User:Dummy index/Chromatic pairs and how we define haplotonic: Difference between revisions
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# Number of notes. about 5-notes. here I tentatively state the best is 4–6 notes. | # Number of notes. about 5-notes. here I tentatively state the best is 4–6 notes. | ||
# (haplotonic)+(albitonic)=(chromatic). strong. | # (haplotonic)+(albitonic)=(chromatic). strong. (strict, but local) | ||
# Semitone-free MOS. some authors might consider this property. All labelled scales are s > 125 ¢. | # Semitone-free MOS. some authors might consider this property. All labelled scales are s > 125 ¢. | ||
In fact, it can be seen from condition 3 that the haplotonic scale is up to 9 notes. | 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. | 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 | * 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) | * (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). You can then use ''n''*(haplotonic)+(albitonic)=(...) to move a few steps at once (<q>possibly multiple copies of one of them</q>). | * 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 ~~ | ~~ Exercise ~~ | ||
* I would like to exclude 1L | * 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. | * 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? | * 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". | ** 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. | |||
* Fractional-octave? | |||