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 ~~<span><math>φ</math></span>~~ is only the first of an infinite ~~continuum~~ 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.

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.

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”.

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Confusingly, silver is a noble metal, while gold is not; this all would have been simpler if multiple metaphors hadn't already arisen in this domain, but what can we do.

So, in the end, we have six types of metallic generators:

So, in the end, we have six types of metallic generators. Noble generators and isotopic aristocratic generators can all be referred to as aristocratic generators when the generic category is preferred, although at that point we would probably be even better served to simply use the further generic category "metallic generators":

{| class="wikitable"

|

|'''period interval'''

|'''non-period interval'''

| colspan="2" |'''non-period interval'''

|-

|'''golden mean'''

|golden generator

|noble generators

| rowspan="3" |aristocratic generators

|-

|'''beyond golden mean'''

@@ Line 10: / Line 10: @@
 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 <span><math>φ</math></span> is only the first of an infinite continuum 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.
+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.
-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”.
@@ Line 89: / Line 87: @@
 Confusingly, silver is a noble metal, while gold is not; this all would have been simpler if multiple metaphors hadn't already arisen in this domain, but what can we do.
-So, in the end, we have six types of metallic generators:
+So, in the end, we have six types of metallic generators. Noble generators and isotopic aristocratic generators can all be referred to as aristocratic generators when the generic category is preferred, although at that point we would probably be even better served to simply use the further generic category "metallic generators":
 {| class="wikitable"
 |
 |'''period interval'''
-|'''non-period interval'''
+| colspan="2" |'''non-period interval'''
 |-
 |'''golden mean'''
 |golden generator
 |noble generators
+| rowspan="3" |aristocratic generators
 |-
 |'''beyond golden mean'''