Re: Laka 17-limit minimax planar temperament
- As an owner of a Tonal Plexus, I'm interested in this but I'm afraid the learning curve of regular temperament theory and terminology is rather steep for me. Could you help me a little bit? You list a number of temperaments that would be approximated well by 205tet, right?
For instance, what's the double cicle of diaschismic temperament? And what are hemithirds?
How many notes do those scales have? If less than 205, then the pitches belonging to the scale would have to be found among the 205 keys (the other keys could be re-tuned to duplicates). If more than 205, some kind of selection would have to be made. (Using what principle?)
Unless you are only talking about the 205 keys of the keyboard (midi notes), and what temperaments could be mapped onto them.
My experience with the TPX is that even though any tunings can be mapped to the keys, and even though in the default tuning, transposed patterns have similar shapes, it is not really a genralized keyboard; it definitely works best with the default 205tet tuning. With that tuning, it's an excellent tool for trying out harmonies and melodies.
The 41tet fifths are practically pure, and you can approximate any other interval with a maximun error of 3 cents. That's part of the reasoning behind 205 but it has also to do with the keyboard layout. It's divided into 41 areas that each have 5 keys, and the keys are physically different so that moving on a 41-chain of fifths you always move to a corresponding, same-shaped key in another area. So the middle keys of these areas make up a chain of 41 virtully pure fifths, and to make a correction (ca. 6 or 12 cents up or down) from those 41tet pitches you play a key one or twor steps lower or higher than the middle key.
--- In firstname.lastname@example.org, "genewardsmith" <genewardsmith@...> wrote:
> --- In email@example.com, Graham Breed <gbreed@> wrote:
> > The problem is, 205 isn't that great a division. It was
> > chosen because it's a multiple of 41, and 41 is good.
> It depends on what you use it for. It's a great division not only for quanic and laka, but 5-limit amity, where it delivers 5-limit microtempering with a temperament which is not too terribly complex, and gets you away from the circle-of-fifths of helmholtz or the double circle of diaschismic, with more accuracy than diaschismic or hanson. It's also pretty good for hemithirds.
- --- In firstname.lastname@example.org, Mike Battaglia <battaglia01@...> wrote:
>This is a tough question.
> On Wed, Oct 5, 2011 at 8:16 AM, Keenan Pepper <keenanpepper@...> wrote:
> > Basically the only thing slendro and slendric have in common is that they both have scales with 5 roughly equal steps in an octave. Slendric is very accurate, but slendro, like all gamelan scales, is very inaccurate and based on an aesthetic of ever-present beating. Slendro is an irregular circulating temperament where all five empat intervals are used as strong consonances; slendric only really gets good when you have at least 11 notes.
> Does the actual slendro even make sense if viewed as 1L4s? I vaguely
> remember hearing that it was more like 3L2s or something.
My personal pet theory predicts that the Platonic ideal slendro is 3L2s (or, alternatively, indistinguishable from 5-equal, but that contradicts the observation that the modes are distinguishable), but in practice I don't know. The gamelan angklung scale, which is basically 4 notes out of slendro, definitely sounds like ssL within a 3/2, which would imply that the full slendro scale is a superpyth-like 2L3s.
I'm sure that if you gave a gender or something tuned perfectly to 1L4s slendric to most Balinese musicians, they wouldn't even bat an eye. They'd say "of course it's slendro, what else could it be?". But of course this doesn't mean that 1L4s is the ideal slendro tuning; it only means that the requirements for being an acceptable slendro tuning are none too strict.
There's no shortage of papers about slendro tuning. This one: lit.gfax.ch/Indonesian%20Music--slendro_balungan_tunings.pdf says there are more than 2 step sizes, so it's something like 1L3m1s or 2L2m1s.
All I can say for sure about slendro is that:
* The five steps are so similar in size that you can't tell for sure what the scale imprint is.
* But, the different modes have distinguishable flavors.
* All five "empat" intervals (~3/2) are used similarly; none is treated as a dissonance.
Maybe this means that the "conceptual" scale imprint is simply aaaaa, even though each 'a' is not exactly equal.