Sagittal addition: sensisept

Sensisept is an example of a temperament that has issues with symbol addition. With this notation, the flags add correctly, but there are pairs of symbols that don't add up.

[<1, -1, -1, -2], <0, 7, 9, 13]>

/| [-4, 4, -1> (-7, +19)
|) [6, -2, 0, -1> (+10, -27)
//| [-8, 8, -2> (-14, +38)
/|) [2, 2, -1, -1> (+3, -8)
)||( [-3, -1, 2> (-4, +11)
||\ [-7, 3, 1> (-11, +30)

If you add |) + //| , the tempered result is )||( , as you can see if you add the numbers in the right-hand column. But if you add the monzos, you get [-2, 6, -2, -1> 729/700, which isn't in the list. There isn't anything you can add either to |) or to the alternative .//| to get )||( . There's just one alternative that works out, and that's:

|) + '|) = )/|\

The problem with )/|\ is that either /| has to be replaced with '|( , or /|) has to be replaced with '(| . Keeping /| allows ||\ to be replaced with ~~||: /| + )/|\ = ~~|| . But there's nothing you can add to /| in order to get '(| . Besides, /| + |) = /|) is much easier to remember. And replacing //| with '|) would require adding '|( + /| : two different symbols for the same interval.

These are the sorts of things that happen with temperaments. Probably the best that can be done in general is to make sure that the flag combinations make sense.

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> Sensisept is an example of a temperament that has issues with symbol
> addition. With this notation, the flags add correctly, but there are
> pairs of symbols that don't add up.
>
> [<1, -1, -1, -2], <0, 7, 9, 13]>
>
> /| [-4, 4, -1> (-7, +19)
> |) [6, -2, 0, -1> (+10, -27)
> //| [-8, 8, -2> (-14, +38)
> /|) [2, 2, -1, -1> (+3, -8)
> )||( [-3, -1, 2> (-4, +11)
> ||\ [-7, 3, 1> (-11, +30)
>
> If you add |) + //| , the tempered result is )||( , as you can see if
> you add the numbers in the right-hand column. But if you add the
monzos,
> you get [-2, 6, -2, -1> 729/700, which isn't in the list. There isn't
> anything you can add either to |) or to the alternative .//| to get
)||(

The adding of the prime exponent vectors is irrelevant.

There is no problem with using |) + //| = )||(

If flags add then values should add.
If flags don't add then we don't care if the values add or not.
If values don't add then flags should not add.
If values add then we don't care if the flags add or not.

-- Dave Keenan

Dave Keenan wrote:

> The adding of the prime exponent vectors is irrelevant.
> > There is no problem with using |) + //| = )||(
> > If flags add then values should add.
> If flags don't add then we don't care if the values add or not.
> If values don't add then flags should not add.
> If values add then we don't care if the flags add or not.

Okay, that simplifies things. I assume that a notation where the flags (and values) add is preferable to one where the flags and values don't add (unless it's unsuitable for other reasons), but if that doesn't work out, it's not a problem.

I'm in the process of transferring files to my laptop in preparation for a move in a couple of weeks, so it might be a while before I can get back to working on notations.

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@...> wrote:
> Okay, that simplifies things. I assume that a notation where the flags
> (and values) add is preferable to one where the flags and values don't
> add (unless it's unsuitable for other reasons), but if that doesn't
work
> out, it's not a problem.

Agreed.

Regards,
-- Dave Keenan