User:Eufalesio/Harmonic Segments Along Fifths: Difference between revisions
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* Harmonic segments conforming HSAFs up to the 13th* are [[strictly proper]] [[constant structure]]<nowiki/>s. | * Harmonic segments conforming HSAFs up to the 13th* are [[strictly proper]] [[constant structure]]<nowiki/>s. | ||
* The kth HSAF is a subset of the 6k::12k harmonic segment. | * The kth HSAF is a subset of the 6k::12k harmonic segment. | ||
* Because they are formed from harmonic series segments, they are chiral scales*, whose left-handed counterparts are built from [[subharmonic series]] segments. The left-handed versions are '''not''' HSAFs per se. They are only the chiral version of the HSAF. | * Because they are formed from harmonic series segments, they are chiral scales*, whose left-handed counterparts are built from [[subharmonic series]] segments. The left-handed versions are '''not''' HSAFs per se. They are only the chiral version of the HSAF, which you might call a SSAF, for Subharmonic Segment [...]. | ||
<nowiki>*</nowiki>except the first | <nowiki>*</nowiki>except the first | ||
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For every provided HSAF, the [[EFR]] and used segment are written out explicitly. | For every provided HSAF, the [[EFR]] and used segment are written out explicitly. | ||
=== HSAF 1 - Pythagorean Trial === | === HSAF/SSAF 1 - Pythagorean Trial === | ||
<code>6:8:9:12</code>. Harmonic segment: '''3:4'''. | <code>6:8:9:12</code>. Harmonic segment: '''3:4'''. | ||
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<code>42:44:46:48:50:52:54:56:63:66:69:72:75:78:81:84</code>'''.''' Harmonic segment: '''21::28'''. | <code>42:44:46:48:50:52:54:56:63:66:69:72:75:78:81:84</code>'''.''' Harmonic segment: '''21::28'''. | ||
The fourth prime HSAF. The most reasonable heHSAF with 29/21 and 10/7 contains 7::14 as a subset. A good seHSAFs is with 11/8 and 13/9. | The fourth prime HSAF. The most reasonable heHSAF with 29/21 and 10/7 contains 7::14 as a subset. A good seHSAFs is with 11/8 and 13/9. SSAF 7 is surprisingly a subharmonic interpolation of HSAF 3. | ||
It is naturally a [[17edo]] detemper in the no-5,17,19,add-25-29-limit subgroup. Its extension can be seen as a strange liese extension detemper ([[2L 15s]] 15|1 10b). | It is naturally a [[17edo]] detemper in the no-5,17,19,add-25-29-limit subgroup. Its extension can be seen as a strange liese extension detemper ([[2L 15s]] 15|1 10b). | ||