li’l miss’ scale oven: scale mapping & quantizing

Scale Mapping and Quantizing with the IQ Kitchen Appliance

Sometimes you want to map one scale to another scale. This sort of operation was once the provence of advanced Excel wizards who worked long and hard performing these deft acts of mysterious scale manipulation.

LMSO makes the operation of scale mapping extremely easy and intuitive. In LMSO, the key is to use the Interactive Quantizer (IQ) Kitchen Appliance. Conceptually it works like the groove quantizer on your sequencer, but it works with pitch instead of rhythm. Now you can control the groove of both your beats and your melodies.

Step by Step Guide

Let’s just dive in and try this out. Here’s how to create a 12 note subset of 41 tone equal temperament. That means we’re going to make a scale with twelve notes, but those twelve notes are going to be from 41 tone equal temperament. The advantages of scales that repeat over twelve notes are many for those who have standard western keyboard controllers — it’s convenient for mapping to those keyboards, and of course it also can be familiar and easy to play. This means 12 note destinations are a a safe and comfortable place to get started with doing scale mappings and quantizations. It’s also a shockingly powerful technique that might just change the way you work with tunings.

Start by opening a twelve note scale like 12tET, Pythagorean, or 1/4 comma meantone. Do this by dropping relevant scale file on the LMSO icon, or by the double-clicking on the file, or by selecting Open in the File menu.
Select Oven->New Oven to create a new recipe based on the template oven you just opened. (I recommend opening a new oven from a template oven in this way both because the scales will show their derivation, and so you don’t accidentally overwrite the original scale after making the edit.)
From the “Scale Pattern” menu, select “Interactive Quantize”. A pink window will open up next to your oven with your scale shown graphically.
Here’s the big step. Since there are 1200 cents in an octave, the step sizes in 41 tones per octave are are 1200/41. So type "1200/41" into the “nearest cents” box in the Quantizer. As you do this, notice how the displays are updated to provide instant feedback so that you can see and understand exactly what the effects of the edit will be.
Press the [Quantize] button. The Quantizer closes and your Recipe’s Scale Pattern is mapped to the new scale.
Change the name of the scale to "12 of 41tET” or "12->41tET” or whatever seems to make sense to you, and save your new scale by selecting File->Save.

Exercises

Now you try it.

First try to create a 12 note subset of 17 tone equal temperament instead of 41.
Once you have that down and are playing with it (a nice sounding scale, by the way), try a stretched and compressed octave version, using a 1213 cent octave and a 1188 cent octave.
Save all these files. Bake them to your synths. Improvise — you are sure to be inspired.
How do the compressed and stretched variations compare in mood?
If you’re on a roll now and all gung ho and breathless with exuberation, drunk with the possibilities (which I certainly hope you will be!), try out 12 of 43tET and compare it to 12 of 41tET. Can you sense the different moods that these two scales convey? Congratulations! You are now on the path to the deep tuning wisdom of the ancients.

Advanced topics

You may also map your scale partially to 41tET, you could have used the slider to choose the percentage of quantization desired. The percentage feature is quite useful when using the “nearest odd limit” setting, since intervals near just intervals have a lot of shimmer, which is called pleng in Indonesia, sort of meaning vitality and movement rather than the static deadness (as it is thought of in Indonesia and other parts of the world) of the simple just intonation intervals, especially distressing when played on harmonic timbres, such as from wavetable synthesizers. This timbres really sound a lot more alive by tuning them to almost-but-not-quite just intonation.

Because you quantized to a destination specified in cents, your Scale Pattern now appears as cents. But because it is actually a pattern of equal divisions, Srutis Difference would be better choice for displaying the pattern. Go to the Scale Pattern Menu and select “Srutis Difference” as the pattern type. I recommend always doing this after Quantizing to an equal pattern. Also, sruti-based scales are trivially easy to compress and stretch with only one step — you just change the Repeat Ratio. Now compare LMSO’s ease in scale stretching against spending hours working in a spread-sheet — well there is no comparison!

Alien Artifacts?

Quarter-Comma Meantone is a famous temperament discovered by Pietro Aaron in in 1523—almost 500 years ago.

That’s odd, quarter comma meantone looks almost the same as 19tET. What could it mean?

And it’s well-nigh indistinguishable from 31tET. Coincidence? Or space-alien conspiracy of ancient astronauts? We think the facts speak for themselves!

The scale that you made will intriguingly have different sizes of fifths and other intervals instead of all being the same. You can easily alter which ones appear where by bringing your Oven window to the front and then using the Mode Rotate Left, Rotate Right, and Reverse commands in the Scale Pattern Menu. Make sure that you have all or none of the Scale Pattern selected when you do this since the commands can also be applied to any selected subset or section of the scale.
Did you know that if you map 12 to 31tET or 19tET, the result is nearly identical to meantone temperaments from the Renaissance and Baroque era? That’s some powerful trivia to use if anyone thinks what you are doing is too futuristic or weird. Just proves there is nothing new under the sun — scale quantizing operations like we are trying out here are a lost technique many hundreds of years old!

Secret Tuning Knowledge

So why would you want to do this? Actually, this sort of 12 note mapping in particular is one of the best kept secrets in pop music. Did you know that many top hits do not use 12 note equal temperament? Instead, the insider studio wizards at the big studios typically retune to a mapping of 12 into another temperament, just as we have done here. They do this because the result is something that is subtley and intriguingly different from what folks are used to hearing. This provides aural interest—and big sales.

Sounds amazing right? Try playing along in 12 tone equal temperament with a striking pop hit on CD or the radio. Sometimes you find that your notes just don’t sound quite the same and the chords sound “off”. You might want to try out different mappings of 12. This also explains why bands doing cover songs can never get the same sound that appears on the original studio albums. Now you know the secret. Be careful though, this knowledge is a dangerous weapon.

Now the pop approach makes it a no-brainer to cram striking and intriguing tunings right into mainstream music with zero cost—the keyboard plays the same and the song is recognizable, but has a subtle edge of aural interest that teases and tweaks the ears of the listener, creating solid gold. You can experiment with different temperaments and create different moods and effects that can complement the effects you are trying to convey with your music.

Again, this is an extremely powerful technique. It is so powerful it is rightly termed a weapon. With knowledge comes responsibility. Use your new knowledge with caution and respect.

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