User:Eufalesio/Harmonic Segments Along Fifths: Difference between revisions
HSAF 1 is a stickler Tags: Visual edit Mobile edit Mobile web edit Advanced mobile edit |
Declared idiosyncratic terms and explained etymologies |
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{{Editable user page}} | {{Editable user page}}{{Idiosyncratic terms|"Zontatonic", "Íegmul" and "Ngwóoghe" were coined by Eufalesio and "Veljeuwof" by Lawitalawitaluna to have explicit names for HSAF 2, 3, 4, 8.}} | ||
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). | 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). | ||
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=== HSAF 2 - ''Zontatonic'' === | === HSAF 2 - ''Zontatonic'' === | ||
<code>12:14:16:18:21:24</code>. Harmonic segment: '''6::8'''. | <code>12:14:16:18:21:24</code>. Harmonic segment: '''6::8'''. Its name is derived as a portmanteau of [[color notation]] ''zo'' (septimal) and "pentatonic", which in this case refers specifically to HSAF 2, though the longer yet more understandable "septimal minor pentatonic" is a possible substitute. | ||
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]]. | ||
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=== HSAF 3 - ''Íegmul'' === | === HSAF 3 - ''Íegmul'' === | ||
<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'''. Its name is derived from the ''Rraei'' word for ''hearth,'' íegmul [ˈi.egmuɫ]. | ||
Second prime HSAF. It is naturally a [[7edo]] detemper in the [[2.3.5.11 subgroup]], and either a [[porcupine]] ([[1L 6s]] 3|3) or [[dicot]]/[[mothra]] detemper ([[3L 4s]] 5|1 #5). | Second prime HSAF. It is naturally a [[7edo]] detemper in the [[2.3.5.11 subgroup]], and either a [[porcupine]] ([[1L 6s]] 3|3) or [[dicot]]/[[mothra]] detemper ([[3L 4s]] 5|1 #5). | ||
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=== HSAF 4 - ''Ngwóoghe'' === | === HSAF 4 - ''Ngwóoghe'' === | ||
<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'''. Its name is derived from the Feñkioó word for ''stencil,'' ngwóoghe [ŋwôːɣe] | ||
First composite HSAF, containing HSAF 2 as a subset. It is naturally a [[10edo]] detemper in the [[2.3.5.7.13 subgroup]], a [[negri]] detemper ([[1L 8s]] 4|4) if you exclude 17/12, and a [[pajarous]] detemper, 2L 8s 6|2 #7 scale. | First composite HSAF, containing HSAF 2 as a subset. It is naturally a [[10edo]] detemper in the [[2.3.5.7.13 subgroup]], a [[negri]] detemper ([[1L 8s]] 4|4) if you exclude 17/12, and a [[pajarous]] detemper, 2L 8s 6|2 #7 scale. | ||
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=== HSAF 8 - ''Veljeuwof'' === | === HSAF 8 - ''Veljeuwof'' === | ||
<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.''' Its name is derived form the TBA word for ''twenty, veljeuwof'' [TBA]. | ||
It contains HSAF 2 and HSAF 4. As a superset of HSAF 4, it adds many new interesting intervals with odds 9, 11, 15, 21, 25, 29, 31, 35 along its modes. It is also the last HSAF to fit within the [[31-limit]]. | It contains HSAF 2 and HSAF 4. As a superset of HSAF 4, it adds many new interesting intervals with odds 9, 11, 15, 21, 25, 29, 31, 35 along its modes. It is also the last HSAF to fit within the [[31-limit]]. | ||