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July 3rd, 2016, 12:43 AM   #1
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The Diatonic Set and Choice of Solfege

Greetings,

Think of the diatonic set as basically the white keys on the piano. Or, more to the point, as do-re-mi-fa-so-la-ti-do. It contains the notes of the familiar major scale. But it also represents the natural minor scale and the church modes -- one simply starts on a different note. Dorian mode, for instance, would run re-mi-fa-so-la-ti-do-re. All the modes are, in other words, permutations of the diatonic set.

Now, here's my question: I use a solfege system called "la-based minor" that straighforwardly reflects this structure. It could as well be called "ti-based minor", etc. I simply choose the appropriate syllable as "home", as I've described above. To me, this way of working has an elegance to it, in that I'm simply rotating the diatonic set to get to another mode. But there is a competing way, the way I learned first: here, you append to the diatonic set the chromatic notes that intervene: C#, Eb, etc. You always take, for instance, "C" as the home pitch for the key. A different mode is then constructed by exchanging syllables from the diatonic set with some from the chromatic set as needed to create a new shape (one that matches the shape you would have gotten by simply rotating the diatonic set). So dorian mode, instead of "re-mi-fa-so-la-ti-do-re" as above becomes "do-re-me-fa-so-la-te-do". The original "mi" has changed to "me", and "ti" has changed to "te" to create the proper shape.

A huge debate rages about which of these systems is correct. Considerations like how well each aligns with functional harmony play into it. But what I'm interested in here is simply this: (For people with better abstract algebra skills than mine), can one or the other system be shown to be superior, i.e., more elegant, on pure mathematical grounds?

Thanks for any help or input.
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July 3rd, 2016, 12:59 AM   #2
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Math Focus: tetration
https://en.wikipedia.org/wiki/Pythagorean_comma
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July 3rd, 2016, 01:01 AM   #3
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Math Focus: tetration
https://en.wikipedia.org/wiki/Pythagorean_tuning
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July 3rd, 2016, 01:30 AM   #4
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Math Focus: tetration
https://en.wikipedia.org/wiki/Regular_temperament
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July 3rd, 2016, 01:32 AM   #5
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Math Focus: tetration
https://en.wikipedia.org/wiki/Perfect_fifth
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July 3rd, 2016, 02:01 AM   #6
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Not applicable

Hi Manus, thanks for the links. But unfortunately they don't speak at all to the question I'm trying to get at here. I'm not concerned with tuning systems, but rather with solfege systems, specifically movable do with la-based minor vs. movable do with do-based minor, and how they can be described algebraically.
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July 3rd, 2016, 02:22 AM   #7
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Math Focus: tetration
But solfege is also tuning but with your voice.
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July 3rd, 2016, 02:38 AM   #8
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Insofar as you have to have proper intonation,yes, but that's not germane to the question.
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July 3rd, 2016, 02:43 AM   #9
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What is that question then actually?
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July 3rd, 2016, 10:04 PM   #10
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Math Focus: tetration
Quote:
Originally Posted by hacisl View Post
Greetings,

Think of the diatonic set as basically the white keys on the piano. Or, more to the point, as do-re-mi-fa-so-la-ti-do. It contains the notes of the familiar major scale. But it also represents the natural minor scale and the church modes -- one simply starts on a different note. Dorian mode, for instance, would run re-mi-fa-so-la-ti-do-re. All the modes are, in other words, permutations of the diatonic set.

Now, here's my question: I use a solfege system called "la-based minor" that straighforwardly reflects this structure. It could as well be called "ti-based minor", etc. I simply choose the appropriate syllable as "home", as I've described above. To me, this way of working has an elegance to it, in that I'm simply rotating the diatonic set to get to another mode. But there is a competing way, the way I learned first: here, you append to the diatonic set the chromatic notes that intervene: C#, Eb, etc. You always take, for instance, "C" as the home pitch for the key. A different mode is then constructed by exchanging syllables from the diatonic set with some from the chromatic set as needed to create a new shape (one that matches the shape you would have gotten by simply rotating the diatonic set). So dorian mode, instead of "re-mi-fa-so-la-ti-do-re" as above becomes "do-re-me-fa-so-la-te-do". The original "mi" has changed to "me", and "ti" has changed to "te" to create the proper shape.

A huge debate rages about which of these systems is correct. Considerations like how well each aligns with functional harmony play into it. But what I'm interested in here is simply this: (For people with better abstract algebra skills than mine), can one or the other system be shown to be superior, i.e., more elegant, on pure mathematical grounds?

Thanks for any help or input.
Isn't that just the difference of minor and major?
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