Porcupine: Difference between revisions

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In the following table, odd harmonics 1–11 are in '''bold'''.

{| class="wikitable center-all right-2 left-3 right-6 left-7"

{| class="wikitable center-all right-2 left-3 right-7 left-8"

! colspan="5" | Up from the tonic, aka fourthward

! colspan="5" | Down from the octave, aka fifthward

|-

! #

! Cents

! Cents*

! Ratios

! Porcupine notation

! Porcupine<br>notation

! Ups and downs<br>notation

! #

! Cents

! Cents*

! Ratios

! Porcupine notation

! Porcupine<br>notation

! Ups and downs<br>notation

|-

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| M3

|}

<nowiki/>* In 11-limit [[CWE tuning]], octave reduced

~~The~~ specific tuning shown ~~is the full 11-limit [[CWE tuning]]~~, ~~but of course~~ there is a range of acceptable porcupine tunings that includes generators as small as 160 cents ([[15edo]]) and as large as 165.5 cents ([[29edo]]). However, the 29edo patent val does not support 11-limit porcupine proper, since it does not temper out [[64/63]].

Besides the specific tuning shown here, there is a range of acceptable porcupine tunings that includes generators as small as 160 cents ([[15edo]]) and as large as 165.5 cents ([[29edo]]). However, the 29edo patent val does not support 11-limit porcupine proper, since it does not temper out [[64/63]].

== Chords and harmony ==

[[12/11]], [[11/10]], and [[10/9]] are all represented by the same interval, the generator. This makes chords such as 8:9:10:11:12 exceptionally common and easy to find.

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The interval representing both [[25/24]] and [[81/80]] can be found in this interval chain at -7 steps, and ranges from about 45 to 80 cents depending on the tuning. This can be considered the "chroma" of porcupine temperament.

~~== Chords ==~~

~~{{Main| Chords of porcupine }}~~

== Scales ==

@@ Line 23: / Line 23: @@
 In the following table, odd harmonics 1–11 are in '''bold'''.
-{| class="wikitable center-all right-2 left-3 right-6 left-7"
+{| class="wikitable center-all right-2 left-3 right-7 left-8"
 ! colspan="5" | Up from the tonic, aka fourthward
 ! colspan="5" | Down from the octave, aka fifthward
 |-
 ! #
-! Cents
+! Cents*
 ! Ratios
-! Porcupine notation
+! Porcupine<br>notation
 ! Ups and downs<br>notation
 ! #
-! Cents
+! Cents*
 ! Ratios
-! Porcupine notation
+! Porcupine<br>notation
 ! Ups and downs<br>notation
 |-
@@ Line 181: / Line 181: @@
 | M3
 |}
+<nowiki/>* In 11-limit [[CWE tuning]], octave reduced
-The specific tuning shown is the full 11-limit [[CWE tuning]], but of course there is a range of acceptable porcupine tunings that includes generators as small as 160 cents ([[15edo]]) and as large as 165.5 cents ([[29edo]]). However, the 29edo patent val does not support 11-limit porcupine proper, since it does not temper out [[64/63]].
+Besides the specific tuning shown here, there is a range of acceptable porcupine tunings that includes generators as small as 160 cents ([[15edo]]) and as large as 165.5 cents ([[29edo]]). However, the 29edo patent val does not support 11-limit porcupine proper, since it does not temper out [[64/63]].
+== Chords and harmony ==
+{{Main| Chords of porcupine }}
 [[12/11]], [[11/10]], and [[10/9]] are all represented by the same interval, the generator. This makes chords such as 8:9:10:11:12 exceptionally common and easy to find.
@@ Line 197: / Line 201: @@
 The interval representing both [[25/24]] and [[81/80]] can be found in this interval chain at -7 steps, and ranges from about 45 to 80 cents depending on the tuning. This can be considered the "chroma" of porcupine temperament.
-== Chords ==
-{{Main| Chords of porcupine }}
 == Scales ==