matrices, scale tree, other stuff

Here's another quick and not properly thought out e-mail.

The easiest way of finding the determinant of a matrix is to use a computer.
Spreadsheets these days seem to be able to do it. The inverse of a
non-square matrix is not defined.

Monzo:

>the result my spreadsheet gave me
>was 0. What does this mean?

In my terminology, the intervals you chose are not a basis. The determinant

| 4 -1 0|
|-2 0 -1|
| 2 -1 -1|

means equating the intervals (4 -1 0)h (-2 0 -1)h and (2 -1 -1)h. However,
any two of these will give the third. (4 -1 0)h = (2 -1 -1)h - (-2 0 -1)h.
So, one interval is redundant.

So the thing I was playing with a month or so ago is Wilson's scale tree. I
couldn't work it out from the web page. Anyway, there is another
interpretation. Take this:

2 3
5
7 8
9 12 13 11
11 16 19 17 18 21 19 14
13 20 25 23 26 31 29 22 23 31 34 29 27 30 25 17

5 is derived from 2 and 3. This means a 5 note MOS has 2 intervals of one
size and 3 of another. Similarly a 7 note MOS has 5 intervals of one size
and 2 of another and a 12 note MOS has 5 intervals of one size and 7 of
another.

The sizes of the generating intervals follow the same pattern. Has this
been mentioned? Also, an m&n scale, where n of one interval and m of the
other make up an "octave", can be an MOS iff m and n are mutually prime.

The neutral scale I mentioned a while ago is an MOS with the generating
interval a neutral third. Hence the "symmetric" tag I applied to it.

The time I tried an acoustic piano, it probably wasn't very well adjusted.
I could press the keys down alright, but no sound came out. I ended up
poking it with one finger to get the necessary force. The kids who'd had
piano lessons had no trouble, so it's all in the action.

Carl Lumma:

>I think somebody said they could play faster on an electric piano than an
>acoustic one. Many harpsichordists say their instrument is faster too.

I said I was faster on a cheap keyboard than an electric piano. This was
because "pressing" the keys worked better with the cheap keyboard. I also
said it was easier to control dynamics with the expensive one. Ideally, I'd
have one of each depending on what kind of music I wanted to play.

>Maybe for runs. But ask yourself why nobody plays Rachmaninov on a synth.

Yes. Rachmaminov wrote for a particular instrument, so you wouldn't expect
the music to transfer to another one. I keep asking myself why people still
play Bach on a piano, and "conservatism" seems to be the answer.

>There's more to speed than runs. Repetition is the most important place to
>have speed, and the piano has got everything else beat by a mile.

Rubbish. Sequencers are the thing. Record once, loop it, double the
tempo...

>Because
>the keys have momentum and move independently of one's finger, and because
>the action has momentum and moves independently of the key.

Ah. Is this for repeating the same note?

>It should not be difficult to build a synth action that has all the
>desirable properties of a piano action, and requires no regulation. It
>should also be possible to design synth actions that do new types of
>things, that pianos don't.

Sure. Regardless of the keyboards, though, there are some places where
synths have the upper hand. One is that it's much easier to retune a synth.
This is the killer for me. Another is that you can get a higher variety of
sounds from a synth. Only playing one voice at a time as if it were an
acoustic instrument isn't showing it in its best light. For that matter,
using the preset voices doesn't give me what I want.

I'm not much interested in a synth that sounds like any particular acoustic
instrument. I am interested in one that plays in a less stale way. For a
sample base synth, this would mean cross-fading between samples as I go up
and down the keyboard, or the key velocity changes. My TX81Z, bless it, is
great for this. If you don't like the sound, try sending it through guitar
effects.

Yes, the quantum harmonics stuff I mentioned before is pretty much fuzzy
logic. It's still close to QM in that they can both come from probability
matrices.

The thing about this American Indian tribe and colours is a bit deeper than
has been mentioned. As well as having a single name for blue and green,
they were found to consider blue and green as more related than native
English speakers. I don't know if similar experiments have been done with
French/English speakers and different kinds of brown.

Another set of experiments was done with people who speak languages where
pitch carries meaning. I think Mandarin Chinese, Thai and Swedish are
examples, I don't know who the experiments were done with. It was found
that they perceived pitch with different parts of their brains, so it was
more to do with meaning than emotion.