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1

Any single string creates harmonics as it rings. Up to eight parts a C would generate C C G CEG Bb and C, essentially a dominant 7th chord. The lower partials are louder and than the upper partials due to string length influencing volume. A longer portion of the string vibrating will be louder. Tempered tuning requires that octaves and fifths sound good ...


3

It is significant when you are trying to tune an instrument by ear, using the purity of intervals as your guide. You (and the pages you link) refer to jumping up 7 octaves vs. 12 fifths, but don't forget that any notes you reach that way can also be brought down by one or more octaves as well. To illustrate this, let's bring all the notes down into the same ...


3

It is only significant to someone designing an instrument with a finite set of fixed pitches like a keyboard. Tuning such an instrument in a system based on pure fifths causes octaves to not be equivalent - which is terrible because the octave is the only truly pure interval, you can hear the beats from a mile away because it doesn't form a difference tone ...


5

As some of the other answers have eluded to, there are two basic problems with your question: The first is the question of how you generalize a "tritone" in a non-12-TET based system. One possibility is to interpret it literally as three whole tones (which then begs the question as to how you define a whole tone in a non 12-tone system). Another ...


0

To answer 2: yes, for any n, if n is even, then half an octave is n/2 divisions. (This is rather boringly obvious, so perhaps I don't understand the question.) I don't understand what you mean by "unique".


0

Two other importantnotes in a given key (which are the basis for main chords) are the 4th and 5th notes of a major scale, being 5 and 7 semitones from the root respectively. Giving the subdominant and the dominant. That puts a tritone right between them, neither one or the other, but too close to sound consonant. Yes, mathematically it could be construed ...



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