EFD: Difference between revisions

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An '''EFD''' ('''equal frequency division''') or '''AD''' ('''arithmetic division''') is a kind of [[Arithmetic tunings|arithmetic]] and [[~~Harmonotonic tunings|harmonotonic~~]] tuning in which each period is divided to a number of steps of equal frequency difference~~. It is a [[period]]ic [[tuning system]]~~.

An '''EFD''' ('''equal frequency division''') or '''AFD''' ('''arithmetic frequency division''') is a kind of [[Arithmetic tunings|arithmetic]] and [[period]]ic [[tuning]] in which each period is divided to a number of steps of equal frequency difference.

== Specification ==

Its full specification is ''n''-EFD-''p'' or ''n''-AD-''p'': ''n'' equal frequency divisions of ''p'', or ''n'' arithmetic divisions of ''p'' .

Its full specification is ''n''-EFD-''p'' or ''n''-AFD-''p'': ''n'' equal frequency divisions of ''p'', or ''n'' arithmetic frequency divisions of ''p'' .

== Formula ==

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=== Vs. OD ===

An [[OD|n-~~ODp~~]] is equivalent to an n-~~EFDp~~ except that the period <math>p</math> of the OD must be rational.

An [[OD|''n''-OD-''p'']] is equivalent to an ''n''-EFD-''p'' except that the period <math>p</math> of the OD must be rational.

=== Vs. ELD ===

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! 4

|-

! frequency (f)

! frequency (''f'', ratio)

| (1 + (0/4)(φ - 1)) = (0φ + 4)/4 = 1

| 1 + (1/4)(φ - 1) = (1φ + 3)/4

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| 1 + (4/4)(φ - 1) = (4φ + 0)/4 = φ

|-

! pitch (~~log₂f~~)

! pitch (log₂''f'', octaves)

| (0)

| 0.21

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| 0.69

|-

! length (1/f)

! length (1/''f'', ratio)

| (1)

| 4/(φ + 3) = 0.87

@@ Line 1: / Line 1: @@
-An '''EFD''' ('''equal frequency division''') or '''AD''' ('''arithmetic division''') is a kind of [[Arithmetic tunings|arithmetic]] and [[Harmonotonic tunings|harmonotonic]] tuning in which each period is divided to a number of steps of equal frequency difference. It is a [[period]]ic [[tuning system]].
+An '''EFD''' ('''equal frequency division''') or '''AFD''' ('''arithmetic frequency division''') is a kind of [[Arithmetic tunings|arithmetic]] and [[period]]ic [[tuning]] in which each period is divided to a number of steps of equal frequency difference.
 == Specification ==
-Its full specification is ''n''-EFD-''p'' or ''n''-AD-''p'': ''n'' equal frequency divisions of ''p'', or ''n'' arithmetic divisions of ''p'' .
+Its full specification is ''n''-EFD-''p'' or ''n''-AFD-''p'': ''n'' equal frequency divisions of ''p'', or ''n'' arithmetic frequency divisions of ''p'' .
 == Formula ==
@@ Line 22: / Line 22: @@
 === Vs. OD ===
-An [[OD|n-ODp]] is equivalent to an n-EFDp except that the period <math>p</math> of the OD must be rational.
+An [[OD|''n''-OD-''p'']] is equivalent to an ''n''-EFD-''p'' except that the period <math>p</math> of the OD must be rational.
 === Vs. ELD ===
@@ Line 44: / Line 44: @@
 ! 4
 |-
-! frequency (f)
+! frequency (''f'', ratio)
 | (1 + (0/4)(φ - 1))<br>= (0φ + 4)/4<br>= 1
 | 1 + (1/4)(φ - 1)<br>= (1φ + 3)/4
@@ Line 51: / Line 51: @@
 | 1 + (4/4)(φ - 1)<br>= (4φ + 0)/4<br>= φ
 |-
-! pitch (log₂f)
+! pitch (log₂''f'', octaves)
 | (0)
 | 0.21
@@ Line 58: / Line 58: @@
 | 0.69
 |-
-! length (1/f)
+! length (1/''f'', ratio)
 | (1)
 | 4/(φ + 3) = 0.87