## Search found 33 matches

- 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 (+...

- 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...

- 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...

- 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...

- 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...

- 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...

- 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 ...

- 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...

- 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...

- 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...