pm
Forum: Linear Temperament notations
Topic: 5-limit misty (12p&51p) notation
Replies: 9
Views: 140

Re: 5-limit misty (12p&51p) notation

[⟨3 0 26], ⟨0 1 -4]⟩ and [ ⟨ 3 5 6 ] ⟨ 0 -1 4 ] ⟩ are equivalent -- the wedge product for both is <<3 -12 -26]] -- but [<3 -3 14|, <0 1 -4|] has a wedge product of <<3 -12 -2]] so there must be some mistake. I'd leave the mapping and correct the generator size to 1903 cents. 7-limit misty (which has...
by herman.miller
Tue Mar 23, 2021 10:41 am
Forum: Linear Temperament notations
Topic: 5-limit misty (12p&51p) notation
Replies: 9
Views: 140

5-limit misty (12p&51p) notation

Misty [<3 5 6] <0 -1 4]> is one of the few 5-limit rank 2 temperaments that would benefit from using schisma accents. I worked out a chart of 5-limit notation for misty[99] and I was able to notate most pitches with 5-limit sagittals with two exceptions. For those two pitches (a quarter tone below G...
by herman.miller
Mon Mar 22, 2021 12:35 pm
Forum: Linear Temperament notations
Topic: Schisma accents in regular temperament notation
Replies: 1
Views: 40

Schisma accents in regular temperament notation

I was looking at 5-limit hanson temperament and I noticed that the schisma tempers to 0.6 cents, and thus the schisma accent might actually be useful if you have a large enough scale to notate. It turns out that the schisma maps to +53 generators of hanson, so that's not likely to be useful, but I w...
by herman.miller
Sun Mar 21, 2021 12:07 am
Forum: Linear Temperament notations
Topic: 5-limit ripple (12p&23p) notation
Replies: 3
Views: 61

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

You can respell G#:Eb as G#:D# without any trouble. It makes more sense to notate G#. as Ab -- I almost ended the sentence there, but that would be confusing since Ab would have looked like Ab. -- using . and ' as accidentals makes it a bit awkward to mention them in a sentence. You can see how that...
by herman.miller
Sat Mar 20, 2021 11:09 am
Forum: Linear Temperament notations
Topic: 5-limit ripple (12p&23p) notation
Replies: 3
Views: 61

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: 28
Views: 426

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: 28
Views: 426

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: 28
Views: 426

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...