Diatonic functional harmony: Difference between revisions

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Building on Kite's logic, Aura then decided to apply similar distinctions among quartertones, and thus make the argument that quartertones don't have to denote exactly one fourth of a whole tone in as of themselves, but rather, they only have to add up to a whole tone when paired up correctly. However, the catch was that that for quartertones, there are sometimes multiple correct options, making things more complicated. Aura decided to define the musical functions of quartertones initially on an informal basis by drawing a distinction between the terms "'''Parachromatic'''" (from the prefix ''para-'' in both the senses of ''alongside'' and ''resembling''<ref>[[Wiktionary: para- #Etymology 1]]</ref>, and the word ''chromatic'') and "'''Paradiatonic'''" (from the same two senses of the prefix ''para-'' and the word ''diatonic'') for purposes of classifying quartertone intervals.

According to Aura, paradiatonic quartertones are be analogous to diatonic semitones in that they are denoted as seconds, albeit inframinor seconds by default, while parachromatic quartertones are analogous to chromatic semitones in that they are denoted as primes, albiet as ultraprimes by default. However, the distinction goes further than that- a parachromatic quartertone and a paradiatonic quartertone add up to a diatonic semitone, while two parachromatic quartertones add up to a chromatic semitone. Given both these definitions for "paradiatonic" and "parachromatic", and given that a diatonic semitone and a chromatic semitone add up to a whole tone when paired correctly, it can be deduced that a whole tone can be assembled from three parachromatic quartertones and one paradiatonic quartertone. Because there are sometimes multiple correct options for assembling parachromatic and paradiatonic intervals to make a 9/8 whole tone, Aura ended up choosing the simplest configuration of paradiatonic and parachromatic intervals to assemble in order to create a 9/8 whole tone- a configuration that only requires one type of parachromatic quartertone and one type of paradiatonic quartertone. As a result of multiple factors, Aura ended up choosing the combination of three 33/32 parachromatic quartertones and one [[4096/3993]] paradiatonic quartertone as the JI basis for this in regards to both Diatonic theory and [[Alpharabian tuning]], and, through interactions with others in the Xenharmonic community, Aura was later influenced by others on Discord to take [[MOS]]-based structural considerations into account. This eventually resulted in the first formal definition of a "'''parachroma'''" (an interval that can be easily tempered to equal half of a MOS-chroma), and, thorough applying the aforementioned thought process about classifying quartertones, the '''paralimma''' (the interval that remains after subtracting three parachromas from a MOS-step).

According to Aura, paradiatonic quartertones are be analogous to diatonic semitones in that they are denoted as seconds, albeit inframinor seconds by default, while parachromatic quartertones are analogous to chromatic semitones in that they are denoted as primes, albiet as ultraprimes by default. However, the distinction goes further than that- a parachromatic quartertone and a paradiatonic quartertone add up to a diatonic semitone, while two parachromatic quartertones add up to a chromatic semitone. Given both these definitions for "paradiatonic" and "parachromatic", and given that a diatonic semitone and a chromatic semitone add up to a whole tone when paired correctly, it can be deduced that a whole tone can be assembled from three parachromatic quartertones and one paradiatonic quartertone. Because there are sometimes multiple correct options for assembling parachromatic and paradiatonic intervals to make a 9/8 whole tone, Aura ended up choosing the simplest configuration of paradiatonic and parachromatic intervals to assemble in order to create a 9/8 whole tone- a configuration that only requires one type of parachromatic quartertone and one type of paradiatonic quartertone. As a result of multiple factors, Aura ended up choosing the combination of three 33/32 parachromatic quartertones and one [[4096/3993]] paradiatonic quartertone as the JI basis for this in regards to both Diatonic theory and [[Alpharabian tuning]], and, through interactions with others in the Xenharmonic community, Aura was later influenced by others on Discord to take [[MOS]]-based structural considerations into account. This eventually resulted in the first formal definition of a "'''parachroma'''" (an interval that can be easily tempered to equal half of a MOS-chroma), and, thorough applying the aforementioned thought process about classifying quartertones, the '''paralimma''' (the interval that remains after subtracting three parachromas from a Major MOS-step).

=== Basic Paradiatonic Functions ===

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 Building on Kite's logic, Aura then decided to apply similar distinctions among quartertones, and thus make the argument that quartertones don't have to denote exactly one fourth of a whole tone in as of themselves, but rather, they only have to add up to a whole tone when paired up correctly.  However, the catch was that that for quartertones, there are sometimes multiple correct options, making things more complicated.  Aura decided to define the musical functions of quartertones initially on an informal basis by drawing a distinction between the terms "'''Parachromatic'''" (from the prefix ''para-'' in both the senses of ''alongside'' and ''resembling''<ref>[[Wiktionary: para- #Etymology 1]]</ref>, and the word ''chromatic'') and "'''Paradiatonic'''" (from the same two senses of the prefix ''para-'' and the word ''diatonic'') for purposes of classifying quartertone intervals.
-According to Aura, paradiatonic quartertones are be analogous to diatonic semitones in that they are denoted as seconds, albeit inframinor seconds by default, while parachromatic quartertones are analogous to chromatic semitones in that they are denoted as primes, albiet as ultraprimes by default.  However, the distinction goes further than that- a parachromatic quartertone and a paradiatonic quartertone add up to a diatonic semitone, while two parachromatic quartertones add up to a chromatic semitone.  Given both these definitions for "paradiatonic" and "parachromatic", and given that a diatonic semitone and a chromatic semitone add up to a whole tone when paired correctly, it can be deduced that a whole tone can be assembled from three parachromatic quartertones and one paradiatonic quartertone.  Because there are sometimes multiple correct options for assembling parachromatic and paradiatonic intervals to make a 9/8 whole tone, Aura ended up choosing the simplest configuration of paradiatonic and parachromatic intervals to assemble in order to create a 9/8 whole tone- a configuration that only requires one type of parachromatic quartertone and one type of paradiatonic quartertone.  As a result of multiple factors, Aura ended up choosing the combination of three 33/32 parachromatic quartertones and one [[4096/3993]] paradiatonic quartertone as the JI basis for this in regards to both Diatonic theory and [[Alpharabian tuning]], and, through interactions with others in the Xenharmonic community, Aura was later influenced by others on Discord to take [[MOS]]-based structural considerations into account.  This eventually resulted in the first formal definition of a "'''parachroma'''" (an interval that can be easily tempered to equal half of a MOS-chroma), and, thorough applying the aforementioned thought process about classifying quartertones, the '''paralimma''' (the interval that remains after subtracting three parachromas from a MOS-step).
+According to Aura, paradiatonic quartertones are be analogous to diatonic semitones in that they are denoted as seconds, albeit inframinor seconds by default, while parachromatic quartertones are analogous to chromatic semitones in that they are denoted as primes, albiet as ultraprimes by default.  However, the distinction goes further than that- a parachromatic quartertone and a paradiatonic quartertone add up to a diatonic semitone, while two parachromatic quartertones add up to a chromatic semitone.  Given both these definitions for "paradiatonic" and "parachromatic", and given that a diatonic semitone and a chromatic semitone add up to a whole tone when paired correctly, it can be deduced that a whole tone can be assembled from three parachromatic quartertones and one paradiatonic quartertone.  Because there are sometimes multiple correct options for assembling parachromatic and paradiatonic intervals to make a 9/8 whole tone, Aura ended up choosing the simplest configuration of paradiatonic and parachromatic intervals to assemble in order to create a 9/8 whole tone- a configuration that only requires one type of parachromatic quartertone and one type of paradiatonic quartertone.  As a result of multiple factors, Aura ended up choosing the combination of three 33/32 parachromatic quartertones and one [[4096/3993]] paradiatonic quartertone as the JI basis for this in regards to both Diatonic theory and [[Alpharabian tuning]], and, through interactions with others in the Xenharmonic community, Aura was later influenced by others on Discord to take [[MOS]]-based structural considerations into account.  This eventually resulted in the first formal definition of a "'''parachroma'''" (an interval that can be easily tempered to equal half of a MOS-chroma), and, thorough applying the aforementioned thought process about classifying quartertones, the '''paralimma''' (the interval that remains after subtracting three parachromas from a Major MOS-step).
 === Basic Paradiatonic Functions ===