Metallic MOS: Difference between revisions

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Scales based on this mean — or “phi”, as it is often called, after the Greek letter used to represent it — are relatively well-known, and these “golden” scales have been described by [[wikipedia:Erv_Wilson|Erv Wilson]], [[Kraig Grady|Kraig_Grady]], [http://www.elvenminstrel.com/music/tuning/horagrams/horagram_intro.htm David J. Finnamore], [https://ia800908.us.archive.org/31/items/mosedo.html/mosedo.html Billy Stiltner], [[wikipedia:Paul_Erlich|Paul Erlich]], [[Graham Breed|Graham Breed]], [[Dave Keenan|Dave Keenan]], [[Margo Schulter|Margo Schulter]], [[Das Goldene Tonsystem|Thorvald Kornerup]] and many others.

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.<span><math>φ</math></span>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.

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.

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

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.<span><math>φ</math></span>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. 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.

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 Scales based on this mean — or “phi”, as it is often called, after the Greek letter used to represent it — are relatively well-known, and these “golden” scales have been described by [[wikipedia:Erv_Wilson|Erv Wilson]], [[Kraig Grady|Kraig_Grady]], [http://www.elvenminstrel.com/music/tuning/horagrams/horagram_intro.htm David J. Finnamore], [https://ia800908.us.archive.org/31/items/mosedo.html/mosedo.html Billy Stiltner], [[wikipedia:Paul_Erlich|Paul Erlich]], [[Graham Breed|Graham Breed]], [[Dave Keenan|Dave Keenan]], [[Margo Schulter|Margo Schulter]], [[Das Goldene Tonsystem|Thorvald Kornerup]] and many others.
-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.<span><math>φ</math></span>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.
+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.
-Since no other types of scales besides MOS scales will be discussed here, we can assume MOS scale whenever we write “scale”.
+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.<span><math>φ</math></span>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. 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.