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 Forum index » How-tos » Micro Tuning
Are there hex harmonic keyboard mappings for 31 & 41et?
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Octahedra



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PostPosted: Wed Apr 22, 2009 12:19 pm    Post subject: Are there hex harmonic keyboard mappings for 31 & 41et? Reply with quote  Mark this post and the followings unread

I've been working out key mappings of various scales to special keyboards, to decide how much they might help with the kind of microtonal work I'm getting into.

31 and 41 equal temperament both fit into the Hunt system (Tonal Plexus) which has built-in automatic pitch-bend retuning of your synth. Although the key colour coding is designed for 41 only.

Now for the Axis hexagonal keyboards. The whole point of this layout is that it's isomorphic - you can transpose by playing the same thing in a different place on the keyboard. You don't need to change your finger positions as on a piano to reach different sets of black and white notes.

I tried to find isomorphic mappings of 31 & 41et for this keyboard. Starting from C at the bottom middle; fifths going upwards; minor thirds up & left; major thirds up & right. But in both cases you don't get every note in every octave.

I've drawn it all out. The red & blue bands show the octaves and the light/dark code is for natural, sharp/flat, double sharp/flat etc. No octave band ever gets a complete set of all 31 or 41 notes!

Have I proved that it's impossible, or is someone going to find a hideous mistake in my working out? scratch

Gordon


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Failed attempt to map 31 equal temperament to hexagonal harmonic keyboard
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Octahedra



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PostPosted: Fri Apr 24, 2009 11:11 am    Post subject: Reply with quote  Mark this post and the followings unread

I found a different set of intervals for the 3 keyboard axes and tried those. Up = fifths; up & left = seconds; up & right = fourths...

41et is still unuseable like this.

31et seems to be fine now. Everything has sloped over a bit. The unbroken range goes from a D# (bottom left-ish) to a G (top right-ish) giving over 4 octaves. There are some notes above and below that range, which I've drawn round in red, but they're going to be very hard to use because of the gaps in the scale near the corners of the keyboard.

Some octaves have 5 or 6 notes appearing more than once, so it might be possible to get a couple more notes than 31 per octave without losing the isomorphic layout. But definitely not 41...

Gordon


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31 equal temperament on hex keyboard: probably OK
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xjscott



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PostPosted: Fri Apr 24, 2009 7:37 pm    Post subject: Reply with quote  Mark this post and the followings unread

Not every mapping covers all notes. In your first you are skipping 18 and 10 steps which are both even, so you won't have any keys that are an odd number of steps from your starting point.

I can see you chose that to maintain the 5ths and thirds, and so that's what you got - a subset of the tuning that maintains those intervals in the mapping. Obviously, by retaining 5ths and thirds in the same positions, you are stuffing 31 or 41 notes into the same physical space as was 12 before and that just isn't physically possible.

The 5ths and 3rds arrangement kind of sucks anyway though.

There are dozens of mappings that work well for either of those tunings, and for any tuning for that matter.

Just pick one and work with it. That's what I do. In other words, pick any old mapping, starting with ones that cover all the keys. Then play with it and see where all the intervals are. Doing this, I find there are really no bad mappings with any given scale. There are only different arrangements.

Some mappings work well for some things, others for others. One consideration might be where the chromatic scale falls out of the mix, if that is a consideration for a piece.

As far as which keyboard, I like a velocity response, so I got the Axis. The Opal is another good choice. For a larger layout with more keys and velocity sensitivity as well, there are the Starr Microzones. He makes some square grid ones called Z-boards but the two hexagonal ones are the way to go, with either 288 keys on the U-648 or 810 keys on the U-990, depending on budget. One really cool feature about Microzones is the keys can be popped out and rearranged so you can have your own visual patterns appropriate to the particular tuning.
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seraph
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PostPosted: Fri Apr 24, 2009 11:40 pm    Post subject: Reply with quote  Mark this post and the followings unread

xjscott wrote:
One really cool feature about Microzones is the keys can be popped out and rearranged so you can have your own visual patterns appropriate to the particular tuning.


well...there ia a simpler solution I have already investigated Wink that's an hexagonal key with a round sticker I attached on it.
You can use stickers to visually mark pitches. Once you change tuning you can re-arrange the stickers Wink


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xjscott



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PostPosted: Sat Apr 25, 2009 1:02 am    Post subject: Reply with quote  Mark this post and the followings unread

I thought the easily removable keys thing was pretty cool. There had been an early Microzone prototype that used something like sticky tape and that had been criticized by one microtonalist who saw it. I asked Harvey about it and he said that was a long time ago and they now are in little rubberized recessions so you can just pop them in and out. Sounds pretty cool.

With the stickers and fixed keys, one would have to be peeling those stickers on and off all the time, and also the stickers would clash with the underlying color scheme of the fixed keys. That is unless someone did something totally crazy like have a custom build that was a solid color of keys so that the only color variations were from the stickers, but that sure seems like it would be a lot of trouble and then they'd have this single color instrument that would be kind of like one of those solid color jigsaw puzzles - something for only the most hard core of persons.
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PostPosted: Sat Apr 25, 2009 2:10 am    Post subject: Reply with quote  Mark this post and the followings unread

xjscott wrote:
...That is unless someone did something totally crazy like have a custom build that was a solid color of keys so that the only color variations were from the stickers

Very Happy
that's exactly what I told Peter Davies to do with my Chameleon Shocked


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PostPosted: Sat Apr 25, 2009 2:12 am    Post subject: Reply with quote  Mark this post and the followings unread

xjscott wrote:
...With the stickers and fixed keys, one would have to be peeling those stickers on and off all the time...

that is actually a good thing Shocked because I intend to "stick" to a particular tuning for a long time Wink

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Octahedra



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PostPosted: Sat Apr 25, 2009 2:32 am    Post subject: Reply with quote  Mark this post and the followings unread

xjscott wrote:
Not every mapping covers all notes. In your first you are skipping 18 and 10 steps which are both even, so you won't have any keys that are an odd number of steps from your starting point.


Surprised ...I thought there must be something right under my nose that I hadn't noticed! Makes perfect sense now.

xjscott wrote:
The 5ths and 3rds arrangement kind of sucks anyway though.


The makers of Axis were selling that as a feature - I thought it might make basic tonality easier. Never actually played the keyboard though, so I don't know how useful it really is.

In the end I did find a way to get all 41 notes (isomorphic) onto the Axis or Opal keyboard. The vertical axis is now in 4ths, not 5ths. The other two axes are only 1 step apart, which reduces the diagonal slope so you only get 4 orphaned notes in the corners. The range is about 3.75 octaves.

Both of the successful mappings here use more than 128 notes, so you need a TBX tuning box, or anything that can map a scale across more than one midi channel.

The ultimate colour coding would be to have a combined red, green & blue LED behind each key, so you can set any key to any colour! Dread to think what it would do to the price though. Shocked Shocked Surprised Sad

Also with scales this big, I'm beginning to wonder whether the notes you need to play together to make a chord, are now getting so far apart that there's less of an advantage to the isomorphic layout anyway...

Gordon


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xjscott



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PostPosted: Sat Apr 25, 2009 12:18 pm    Post subject: Reply with quote  Mark this post and the followings unread

"Less advantage compared to what though?" is the question to ask.

Figuring out transpositions in 41 on a traditional fixed keyboard is far more difficult than on an hexagonal fixed one.

The TP is specifically optimized for 41 so if one has a strongest interest 41 and its multiples through 205 then it makes good sense. If the goal is to find what keyboard arrangement is best for 205tET used for common practice music then look no farther, you have found what you need in the TP.

Once you have tons of notes in a fixed tuning keyboard, you have to have keys be closer together or have certain intervals be farther apart. That's a limitation of working with instruments in physical reality. (Obviously virtual reality systems are another possibility to get past these limits but I prefer to work with physical instruments that can be touched.)

3-d keyboards in a 3-D spatially experienced universe are not particularly practical for playing with fingers given the human anatomy design, so variations of 2-D are the next practical step up from 1-D. Of the three regular polygonal tilings, triangular, square and hexagonal, hexagonal has many advantages over the other two for musical keyboards.

There's also the option of going non-fixed and using dynamic tuning. One can pick a manageable subset at a given time and switch from subset to subset during the course of a piece. That's another tactic I use. Along with 2-d keyboards it is one of the two primary tactics for managing scale complexity. I discussed these in the xenharmonics seminar I gave at the e-m festival last year.

The physical key spacing and keyshape on the Axis is very good for performance and one of its advantages over the Microzones. The Microzones have different spacing and keys are flatter on top, so are conducive to a different performance style and types of pieces. There is a reasonable case to have both and use them for different things. Microzones have a big advantage in the larger numbers of keys so one can have a wider range for any given tuning and mapping. They also have an interesting collection of continuous controllers, such as the joystick.
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PostPosted: Sat Apr 25, 2009 3:50 pm    Post subject: Reply with quote  Mark this post and the followings unread

xjscott wrote:

There's also the option of going non-fixed and using dynamic tuning.


Jeff
That's nothing compared to the Samchillian Tip Tip Tip Cheeepeeeee

Cool


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xjscott



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PostPosted: Sat Apr 25, 2009 4:11 pm    Post subject: Reply with quote  Mark this post and the followings unread

Ha ha, I remember reading about that thing. It's the one where the pitches are played differentially rather than absolute pitch, right?

(watches video)

Yep.

Great for melody, possibly not so much so for harmony.

(continues to watch melody)

Oh, I hadn't realized it constrains itself to scale steps rather than chromatic ones. And I don't think it had an LCD last time I read about it.

It's very interesting. He's patented the differential pitch thing, and the prototype he has it looks like he doesn't want to go into production with, so it makes it a tricky thing for others to experiment with. Oh, so he has cross platform software for noncommercial use that implements it available it now. Have you used it?

(video continues)

Arg, so he does do chords after all...

It's not a non-fixed tuning instrument though, it uses a single tuning at a time as the basis of its differential operations.
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Octahedra



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PostPosted: Mon Apr 27, 2009 10:15 am    Post subject: Reply with quote  Mark this post and the followings unread

xjscott wrote:
"Less advantage compared to what though?" is the question to ask.


Ah sorry, I meant compared to any non-isomorphic kind, really. In the default isomorphic 12 note tuning a lot of important chords have the notes so close together you can memorise the patterns visually - and sometimes play up to 3 notes with one finger. I just thought that if a chord has notes a long way apart (as is more likely with a lot of notes per octave), it's harder to find all the notes as you play, and so the isomorphic layout might not be such a help for bigger scales.

What I'm after is a composition tool for trying ideas out before I program the notes into my sequencer. I don't need velocity - in fact I don't really like it on my conventional keyboard. Much more of an organist than a pianist at heart...

xjscott wrote:
There's also the option of going non-fixed and using dynamic tuning. One can pick a manageable subset at a given time and switch from subset to subset during the course of a piece. That's another tactic I use.


Sounds powerful if you can get your head round it and make it work, but maybe a bit inflexible for me. Are you talking about live or studio work where you use that technique? I always work in a sequencer and never perform, and I like setups where I can just jump to any part of the piece at any time and edit it. So I never have sysex or program change messages going around, and all mix parameters and midi controllers are automated as envelopes in Sonar.

These keyboards are so expensive I've always had a backup plan of abandoning the keyboard and just getting the Tuning Box so that all my synths can work microtonally (with scales of more than 128 notes) when controlled by the sequencer. I should probably just shut up for the moment - and go and write more microtonal music with my current setup! See how that goes first...

Gordon
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xjscott



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PostPosted: Mon Apr 27, 2009 10:52 am    Post subject: Reply with quote  Mark this post and the followings unread

I use these techniques in both studio and live work.

I don't have any of the problems you are imagining, things can stay synchronized to their position in the sequencer during cueing when working in the studio. It's not clear to me why that would be a problem.

You are on the PC right? Is the TB really the only choice that can handle scales with more than 128 notes? My own program has been able to handle scales with more than 128 notes for years (currently it can handle more than a million pitches in a piece if one wanted to, but I doubt that's useful), but it's on the Mac only so not a choice for you. It hadn't occurred to me that it would be the only one that could do that. I don't think it's true though. On the PC, Fractal Tune Smithy also has various kinds of support for scales with essentially unlimited numbers of notes, so that's another option for PC users.

Anyway, based on what you are saying, it sort of sounds like you would work best with a large fixed set of notes in a configuration where you could just learn the positions of notes. Given that you don't need velocity sensitivity, the TP would seem to be the ideal choice for your interests, it's 205tET layout is certainly the most dense tuning ever placed on a keyboard and thus can approximate a wide range of tunings while maintaining the relative position of each key so you don't have to be continually relearning new layouts.

BTW, the thing about pressing three keys at once is not an advantage, it's just something that can be done kind of. It's a cool gimmick to demo to people, but I don't feel it's all that musically useful in performance unless one is only playing pieces in a 12 note tuning primarily consisting of root position major and minor triads.
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Octahedra



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PostPosted: Tue Apr 28, 2009 5:34 am    Post subject: Reply with quote  Mark this post and the followings unread

xjscott wrote:
You are on the PC right? Is the TB really the only choice that can handle scales with more than 128 notes? My own program has been able to handle scales with more than 128 notes for years (currently it can handle more than a million pitches in a piece if one wanted to, but I doubt that's useful), but it's on the Mac only so not a choice for you.


Thanks - I know about LMSO and it looks good, but as you guessed I can't use it because I'm PC based. I never thought Scala could do multi-channel scales because it wasn't advertised (It's really hard to find out anything about Scala even when you've got it downloaded and running!) but I had a big rummage around and eventually found this in the help area:

Quote:
In Scala version 2.0 and higher, mappings can also be created and edited using the Edit->Edit mapping menu. Furthermore they are also used for real-time MIDI relaying (Tools->Microtuning MIDI Relay). There there are two ways to use them. Normally, with a single mapping to be used for one input channel or all (Omni). Or, with a multichannel mapping which consists of a set of single mapping files with the same name followed by an underscore and a MIDI channel number from 1 .. 16. For example, if map_1.kbm, map_2.kbm and map_3.kbm are present in the same directory as the filename given (either one of those) then they function independently for MIDI input channels 1, 2 and 3 and messages from other channels will not be mapped, therefore ignored. This is useful if you stack multiple keyboards or have a microtonal keyboard which uses multiple channels to overcome the 128 note number limitation.


So I'll give this a go for now - if I can get Scala to intercept Sonar's midi output before it gets to the midi out port.

Gordon
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xjscott



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PostPosted: Tue Apr 28, 2009 10:26 pm    Post subject: Reply with quote  Mark this post and the followings unread

Octahedra wrote:
I never thought Scala could do multi-channel scales ... but I had a big rummage around and eventually found this in the help area:

Quote:
a multichannel mapping which consists of a set of single mapping files with the same name followed by an underscore and a MIDI channel number from 1 .. 16. For example, if map_1.kbm, map_2.kbm and map_3.kbm are present in the same directory as the filename given (either one of those) then they function independently for MIDI input channels 1, 2 and 3 and messages from other channels will not be mapped, therefore ignored.


Wow, that is great! I didn't know Scala could do that.
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Octahedra



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PostPosted: Tue Jun 09, 2009 4:29 am    Post subject: Reply with quote  Mark this post and the followings unread

So after all that time, I've finally got round to doing something about this.

The exotic keyboards on the market are very expensive for me, and just seemed too much of a risk - without being able to try before buying. So I scrapped that idea.

My H-Pi Tuning Box arrived today, and the components I've ordered to build my own 31-per-octave keyboard are turning up from time to time. Other tunings will have to make do without their ideal keyboard for a few years yet....

Gordon
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seraph
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PostPosted: Tue Jun 09, 2009 4:49 am    Post subject: Reply with quote  Mark this post and the followings unread

Octahedra wrote:
...and the components I've ordered to build my own 31-per-octave keyboard are turning up from time to time...


Gordon
could you elaborate on that Question
thanks Exclamation

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PostPosted: Tue Jun 09, 2009 5:19 am    Post subject: Reply with quote  Mark this post and the followings unread

seraph wrote:
could you elaborate on that Question


I'm going to use a midi encoder from MGB (makers of circuits for the H-Pi gear) and build my own keyboard - probably something like this image below. I've got a huge pile of lever microswitches, which were cheap enough, if a bit clicky, and I still have to work out what's the best way to build playable keys onto them. It's for composing rather than performing, so if it's more-or-less playable then that will have to do.

A lot of work to do yet... I'm still thinking about how to build the frame or board to mount the keys on, too.

Gordon


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