Metallic MOS: Difference between revisions

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But is only the first of an infinite sequence of such metallic means which can be used to generate scales offering interesting musical possibilities. And while some attention has been given to silver scales, what we seek to do here is centralize all met-MOS knowledge and generalize principles across all of the metallic means.

~~The met-~~MOS concepts ~~discussed here~~ are ~~abstract — unrelated to the octave~~, ~~or neutral thirds~~, ~~or any other size to which~~ we ~~might assign the period or generator~~. ~~Being abstract~~, ~~they only depend on the ratio between the period and the generator~~. ~~Therefore we can set one of these two values to 1~~, for ~~convenience, so that we only have to worry about the value of the other. We’ll be conforming here with the convention of setting the period to 1. Since no other types~~ of ~~scales besides MOS scales~~ will be discussed here~~, we can assume MOS scale whenever we write “scale”~~.

MOS concepts are logarithmic, not acoustic. In other words, we are not dealing with frequency ratios here. Frequency ratios related to metallic means, such as “acoustic phi” (approximately 833.09¢), have interesting properties too — creating recursive combination tones, for example — but these musical applications of metallic means will not be discussed here.

MOS concepts ~~are logarithmic~~, ~~not acoustic~~. ~~In other words~~, ~~we are not dealing with frequency ratios here. Frequency ratios related~~ to ~~metallic means, such~~ as ~~“acoustic phi” (approximately 833~~.~~09¢)~~, ~~have interesting properties too — creating recursive combination tones~~, for ~~example — but~~ these ~~musical applications~~ of ~~metallic means~~ will ~~not~~ be discussed here.

The met-MOS concepts discussed here may be used to define generators as fractions of an octave, as is most common. But these concepts are more abstract than that, and may be used to define generators as fractions of ''any'' period. As such, they only depend on the ratio between the generator and the period, and so for convenience we can lock one of these two values to 1 and only vary the value of the other. We’ll be conforming here with the convention of choosing the period as the interval to lock to 1.

Since no other types of scales besides MOS scales will be discussed here, we can assume MOS scale whenever we write “scale”.

= Behavior =

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 But  is only the first of an infinite sequence of such metallic means which can be used to generate scales offering interesting musical possibilities. And while some attention has been given to silver scales, what we seek to do here is centralize all met-MOS knowledge and generalize principles across all of the metallic means.
-The met-MOS concepts discussed here are abstract — unrelated to the octave, or neutral thirds, or any other size to which we might assign the period or generator. Being abstract, they only depend on the ratio between the period and the generator. Therefore we can set one of these two values to 1, for convenience, so that we only have to worry about the value of the other. We’ll be conforming here with the convention of setting the period to 1. Since no other types of scales besides MOS scales will be discussed here, we can assume MOS scale whenever we write “scale”.
+MOS concepts are logarithmic, not acoustic. In other words, we are not dealing with frequency ratios here. Frequency ratios related to metallic means, such as “acoustic phi” (approximately 833.09¢), have interesting properties too — creating recursive combination tones, for example — but these musical applications of metallic means will not be discussed here.
-MOS concepts are logarithmic, not acoustic. In other words, we are not dealing with frequency ratios here. Frequency ratios related to metallic means, such as “acoustic phi” (approximately 833.09¢), have interesting properties too — creating recursive combination tones, for example — but these musical applications of metallic means will not be discussed here.
+The met-MOS concepts discussed here may be used to define generators as fractions of an octave, as is most common. But these concepts are more abstract than that, and may be used to define generators as fractions of ''any'' period. As such, they only depend on the ratio between the generator and the period, and so for convenience we can lock one of these two values to 1 and only vary the value of the other. We’ll be conforming here with the convention of choosing the period as the interval to lock to 1.
+Since no other types of scales besides MOS scales will be discussed here, we can assume MOS scale whenever we write “scale”.
 = Behavior =