Chord complexity: Difference between revisions

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When we look at chords of arbitrary size, it is clear that some meaningful analogue of the former property holds. For instance, for some triad a:b:c, if a and b and c are small, they will tend to exhibit qualities like virtual fundamental generation, timbral fusion, a general sense of "crunchiness" or "periodicity buzz," etc, at least as a general rule of thumb. We will simply call this sensation "'''justiness'''", as an informal and subjective term for the general quality that just intonation chords have.

It is clear right away that this "justiness" is not quite so simple as it is for dyads. For instance, we can look at the chords 16:20:24:30:36:45:54 and 15:19:23:29:35:44:53.~~<ref>TODO~~: ~~add audio examples</ref>~~ The former is basically a stack of three 4:5:6 chords on top of one another, and thus has lots of simple subdyads, subtriads, subtetrads, etc, whereas the latter has been formed by simply subtracting 1 from each note in the former chord. Thus, the latter is "simpler" from the standpoint of the heptadic complexity, but doesn't have many simple subchords at all. And at least to the ears of this author, the former seems to clearly sound much "justier" than than the latter - and in a very immediate way - even though the latter is less complex from a "heptadic" standpoint.

It is clear right away that this "justiness" is not quite so simple as it is for dyads. For instance, we can look at the chords 16:20:24:30:36:45:54 and 15:19:23:29:35:44:53:

'''16:20:24:30:36:45:54''':

[[File:Square_16_20_24_30_36_45_54.ogg]]

'''15:19:23:29:35:44:53''':

[[File:Square_15_19_23_29_35_44_53.ogg]]

The former is basically a stack of three 4:5:6 chords on top of one another, and thus has lots of simple subdyads, subtriads, subtetrads, etc, whereas the latter has been formed by simply subtracting 1 from each note in the former chord. Thus, the latter is "simpler" from the standpoint of the heptadic complexity, but doesn't have many simple subchords at all. And at least to the ears of this author, the former seems to clearly sound much "justier" than than the latter - and in a very immediate way - even though the latter is less complex from a "heptadic" standpoint.

In addition, it is clear that this sensation of justiness has many different sub-aspects, many of which do not evolve in the same way as the combined complexity of chord grows. Terms like "periodicity buzz," "roughness," "combination tones," "virtual fundamentals," etc, all refer to different aspects of justiness, some of which involve primarily looking at subdyads, or isoharmonic chords, etc, or may not require the chord to be strictly "just" at all (such as the Mt. Meru scales). Or, if we are looking at JI chords, we may be evaluating something mathematical about the chord beyond just the complexity of the entire chord at once, or even its subchords, for some of these qualities. Thus, it is clear that justiness is a multidimensional quantity, with several different metrics simultaneously being used to evaluate different aspects of the consonance of a chord.

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 When we look at chords of arbitrary size, it is clear that some meaningful analogue of the former property holds. For instance, for some triad a:b:c, if a and b and c are small, they will tend to exhibit qualities like virtual fundamental generation, timbral fusion, a general sense of "crunchiness" or "periodicity buzz," etc, at least as a general rule of thumb. We will simply call this sensation "'''justiness'''", as an informal and subjective term for the general quality that just intonation chords have.
-It is clear right away that this "justiness" is not quite so simple as it is for dyads. For instance, we can look at the chords 16:20:24:30:36:45:54 and 15:19:23:29:35:44:53.<ref>TODO: add audio examples</ref> The former is basically a stack of three 4:5:6 chords on top of one another, and thus has lots of simple subdyads, subtriads, subtetrads, etc, whereas the latter has been formed by simply subtracting 1 from each note in the former chord. Thus, the latter is "simpler" from the standpoint of the heptadic complexity, but doesn't have many simple subchords at all. And at least to the ears of this author, the former seems to clearly sound much "justier" than than the latter - and in a very immediate way - even though the latter is less complex from a "heptadic" standpoint.
+It is clear right away that this "justiness" is not quite so simple as it is for dyads. For instance, we can look at the chords 16:20:24:30:36:45:54 and 15:19:23:29:35:44:53:
+'''16:20:24:30:36:45:54''':
+[[File:Square_16_20_24_30_36_45_54.ogg]]
+'''15:19:23:29:35:44:53''':
+[[File:Square_15_19_23_29_35_44_53.ogg]]
+The former is basically a stack of three 4:5:6 chords on top of one another, and thus has lots of simple subdyads, subtriads, subtetrads, etc, whereas the latter has been formed by simply subtracting 1 from each note in the former chord. Thus, the latter is "simpler" from the standpoint of the heptadic complexity, but doesn't have many simple subchords at all. And at least to the ears of this author, the former seems to clearly sound much "justier" than than the latter - and in a very immediate way - even though the latter is less complex from a "heptadic" standpoint.
 In addition, it is clear that this sensation of justiness has many different sub-aspects, many of which do not evolve in the same way as the combined complexity of chord grows. Terms like "periodicity buzz," "roughness," "combination tones," "virtual fundamentals," etc, all refer to different aspects of justiness, some of which involve primarily looking at subdyads, or isoharmonic chords, etc, or may not require the chord to be strictly "just" at all (such as the Mt. Meru scales). Or, if we are looking at JI chords, we may be evaluating something mathematical about the chord beyond just the complexity of the entire chord at once, or even its subchords, for some of these qualities. Thus, it is clear that justiness is a multidimensional quantity, with several different metrics simultaneously being used to evaluate different aspects of the consonance of a chord.