User:Aura/Aura's Diatonic Scales: Difference between revisions

Line 17:

'''Mediant''' - This is the note that occurs roughly at intervals between 75/64 and 32/25 away from the Tonic in the scale's direction of construction. This is the first of the two scale degrees with the most possibilities for realization, though in true diatonic scales, it is generally within 20 cents of either 6/5 or 5/4. As only notes at intervals with powers of 2 in either the numerator or the denominator are harmonically or subharmonically connected with the Tonic and 6/5 fails to meet this critera, I often replace the traditional 6/5 Minor 3rd with the 77/64 Minor Third. For more information about the general functionalities and properties of the Mediant, see [[Wikipedia:Mediant]].

'''Serviant''' - This is my term for the note that occurs roughly at an interval of 4/3 away from the Tonic in the scale's direction of construction. Although this is commonly called the "Subdominant" in traditional music theory, the problems with that term are two-fold. Firstly, not all possible "Subdominant" harmonies have the same harmonic properties relative to the Tonic, as there is an extremely close connection between the Tonic and the the 4/3 Perfect 4th, and this is not the case for other intervals between 22/17 and 7/5, which might otherwise be called "Subdominants". Secondly, in music built from the Treble downwards, the notes with these sorts of functions are actually located ''above'' the Dominant. Like with notes at other intervals between 32/25 and 7/5 away from the Tonic- the Serviant tends to resolve towards the Dominant, or, as is the case in Locrian, a certain type of Antitonic. As for the notes at other intervals between 22/17 and 7/5, I would divide them into two classes depending on what side of the 4/3 Perfect 4th they fall on, however, aside from 27/20, none of these other intervals occur in diatonic scales.

'''Serviant''' - This is my term for the note that occurs roughly at an interval of 4/3 away from the Tonic in the scale's direction of construction, and has a function opposite that of the Dominant relative to the Tonic. Although this is commonly called the "Subdominant" in traditional music theory, the problems with that term are two-fold. Firstly, not all possible "Subdominant" harmonies have the same harmonic properties relative to the Tonic, as there is an extremely close connection between the Tonic and the the 4/3 Perfect 4th, and this is not the case for other intervals between 22/17 and 7/5, which might otherwise be called "Subdominants". Secondly, in music built from the Treble downwards, the notes with these sorts of functions are actually located ''above'' the Dominant. Like with notes at other intervals between 32/25 and 7/5 away from the Tonic- the Serviant tends to resolve towards the Dominant, or, as is the case in Locrian, a certain type of Antitonic. As for the notes at other intervals between 22/17 and 7/5, I would divide them into two classes depending on what side of the 4/3 Perfect 4th they fall on, however, aside from 27/20, none of these other intervals occur in diatonic scales.

'''Antitonic''' - This is my general term for notes that occur around half an octave away from the Tonic- specifically the region extending from 7/5 to 10/7- on account of harmonies built on notes in this area tending to oppose that of the Tonic. The exact outcome of this opposition depends on the exact distance of the Antitonic from the Tonic. If the Antitonic is less than half an octave away from the Tonic, it tends to cause the Dominant to become a new Tonic unless followed up by a different note- one that is usually a Major 7th away from the Tonic. Because of this tendency to "kiss up to" and tonicize the Dominant, I call any type Antitonic less than half an octave away from the Tonic a "Sycophant". Conversely, if the Antitonic is more than half an octave away from the Tonic, it tends to contrast with the Tonic in a manner somewhat akin to that of a Dominant, but by sheer brute force and contrary harmonic nature- e.g. if the Tonic harmony is Minor in nature, the Antitonic harmony will be Major- or more rarely, Supermajor- in nature. Furthermore, in scales such as the Locrian scale, any type of Serviant harmony tends to resolve towards either this type of Antitonic, or some other type of substitute for a Dominant. Because of these Dominant-esque tendencies, I call any type of Antitonic more than half an octave away from the Tonic a "Tyrant".

@@ Line 17: / Line 17: @@
 '''Mediant''' - This is the note that occurs roughly at intervals between 75/64 and 32/25 away from the Tonic in the scale's direction of construction.  This is the first of the two scale degrees with the most possibilities for realization, though in true diatonic scales, it is generally within 20 cents of either 6/5 or 5/4.  As only notes at intervals with powers of 2 in either the numerator or the denominator are harmonically or subharmonically connected with the Tonic and 6/5 fails to meet this critera, I often replace the traditional 6/5 Minor 3rd with the 77/64 Minor Third.  For more information about the general functionalities and properties of the Mediant, see  [[Wikipedia:Mediant]].
-'''Serviant''' - This is my term for the note that occurs roughly at an interval of 4/3 away from the Tonic in the scale's direction of construction.  Although this is commonly called the "Subdominant" in traditional music theory, the problems with that term are two-fold.  Firstly, not all possible "Subdominant" harmonies have the same harmonic properties relative to the Tonic, as there is an extremely close connection between the Tonic and the the 4/3 Perfect 4th, and this is not the case for other intervals between 22/17 and 7/5, which might otherwise be called "Subdominants".  Secondly, in music built from the Treble downwards, the notes with these sorts of functions are actually located ''above'' the Dominant.  Like with notes at other intervals between 32/25 and 7/5 away from the Tonic- the Serviant tends to resolve towards the Dominant, or, as is the case in Locrian, a certain type of Antitonic.  As for the notes at other intervals between 22/17 and 7/5, I would divide them into two classes depending on what side of the 4/3 Perfect 4th they fall on, however, aside from 27/20, none of these other intervals occur in diatonic scales.
+'''Serviant''' - This is my term for the note that occurs roughly at an interval of 4/3 away from the Tonic in the scale's direction of construction, and has a function opposite that of the Dominant relative to the Tonic.  Although this is commonly called the "Subdominant" in traditional music theory, the problems with that term are two-fold.  Firstly, not all possible "Subdominant" harmonies have the same harmonic properties relative to the Tonic, as there is an extremely close connection between the Tonic and the the 4/3 Perfect 4th, and this is not the case for other intervals between 22/17 and 7/5, which might otherwise be called "Subdominants".  Secondly, in music built from the Treble downwards, the notes with these sorts of functions are actually located ''above'' the Dominant.  Like with notes at other intervals between 32/25 and 7/5 away from the Tonic- the Serviant tends to resolve towards the Dominant, or, as is the case in Locrian, a certain type of Antitonic.  As for the notes at other intervals between 22/17 and 7/5, I would divide them into two classes depending on what side of the 4/3 Perfect 4th they fall on, however, aside from 27/20, none of these other intervals occur in diatonic scales.
 '''Antitonic''' - This is my general term for notes that occur around half an octave away from the Tonic- specifically the region extending from 7/5 to 10/7- on account of harmonies built on notes in this area tending to oppose that of the Tonic.  The exact outcome of this opposition depends on the exact distance of the Antitonic from the Tonic.  If the Antitonic is less than half an octave away from the Tonic, it tends to cause the Dominant to become a new Tonic unless followed up by a different note- one that is usually a Major 7th away from the Tonic.  Because of this tendency to "kiss up to" and tonicize the Dominant, I call any type Antitonic less than half an octave away from the Tonic a "Sycophant".  Conversely, if the Antitonic is more than half an octave away from the Tonic, it tends to contrast with the Tonic in a manner somewhat akin to that of a Dominant, but by sheer brute force and contrary harmonic nature- e.g. if the Tonic harmony is Minor in nature, the Antitonic harmony will be Major- or more rarely, Supermajor- in nature.  Furthermore, in scales such as the Locrian scale, any type of Serviant harmony tends to resolve towards either this type of Antitonic, or some other type of substitute for a Dominant.  Because of these Dominant-esque tendencies, I call any type of Antitonic more than half an octave away from the Tonic a "Tyrant".