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Originally Posted by Lord Larehip
Tell me why we have perfect intervals. Why can't a 5th, for example, be major or minor?
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I did, read my post through and see if you can spot where.
Quote:
Originally Posted by Lord Larehip
Scales are not laid out this way. It's customary, and far more useful, to use numbers to represent the scale degrees or positions:
1, 2, 3, 4, 5, 6, 7, 8
In a major scale, the two half-steps occur between 3 and 4 and also 7 and 8.
In a minor scale, the two half-steps occur between 2 and 3 and also 5 and 6.
For every major, there is a corresponding or relative minor. Both scales use the identical notes.
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I'm really not sure why you feel the need to explain all of this just because I defined a scale as a sequence of intervals and told everyone what those intervals were for the two most common scales. You're just repeating what I said in a different (much longer) way.
Quote:
Originally Posted by Lord Larehip
The term root note is used for the lowest note in a chord. It's customary to refer to the notes in a scale as:
1. Tonic
2. Super tonic
3. Mediant
4. Subdominant
5. Dominant
6. Submediant
7. Subtonic/Leading tone
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Its true that semantically the root is the lowest note of a given chord, but there's nothing wrong with referring to the first note of a scale as the root instead of the tonic.
Quote:
Originally Posted by Lord Larehip
We usually call a minor 7th the subtonic and the major 7th the leading tone. Each one of these positions has certain task to perform. The tonic is the foundation note of the scale. The subdominant and dominant are called that precisely because they are the dominant notes in the scale. They are also inverses of each other. They are the twin pillars holding the scale up. The submediant and mediant add color to the scale via major and minor intervals. The leading tone adds restlessness to the scale and wants to propel it back to the tonic again so that the scale can rest. We say that it wants to resolve. Likewise, the supertonic wants to lead way from the tonic.
Now you may wonder why the mediant at position 3 comes before the submediant at 6. It's because the straight-line scale we are accustomed to is misleading as hell. The tonic is really the note around which the others revolve so it is in the center. The dominant is a 5th above and the subdominant is a 5th below it. The closest notes to the tonic are the supertonic a step above and the leading tone a half-step below it. Both are restless and want to lead away from or back to the tonic. The mediant is a major 3rd above the tonic and the submediant is a minor 3rd below but since they are squeezed between the supertonic and leading tone and the dominant and subdominant, they are in the middle or median positions.
So a scale is like a solar system rather than a ladder (scale is derived from the Italian scala or ladder). The tonic is like the sun in the center, the supertonic and leading tone flank the tonic. Then the mediant and submediant flank the supertonic and leading otne and then the dominant and subdominant flank the mediant and submediant.
Hope that wasn't too confusing.
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All of this is true - (in the germanic tradition and those informed specifically by it), but you really need to stop phrasing all of this as if it is immutable fact. Music isn't about knowing the rules so you can abide by them, its about knowing the rules so that you can break them properly. When you go on forever about a note or scale degrees "function", always discuss it on the basis that this is a common, but not the only, way to deal with it.
Quote:
Originally Posted by Lord Larehip
Scales are assembled using the Fibonacci Sequence. This sequence starts off with two numbers and the third is the sum of the first two. For example:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. Notice how each number is the sum of the two before it? Scales follow this same sequence--5 (pentatonic), 7 (diatonic), 12 (chromatic). The next scale would be 19 notes and then 31 after that. They have built 19-tone keyboards but they are unruly. The cool thing about the Fibonacci Sequence is that the closer to infinity one gets, the more closer any two adjacent numbers in the sequence divide out to Phi or phi. Phi is 1.618 (it's actually irrational) and phi is 0.618 and is the reciprocal or Phi. The same is true of the scales, the closer to infinity they get, the closer any two adjacent scales will divided out to Phi or phi. It's a characteristic of the Fibonacci Sequence. You can look around the web for all the cool stuff there is about Phi and phi and the Golden Section and the Golden Mean and the Golden Spiral. It's really neat.
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What absolute ****. There's a significant difference between "Based on" and "Coincidentally resembles". The fibonacci sequence and the golden ratio crop up absolutely everywhere, and its very, very rare that the intent has ever been to apply it in advance - Its far more common to simply find that the way something has already been done, consciously or unconsciously resembles or takes advantage of the sequence, not the other way around. (Unless you're James Maynard Keenan and pals, in which case you just write songs around it to be flashy to math geeks).
Also, you'll note that the scales I noted specifically, only went up to 12. I stated, very clearly in the next paragraph, that those indian musical systems split the OCTAVE into 19 (Or more) notes, not that they necessarily use a 19 note scale. You responded to a comment about the division of the
octave, by rambling about the fibonacci sequences supposed (not actual) relationship to
scales.
The musical notes used in western music are based on the division of the octave according to the harmonic series. Of course, this is imperfect, as the harmonic series is actually uneven, and would stretch the octave beyond an exact doubling of frequency if followed exactly, so rather than do that, the harmonic series is "tempered" by moving the exact frequencies of the tuned notes very slightly in order to both rectify that issue and maintain the consonance between as many notes as possible in as many contexts.
As these are compromises, there are varying temperaments which have been used over time - Pythagorean temperament is a sequence of 3:2 ratios of pitch, equal temperament is the system used in most modern western music, and well temperament is primarily used for historically correct recordings of older pieces. There are others but they're rare to hear.
Of course other cultures will use their own temperaments in their traditional musics too, and may even choose to divide the octave into greater or lesser numbers of discrete tones. Typically this will have precisely no relation to the fibonacci sequence unless by complete accident.
Oh, and you mean "Unwieldy", not unruly.