Using Chromatic Remapping To Generate Musical Inspiration

Previously, I looked in some depth at the Ableton 'Scale' effect, one of the quieter backwaters of the 'built-in' MIDI effects. That blog started out concentrating on how to invert a keyboard, but ended up producing lots of chromatic maps that take incoming notes and map them to different outgoing note pitches. Which led to another investigation, the results of which you are now reading...

While I was producing the variations on chromatic inverted scales for the previous blog, I realised that these were all specific cases of a much more general set: the set of remapping of incoming notes to single outgoing notes on a one-to-one basis. In other words, each and every incoming note is converted to one, and only one, outgoing note. There are a lot of these maps: there are 12 input notes and 12 output notes, so I think that means that there are 12! combinations, which is just under 480 million. So me making 30-odd of them available is a tiny fraction of the whole set! And that's where I realised that I could make them all available in a MaxForLive plug-in utility, and MIDI_ChromatixT_mr was born.

In the screenshot, MIDI_Chromatix_mr is shown in its normal location in the MIDI processing chain - just in front of the Scale effect (Alternatively, you could use any of the many available MIDI Scale-type effects available in MaxForLive). The diagram below shows how everything fits together:

Incoming notes are mapped to different pitches by MIDI_ChromatixT_mr, and then restricted to the chosen notes in the scale set by the Scale effect. In the example screenshot above, the C minor preset scale has been altered so that only 5 output pitches can occur. This constrains the output notes to just the pitches C, D#, F, G# and A#. Incoming notes can be at any pitch, and they will be mapped to new pitches by the map. So an incoming A might be mapped to C, whilst an F could be mapped to a D#, etc. 

The grid in MIDI_ChromatixT_mr sets the mapping of incoming notes. In the screenshot above, the vertical cursor line is showing an incoming D (moving across from left to right), whilst the orange marker is in the A# row (counting up from bottom to top). Now, whilst it is possible to edit the mappings (Click on the 'Auto/Fix' button so it shows 'Fix', and the mapping will be fixed and editable), the 'Generate' button creates new random mappings with a single click. So it is easy to just keep clicking on the 'Generate' button until it has created a random mapping that you like - the usual M4L store/recall buttons on the left can be used to save it if you wish. 

But the really interesting part of MIDI_ChromatixT_mr is the 'Auto' button, when it is set to 'Auto' then the 'Generat' button will be pressed every time the bar count to the left of the 'Auto' button matches the number set in the pop-up selector on the far left. So if the selector is set to 4, then every 4 bars, a new chromatic mapping will be produced, and incoming notes will be mapped using that new mapping instead of the one used in the previous 4 bars. This then repeats every 4 bars.

What this means is that every time the bar count reaches the number of bars shown by the selector, then incoming notes will be mapped differently, using a new one of the millions of possible chromatic mappings. So whatever notes are in the (monophonic is recommended) track sequence that is driving MIDI_ChromatixT_mr, the output will be a scale-constrained version of the remapped versions of them. The D to A# mapping in one set of bars could be replaced with a D to G# in the next set of bars, then a D to F mapping in the next set of bars. 

It's a bit like shuffling cards and then dealing them out for a card game. The shuffling means that you get a different hand of cards each time, but the number of cards you get (and the game you are playing) are fixed. So whilst the notes get remapped to new pitched notes, they are still constrained to just the notes in the scale you have set. 

What this does musically is take a monophonic sequence in a track, and play those notes, remapped to new pitches whilst still being constrained by the scale, and yet the timing and velocity of those new notes remains exactly as it was in the original sequence. So it's a bit like an randomiser and a bit like an arpeggiator, but until that 'Generate' button is activated, the mapping is fixed, so if you find a mapping that you like, click on the 'Auto' button so that it says 'Fix', and then session record the output with the 'doughnut' session record button in Live. Of course, an easy alternative is just to let it free run, generating new mappings every 4 or 8 bars, and to record everything, and then just extract the bits you like. 

In a few minutes, MIDI_ChromatixT_mr will run through lots of variations of your monophonic track sequence, all following the timing and the velocity exactly, but with different pitches every time the 'Generate' happens. It's a bit like having an assistant who can keep running through variations, one after the other, and who never gets tired or bored, and never loses patience. MIDI_ChromatixT_mr is an automatic 'Can you just do that twisted around a bit?' generator.

Demonstration 1

SoundCloud demo 001

The problem with random music generators is the they are often too random, and when they do come up with something interesting, then it has happened and gone almost before you realise. MIDI_ChromatixT_mr repeats each random variation for the number of times that you set the bar selector, and so if it is set to 4 bars, then you will hear the same variation 4 times, before it moves on to the next one. This is probably best heard rather than described in words, so here's a demonstration of a simplee piano and bass duet produced entirely from an 8-note track sequence and a 4 note bass track sequence, with MIDI_ChromtixT_mr producing all the variations every 4 bars. Once the 12 notes have been set in the track sequences, everything else is just a straight recording. 

Demonstration 2

SoundCloud demo 002

This second demonstration has the same bass, and has two independently variations piano lines using the same technique, spaced an octave apart. 

The top line adds a 16 note sequence, but with a random velocity added to provide additional variety. Again, once set running, the recording has had no user manipulation. 

Download

As usual, MIDI_ChromatixT_mr can be downloaded from MaxForLive.com. Enjoy!

The Name?

Why such a weird name? Well, I thought about all sorts of variations (!) on chromatic remapped, or even diffuser (cryptographers call this type of device a 'diffuser') and the first version was completely manual and was 'Chromatix. When I then added the automatic 'every n-bars' generation feature, then it needed something to indicate time, so I added a 'T' at the end. As a result, you aren't likely to forget this M4L device.

Monophonic?

Yep. Try poly tracks and see what happens...

Scale Inversion of MIDI Notes...

Hidden away inside Ableton Live are some interesting comments. One that is in plain sight is in the presets for the 'Scale' MIDI Effect. If you look carefully at all of the sometimes exotically named scales, you will see one that is named 'Inverted and Useless'.

Now that got my interest immediately. Inverted keyboards have always fascinated me, and I had already done a MIDI Effect that could invert a keyboard, and lots more besides: MIDI f(x)_mr. But why would Ableton describe one of their own presets as 'Useless'? Here are the default 'Scale' settings, which pass notes through unchanged:

The mapping of input to output is very straight-forward:

Here is the 'Inverted' version, which takes the diagonal mapping and just reverses it, which intuitively ought to be fine - after all, all that has happened is that the diagonal now goes the other way, so the notes should too...

Unfortunately, when I tired playing the MIDI output of a keyboard through the Scale MIDI Effect using the 'Inverted and Useless' preset and driving a piano instrument, then I quickly learned why it was described as useless. Some arpeggios work ok, but others have sudden jumps of just under an octave, and some chords sounded very weird indeed, even when I deliberately adjusted them for the inversion. Something was definitely wrong... This needed deeper investigation with a specialist setup.

Investigation Setup

First, I created an arpeggio clip stretching over about three octaves, and then I surrounded the 'Scale' MIDI Effect with some display tools: two MIDI HugeNoter_mr 'big' note displays, and a variation of one of my favourite tools, the MIDIKeyMon_mr, which I described in a previous blog entry. (MIDIKeyMonFull_mr shows the whole MIDI keyboard range and has a summary scrolling window showing the notes played.) HugeNoter is great when you need to display notes in a way that is difficult to miss, and is available from MaxForLive.com.

But the important part of this setup is the Ableton 'Scale' MIDI Effect in the middle. As you can see, in the case shown in that screenshot a C3 note input has become a B3 output. So there's obviously some pitch changing going on, but C3 inverting to a B3 seems strange. So I wrote down the input and output of the Ableton 'Scale' MIDI Effect with the 'Inverted and Useless' preset:

After noting down all those inputs and outputs, here's part of what I got:

It isn't easy to see what's actually happening here, so here are plots of the input and output:

So the purple input is a rising series of notes, and appears as a sloping line going up from left to right. The blue-green output does have a series of descending notes, from 71 (B3) to 60 (C3), but either side of that descending series is a sudden jump - the output jumps from 48 (C2) to 71 (B3) when the input changes from 59 (B2) to 60 (C3), and the output changes from 60 (C3) to 83 (B4) when the input changes from 71 (B1) to 72 (C4). Both of these intervals are 13ths, which my head (and ears) don't really think of as an octave plus a semitone - they just sound wrong.

The results show why the 'Scale' effect only shows an octave grid - it is just working on an octave at a time, and mapping the notes in that octave to new values. For any rising scale then this is fine, but when you have an 'Inverted' scale, then you get jumps because each octave map is being transposed to try and do an inversion across the whole range. 

If we look at the whole range, then it looks like this:

And what the 'Inverted and Useless' scale effect preset is trying to do is turn those descending blue-green segments into an inversion of the rising purple line, and the effect is a broken series of invited scales with discontinuities at the ends of each octave:

What is really needed is an inverter that inverts properly over the whole range, of course! The 'Scale' effect is designed to provide a way of mapping rising scales to other rising scales, and it was never designed to invert the complete MIDI keyboard range.

But since I had started investigating, I wondered if there was any way to improve on the existing 'Inverted and Useless' preset. C3 mapping to B3 seemed wrong to me, so I looked at the theory behind inverting MIDI keyboards...

Theory: Inverting MIDI Keyboards

The limits of the MIDI keyboard range are:

Lowest Note. 

The lowest note on a MIDI keyboard is number 0, and this is normally referred to as C-2. (But it can be C-1 or C0 - see the next entry)

Middle Note.

There is some variation on MIDI note octaves (the '-2' in the example above) and the middle of the keyboard, because the original MIDI specification isn't very precise about which pitch is MIDI note 60, and so as a result Middle C can be C3 or C4 or even C5, and may be assigned MIDI Note Number 60, 72 or 84. MIDI equipment tends to use C3 = 60 and so that's what I will use here. (Look up 'Is Middle C C3, C4 or C5' or 'Is MIDI note number 60 = C3?' on your favourite Interweb search engine to see lots of people politely failing to agree...)

Highest Note.

The highest note on a MIDI keyboard is number 127, and this is normally referred to as G8 (or G9 or G10 - see the previous entry)

Keyboard ranges.

Most musical keyboards do not have 128 notes, and so they only provide a sub-set of the available notes. 5 octave, 61 note, C-C keyboards are common for professional synthesisers, but monosynths tend to have less notes (44 F-C on a Minimoog), and top-of-the-range workstations tend to have more (88 or more, and often not C-C). 

Octave numbering.

If you go up from A2, you get A#2, B2, C3, C#3... Octaves change when a new C starts (not when you go from G to A as you might expect!). Because the lowest MIDI note is a C (number 0), and the top note is a G (number 127), then the half way point happens in the 3rd Octave, and is between D#3 and E3. 

if we ignore the notes above 120, and consider MIDI as having a range from 0 to 120 (C-2 to C8), then the middle of these 121 notes is number 60, C3. By using sub-sets of the full 128 notes, then any note can be used for inversion, although maximising the usable keyboard range seems to be a good goal, and inverting around D#3 and E3 gives 127 usable notes, whilst inverting around the D#3/E3 (63/64) boundary gives 128 notes. 

Exploring inverted scales

The 'Inverted and Useless' preset is just the opposite diagonal to the default chromatic diagonal scale grid.

Because the grid used by the Scale effect is just one octave, then the lowest note when the Base is set to C is a C, and the highest note is a B - this can be seen by looking at the second row up on the grid - the pattern of darker notes reflects the 2 and 3 groupings of 'black/enharmonic' keys on a piano keyboard. If you plot one keyboard against another, then you get a useful diagram of the corresponding keys:

Which explains why the C3 gives a B3 output. Note that this has all white keys mapped to white keys, and all the black keys mapped to black keys, except for the F to G# mappings.

However, there is an extra row in the grid, and if you use this, then you can do a different diagonal: shifted one cell upwards. This gives a different output for a C, and a different diagram.

This time, the mapping is almost all opposites (back mapped to white), except for the G, G# and F keys. Here are the two grids, side by side:

                  

                                         Inverted and Useless                                          Scale Invert mr1

When you play these, then the 'Inverted and Useless' is obvious because it shifts the C downwards to a B. Otherwise they are both chromatic inversions over an octave, and both have a jump at each end of the octave. For someone like me, who likes a C to play as a C, then I prefer 'mr1'.

Alternative inversions

Here are some alternative inversions that I experimented with, trying to minimise the discontinuities, or perhaps, trying to spread them out across the octave.

                                                                                Scale Invert mr2

This scale moves the C from the top row to the bottom row, and so the octave jump is between the C and the C#, instead f the B and the C. It's a different feel, but still an inversion.

The interesting results so far then inspired the following explorations.

                                             Scale Invert mr7                                        Scale Invert mr 8n

The above scales put the jump in a different place on the keyboard, but there are now two discontinuities per octave...

                                          Scale Invert mr1m                                         Scale Invert mr1s

The above scales spread the discontinuities wider... Scale Invert 1s puts the  main discontinuity between E and F, whilst Scale Invert 1m  puts it between F and F#. It really depends on what key you are playing in, really. Having a set of different inverts is actually a great way of creating new melodies, chords or chord progressions, because it removes any bias or preference your fingers have for well-worn scales or fingerings. 

                                                 Scale Invert mr1w                                   Scale Invert mr1q 

The above scales spread the discontinuities wider and in different ways.

                                                                                Scale Invert mr1x

And finally, almost not an inverting scale at all!

Now it is possible to input these scale grids into the Scale effect, but that is a lot of work, and so here's a shared 'Scale Invert' folder containing all of the chromatic scales above, plus several extras, and they are all free for you to download: Scale Invert

MIDI HugeNoter_mr 

HugeNoter_mr is just a way to show MIDI notes and note numbers in a big way. I use it when developing utilities or doing investigations, as in this blog. It shows, from top to bottom, the MIDI note number (in dark blue), the note and octave (in white), and the note and octave split, as described in this blog. The three small grey buttons at the top let you set the justification of the displayed note and octave. MIDI_HugeNoter_mr is available from MaxForLive.com.

MIDIKeyMonFull_mr

MIDIKeyMonFull_mr is a variant of the MIDIKeyMon, but adjusted so that you can see the whole of the MIDI note range without needing to select a range. It also has a scrolling display of previous notes played. A useful utility when working on scale effects... MIDIKeyMonFull_mr is available from MaxForLive.com.

Where's the dark version?

Available at MaxForLive.com.