Reply To: Octave overlap in uTune?

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#9172
tubbutec
Keymaster

I can already see the next question coming from someone else:

But what if I want a scale without the 1/1 entry?
Well there are two solutions to this. One involves math, the other makes use of a feature unique to µTune.

The µTune solution
µTune can deactivate certain notes in a scale. (In the scale editor this is the small arrow next to the note number). If you want to deactivate the root, just deactivate the repeating interval (2/1).
If you try to play a deactivated note, µTune will pick the nearest active note and play that instead.
Deactivated notes will be saved with the scale, and scale files are still compatible with the scala format. By the time of writing however the deactivation is ignored by other systems.

The math solution
This has actually nothing to do with µTune, but applies to all Scala compatible devices.

First of all it is important to understand how a scale is constructed in scala. There is always some base note (1/1) and all other intervals are defined relative to this note. So the entry 9/8 means: 9/8 * 1/1.
As you can see, it is not only unnecessary to include the 1/1 entry, changing it would also be meaningless as it is just a reference for all other intervals.

The scale is repeated with a certain interval, which is the last entry of the scale. In µTune this entry is marked with R, the repeating interval. In this case it it 2/1, an octave. So if all notes of the scale are used, the next notes will be 2/1*1/1, 2/1*9/8, and so on.

So if you want a scale, that does not include its root you must chose a new root. In the example above this would be 9/8. Now you divide all notes by 9/8 so the relations by all intervals are maintained.

00: (9/8) / (9/8) = 1/1
01: (4/3) / (9/8) = 32/27
02: (3/2) / (9/8) = 4/3
03: (16/9) / (9/8) = 128 / 81

Our new scale thus becomes:

01: 32/27
02: 4/3
03: 128/81
R: 2/1

Hoped this was more informative than confusing.