Metallic intonation: Difference between revisions

Line 1:

'''Metallic intonation''' ('''MTI'''){{idiosyncratic}} is a system which uses the irrational [[metallic harmonic series]], based on {{w|metallic mean}}s, rather than the [[harmonic series]] as the basis for an exact or tempered tuning. It was first described by [[User:CompactStar|CompactStar]] in 2024. Metallic intonation is related to and can sometimes overlap with [[merciful intonation]]. Except for the [[1/1|unison]], it consists of only irrational intervals, and is inherently [[nonoctave]]. As the first metallic harmonic, [[acoustic phi]] is a possible candidate to serve as an [[equave]] in the same way as octave.

'''Metallic intonation''' ('''MTI'''){{idiosyncratic}} is a system which uses the irrational [[metallic harmonic series]], based on {{w|metallic mean}}s, rather than the [[harmonic series]] as the basis for an exact or tempered tuning. It was first described by [[User:CompactStar|CompactStar]] in 2024. Metallic intonation is related to and can sometimes overlap with [[merciful intonation]]. Except for the [[1/1|unison]], it consists of only irrational intervals, and is inherently [[nonoctave]]. As the first metallic harmonic, [[acoustic phi]] is a possible candidate to serve as an [[equave]] in the same way as octave. Metallic intonation is suitable for inharmonic timbres which have a spectrum of metallic haromoncs rathr than harmonics.

~~The~~ metallic means are taken as [[basis element]]s of [[subgroup]]s rather than [[prime]]s, but not all metallic means are ~~included~~ because some can be expressed in terms of other metallic means~~, similar to how some integers are composite~~. For example, the fourth metallic harmonic is a redundant generator because it is the golden ratio (the first metallic harmonic) cubed.

In metallic intonation, the metallic means are taken as [[basis element]]s of [[subgroup]]s rather than [[prime]]s, but not all metallic means are necessary because some are analogues of composite integers, in that they can be expressed in terms of other metallic means. For example, the fourth metallic harmonic is a redundant generator because it is the golden ratio (the first metallic harmonic) cubed.

== Harmony ==

@@ Line 1: / Line 1: @@
-'''Metallic intonation''' ('''MTI'''){{idiosyncratic}} is a system which uses the irrational [[metallic harmonic series]], based on {{w|metallic mean}}s, rather than the [[harmonic series]] as the basis for an exact or tempered tuning. It was first described by [[User:CompactStar|CompactStar]] in 2024. Metallic intonation is related to and can sometimes overlap with [[merciful intonation]]. Except for the [[1/1|unison]], it consists of only irrational intervals, and is inherently [[nonoctave]]. As the first metallic harmonic, [[acoustic phi]] is a possible candidate to serve as an [[equave]] in the same way as octave.
+'''Metallic intonation''' ('''MTI'''){{idiosyncratic}} is a system which uses the irrational [[metallic harmonic series]], based on {{w|metallic mean}}s, rather than the [[harmonic series]] as the basis for an exact or tempered tuning. It was first described by [[User:CompactStar|CompactStar]] in 2024. Metallic intonation is related to and can sometimes overlap with [[merciful intonation]]. Except for the [[1/1|unison]], it consists of only irrational intervals, and is inherently [[nonoctave]]. As the first metallic harmonic, [[acoustic phi]] is a possible candidate to serve as an [[equave]] in the same way as octave. Metallic intonation is suitable for inharmonic timbres which have a spectrum of metallic haromoncs rathr than harmonics.
-The metallic means are taken as [[basis element]]s of [[subgroup]]s rather than [[prime]]s, but not all metallic means are included because some can be expressed in terms of other metallic means, similar to how some integers are composite. For example, the fourth metallic harmonic is a redundant generator because it is the golden ratio (the first metallic harmonic) cubed.
+In metallic intonation, the metallic means are taken as [[basis element]]s of [[subgroup]]s rather than [[prime]]s, but not all metallic means are necessary because some are analogues of composite integers, in that they can be expressed in terms of other metallic means. For example, the fourth metallic harmonic is a redundant generator because it is the golden ratio (the first metallic harmonic) cubed.
 == Harmony ==