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Non-traditional key signatures

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Non-traditional key signatures

Postby motet » Mon Dec 18, 2017 5:53 pm

A while ago I made a how-to for non-traditional key signatures, surely one of the most arcane areas of Finale. I've revised it, but can't find where I posted it before, so I offer the revised version here.
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Re: Non-traditional key signatures

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Re: Non-traditional key signatures

Postby Peter Thomsen » Mon Dec 18, 2017 10:17 pm

Nice work, motet!

You can also create the non-standard key signature as a Linear Key Format.
It will not be correctly transposeable along the {circle of fifths}, but it will work in that particular transposition, and it will play back correctly.
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Re: Non-traditional key signatures

Postby motet » Mon Dec 18, 2017 10:49 pm

Does what I've done not play back correctly? I confess to not knowing what linear and non-linear mean in this context.
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Re: Non-traditional key signatures

Postby Peter Thomsen » Mon Dec 18, 2017 11:05 pm

I, too, am not sure why they are called “linear” and “non-linear”.

But the basic facts are:

Linear always, “automatically”, plays back correctly, since there is a “linking” between layout and playback.

In the non-linear key signature there is no linking between layout and playback.
This means that in a non-linear key signature Layout and Playback are fully independent.
You can have a Playback that is completely different from the Layout.
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Re: Non-traditional key signatures

Postby motet » Tue Dec 19, 2017 6:10 am

This plays back correctly, so I guess my instructions sync playback and layout.
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Re: Non-traditional key signatures

Postby motet » Tue Dec 19, 2017 7:16 am

Linear seems better since you can make a natural appear in the key signature. Haven't gotten the pitch to work right--time to ponder the documentation again. I am still a novice.
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Re: Non-traditional key signatures

Postby motet » Tue Dec 19, 2017 7:46 am

as long as the upper and lower halves of the scale are formed by the same sequences of whole and half steps (such as the tetrachords in a standard diatonic scale), the system of keys is considered a linear key format.

I'm not sure I understand this right. 1-2-3-4 and 5-6-7-1 have the whole steps and half steps in the same place in a major scale, but not in a minor scale. Yet a minor scale is one of the hardwired linear key formats.

It seems like a linear key system is a definition of a whole set of keys, like the majors keys are a set of keys.
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Re: Non-traditional key signatures

Postby Peter Thomsen » Tue Dec 19, 2017 6:36 pm

as long as the upper and lower halves of the scale are formed by the same sequences of whole and half steps (such as the tetrachords in a standard diatonic scale), the system of keys is considered a linear key format.

This is a quote from the manual, trying to explain Linear Key Format.

That particular section in the manual is more confusing than helping.
I my opinion that section should be deleted from the manual.
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Re: Non-traditional key signatures

Postby motet » Tue Dec 19, 2017 7:35 pm

I wonder if there's anyone left at MakeMusic who understands the non-standard key signature. It must date back to the early days.

It seems like the linear format lets you modulate to different keys with the same intervals in their scales, but I suspect such a mathematical system would have limited use, especially if the tetrachord requirement really is true. The non-linear thing I documented seems to work, but doesn't have the modulation feature.
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Re: Non-traditional key signatures

Postby Peter Thomsen » Tue Dec 19, 2017 8:19 pm

motet wrote:… It seems like the linear format lets you modulate to different keys with the same intervals in their scales, but I suspect such a mathematical system would have limited use …

You will only get the same intervals in all the scales if the scale pattern is diatonic.
In Other Words:
You will only get the same intervals in all scale transpositions if the scale is a church mode (ionian, dorian, phrygian, lydian, mixolydian, aeolian, locrian).


motet wrote:… especially if the tetrachord requirement really is true …

The tetrachord requirement is not true.
Generally that section is misleading, and that particular sentence (about the tetrachord requirement) is directly wrong.
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Re: Non-traditional key signatures

Postby motet » Tue Dec 19, 2017 8:25 pm

For fun, I tried to do the "harmonic minor" example above and have a B natural in the time signature (not possible with non-linear), but got strange playback--about ever other note was some high pitch.

Anyway, since I'm unlikely to ever use any of this, it's mainly for fun.
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