User:Dummy index/Chromatic pairs and how we define haplotonic: Difference between revisions

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+= Proposal to simplify the definition =
+* In order to distinguish between the fixed category of [[:Category:Haplotonic scales]], etc., and the reciprocal relationship (haplotonic) + (albitonic) = (chromatic), the latter will be called, for example, MOS triplet. Every 3 successive generations of MOS that satisfies the above relationship will be called a MOS triplet.
+** Or moshaplotonic as a parent MOS, moschromatic as a descendant MOS, like that [[moschroma]] and [[mosdiesis]] are relative from any MOS scale of interest.
+* If the number of notes in the scale is important, consider using the [[Pentatonic]] and [[Heptatonic]] pages.
+* Based on the above equation and the nature of MOS, the chromatic must be a direct descendant of the albitonic. So I don't like the existence of mega-albitonic between albitonic and chromatic, even though the meanings of relational and categorical usages don't have to be exactly the same. (I will also withdraw the mini-albitonic that I said.)
+* Categorical haplotonic scales include the last MOS that s &ge; 125 ¢ and some subset of such scales. in <nowiki>[[Chromatic pairs]]</nowiki>, such subsets all may be labelled mini-haplotonic (even if there are more than one).
+* Categorical albitonic scale is the first MOS that s &lt; 125 ¢.
+** If the interval that appears is too narrow to be a semitone, it may be a [[Cluster MOS]].
+* Categorical chromatic scales include direct descendant of albitonic (by adding corresponding haplotonic) and further descendant <del>(by adding same haplotonic)</del>. in <nowiki>[[Chromatic pairs]]</nowiki>, such further descendants all may be labelled mega-chromatic (even if there are more than one).
+= Memos =
+I couldn't find a comprehensive explanation of haplotonic, so I'm going to consider the current situation in my own way.
+* [[Chromatic pairs]], [[Talk:Chromatic pairs]]
+* scales that labelled [[:Category:Haplotonic scales]]
+* Discord Xenharmonic Alliance
+haplotonic is something similar to the black keys of a piano. hmm...
+# Number of notes. about 5-notes. here I tentatively state the best is 4–6 notes.
+# (haplotonic)+(albitonic)=(chromatic). strong. (strict, but local)
+# Semitone-free MOS. some authors might consider this property. All labelled scales are s &gt; 125 ¢.
+In fact, it can be seen from condition 3 that the haplotonic scale is up to 9 notes.
+By the way, many of the scale-lists listed on <nowiki>[[Chromatic pairs]]</nowiki> are actually "chain of albitonic-chromatic pairs". Moreover, the part that is a arithmetic sequence is composed by repeatedly adding the same strong haplotonic scale. And the strong haplotonic is direct parent MOS of first albitonic of the arithmetic chain.
+* Nestoria[7], Nestoria[12], Nestoria[17] — adding Nestoria[5] repeatedly
+* (memo: strong haplotonic is "L will be new s if cutting s from L anymore" so soft-of-basic)
+* What I mean of albitonic-chromatic pairs is strict operation of equation of condition 2. And with MOS tree, albitonic-chromatic relation usually results in direct parent-daughter. Exception is (1L ''x''s)+(1L ''y''s)=(1a (1+''x''+''y'')b) (i dunno another case). Or adopt [[User:Ganaram inukshuk/Notes #Strict definition|his strict definition]]. You can then use ''n''*(haplotonic)+(albitonic)=(...) to move a few steps at once (<q>possibly multiple copies of one of them</q>).
+~~ Exercise ~~
+* I would like to exclude 1L ''x''s from the albitonic-chromatic pair. To reason this... excluding 1L from strong haplotonic.
+* First two strong haplotonic of Barton are Barton[2] and Barton[11]. Barton[2] is too few notes. Barton[11] is too many notes. Barton[3] and all descendants aren't semitone-free. Strong haplotonic can be obtained for any rank-2, but not always any haplotonic (in condition 1 and 3) can be.
+* Seni[5] and Sensi[8] both are labelled Category:Haplotonic scales. Only Sensi[8] is strong haplotonic, but Sensi[5] is shorter genchain, obviously more haplo than Sensi[8]. both haplotonic? mini-haplotonic and haplotonic? haplotonic and strong-haplotonic? Well, shouldn't both be haplotonic? Isn't it just that we want to differentiate it because we're trying to include it in the scale-list?
+** If there are multiple haplotonic scale in condition 1 and 3, it may be nice to name most-notes scale (must be strong haplotonic!) "strong haplotonic" or "maximum haplotonic" or "the end of haplotonic".
+*** Baldy[5] and Baldy[6] both are strong haplotonic, so we need to use different terms to distinguish them. e.g. Baldy4/5/6 are haplotonic and Baldy6 is max-haplotonic. Until Baldy5 become listed, Baldy6 is simply called haplotonic.
+* Fractional-octave?
+* Are they undoubtedly haplotonic? neutral third 3L 4s, mavila 2L 5s, ...
+= Category:Haplotonic scales (November 2024) =
+{| class="wikitable"
+|+ Caption text
+|-
+! Name !! Size of s (¢) !! # of notes<br>1–3: −, 4–6: ☆, 7–9: △ !! Strong !! Remarks
+|-
+| Baldy6 || 180 || ☆ || Yes || Baldy5 is also strong haplotonic for Baldy6-Baldy11 pair
+|-
+| Bleu8 || 140 || △ || Yes ||
+|-
+| Roulette6 || 195 || ☆ || Yes ||
+|-
+| Sensi5 || 130 || ☆ || No || direct parent of Sensi8
+|-
+| Sensi8 || 130 || △ || Yes ||
+|-
+| Silver7 || 128 || △ || Yes ||
+|-
+| Tutone6 || 194 || ☆ || Yes ||
+|}
+= Chromatic pairs (November 2024) =
 A '''chromatic pair''' is a pair of [[mos scale]]s in some [[rank-2 temperament]] (either a full [[Harmonic limit|''p''-limit]] temperament or a [[subgroup temperament]]) that are analogous to the familiar [[5L 2s|diatonic]] and [[chromatic]] scales of standard tuning. The smaller scale is an '''albitonic scale''' (from Latin ''albus'', "white"), named such since the diatonic scale can be played using the white keys of a piano, and the larger of the two is a '''chromatic scale''', analogous to the chromatic scale of standard tuning. Other related scales can be associated to chromatic pairs, namely a '''haplotonic scale''' (from Greek ''haplóos'', "single, simple"), analogous to the pentatonic scale of standard tuning and played using the black keys of a piano.