Xenharmonic Wiki

User:Eufalesio/Harmonic Segments Along Fifths: Difference between revisions

← Older edit
VisualWikitext
Eufalesio (talk | contribs)
autopatrolled
885 edits
Tighten
Eufalesio (talk | contribs)
autopatrolled
885 edits
Ready to delete as it has been published into main space
 
(4 intermediate revisions by the same user not shown)
Line 1: Line 1:
{{Editable user page}}
{{Delete|If main article is to be kept, this is no longer necessary.}}


Harmonic Segments Along Fifths (HSAF) [sing. ''a Harmonic Segment along Fifths''] are a type of octave-[[periodic scale]] built by taking a specific [[harmonic series segment]] that ends in 4/3 and repeating times 3/2. They are a unique mix of [[tetrachord]]<nowiki/>s and [[overtone scales]] that exhibit [[omnitetrachordality]] to some extent, and a type of [[NEJI]] (Near-equivalent Just Intonation). How to approach them musically is not within the scope of this article.
Harmonic Segments Along Fifths (HSAF) [sing. ''a Harmonic Segment along Fifths''] are a type of octave-[[periodic scale]] built by taking a specific [[harmonic series segment]] that ends in 4/3 and repeating times 3/2. They are a unique mix of [[tetrachord]]<nowiki/>s and [[overtone scales]] that exhibit [[omnitetrachordality]] to some extent, and a type of [[NEJI]] (Near-equivalent Just Intonation).


== Definitions ==
== Definitions ==
Line 9: Line 9:
* Its prime mode always contains 4/3 and 3/2.
* Its prime mode always contains 4/3 and 3/2.
* Its prime mode is built like a harmonic series segment up to 4/3, and that same harmonic segment is repeated transposed by 3/2 until it reaches the octave.
* Its prime mode is built like a harmonic series segment up to 4/3, and that same harmonic segment is repeated transposed by 3/2 until it reaches the octave.
* Its [[delta signature]] is +2,+2,+2,+2,[…],+3,+3,+3,[…]. If the HSAF is even-indexed, the +3's start right at 3/2. If the HSAF is odd-indexed, at the step right before 3/2.
* HSAF 1 is 6:8:9:12 with [[delta signature]] +2,+1,+2. Except for HSAF 1, its delta signature is +2,+2,+2,+2,[…],+3,+3,+3,[…]. If the HSAF is even-indexed, the +3's start right at 3/2. If the HSAF is odd-indexed, at the step right before 3/2.


These scales require the harmonic segment to start with a threeven number and end with that number times 4/3, so HSAF are a countable set of scales, and thus can be indexed.
These scales require the harmonic segment to start with a threeven number and end with that number times 4/3, so HSAFs are a countable set of scales, and thus can be indexed.


== Properties ==
== Properties ==
Line 43: Line 43:
|}
|}


=== HSAF 2 - ''Zontatonic'' ===
=== HSAF 2 - Septimal minor pentatonic ===
<code>12:14:16:18:21:24</code>. Harmonic segment: '''6::8'''.  
<code>12:14:16:18:21:24</code>. Harmonic segment: '''6::8'''.  


First usable HSAF, the first prime HSAF, and the only one that is [[Strict variety]] 3 and a [[generator sequence]].
First usable HSAF, the first prime HSAF, and the only one that is [[Strict variety]] 3 and a [[generator sequence]].
Line 77: Line 77:
|}
|}


=== HSAF 3 - ''Íegmul'' ===
=== HSAF 3 ===
<code>18:20:22:24:27:30:33:36</code>. Harmonic segment: '''9::12'''.  
<code>18:20:22:24:27:30:33:36</code>. Harmonic segment: '''9::12'''.  


Line 133: Line 133:
|}
|}


=== HSAF 4 - ''Ngwóoghe'' ===
=== HSAF 4 ===
<code>24:26:28:30:32:34:36:39:42:45:48</code>. Harmonic segment: '''12::16'''.
<code>24:26:28:30:32:34:36:39:42:45:48</code>. Harmonic segment: '''12::16'''.


Line 923: Line 923:
|}
|}


=== HSAF 8 - ''Veljeuwof'' ===
=== HSAF 8 ===
<code>48:50:52:54:56:58:60:62:64:66:68:70:72:75:78:81:84:87:90:93:96</code>. Harmonic segment: '''24::32.'''
<code>48:50:52:54:56:58:60:62:64:66:68:70:72:75:78:81:84:87:90:93:96</code>. Harmonic segment: '''24::32.'''


Retrieved from "https://en.xen.wiki/w/User:Eufalesio/Harmonic_Segments_Along_Fifths"