User talk:Lhearne: Difference between revisions

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::::::::::::::::::::: S1 sm2 m2 Qm2 qM2 M2 SM2 sm3 m3 Qm3 qM3 M3 SM3 s4 P4 Q4 qA4 A4 or d5 Qd5 q5 P5 S5 sm6 m6 Qm6 qM6 M6 SM6 sm7 m7 Qm7 qM7 M7 SM7 s8 P8. where Qm and qM are septimal neutral intervals. This was much easier than 2.5 haha. I wonder why you chose a 9-note scale for your Alpharabian harmonic scale, and not either of the more even 11-note or 13-note MOS scales. The 11 and 13-note scales generated by 11/8 were used first by Wyschnegradsky, in 24edo, who called 11/8 the 'Major Fourth', as you have, and I did once (probably after reading on Wyschnegradsky). Maybe given the reminder of this historical context I may yet come back around... We could write Major and minor, where (Para)Major and (para)minor is implied for M and m fourths and fifths, since we can't agree on anything else, at least yet... Tbh could even just say for fourths and fifths, major and minor means x, and then there aren't any problems... maybe should see what others think of that. Actually then P is between M and m, and N/n is/are between M and m, and the scale of Perfects and Neutrals is 2.3.11 - Mohajira[7]: n2/N2 n3/N3 P4 P5 n6/N6 n7/N7 P8. Mohajira[10]: n2/N2 M2 n3/N3 P4 M4 P5 n6/N6 m7 n7/N7 P8. I kinda want U1/u8 to be M1/m8 as well, so we can have Mohajira[17]: M1 n2/N2 M2 m3 n3/N3 M3 P4 M4 m5 P5 m6 n6/N6 M6 m7 n7/N7 m8 P8, and Mohajira[24]: M1 m2 n2/N2 M2 UM2 m3 n3/N3 M3 m4 P4 M4 A4 or d5 m5 P5 M5 m6 n6/N6 M6 um7 m7 n7/N7 M7 m8 P8. --[[User:Lhearne|Lhearne]] ([[User talk:Lhearne|talk]]) 19:13, 11 February 2021 (UTC)

:::::::::::::::::::::: The reason I consider the 11-prime to be more structural has most everything to do with how it only takes two types of undecimal quartertones (33/32 and 4096/3993) to add up to a 9/8 whole tone, and that the 2.3.11 subgroup does this with simpler interval ratios than do either 7, 13, 17 or even 19- yes, I've checked this mathematically. Simultaneously, quartertones are the smallest intervals which seem to somewhat widely have a sense of their own unique identity. See [[User:Aura/Aura's Ideas on Tonality#Navigational Primes and the Parachromatic-Paradiatonic Contrast|the relevant section on this rather messy page]] in which I detail the specifics of my findings in this realm.

:::::::::::::::::::::: The reason I consider the 11-prime to be more structural has most everything to do with how it only takes two types of undecimal quartertones (33/32 and 4096/3993) to add up to a 9/8 whole tone, and that the 2.3.11 subgroup does this with simpler interval ratios than do either 2.3.7, 2.3.13, 2.3.17 or even 2.3.19- yes, I've checked this mathematically. Simultaneously, quartertones are the smallest intervals which seem to somewhat widely have a sense of their own unique identity. See [[User:Aura/Aura's Ideas on Tonality#Navigational Primes and the Parachromatic-Paradiatonic Contrast|the relevant section on this rather messy page]] in which I detail the specifics of my findings in this realm.

:::::::::::::::::::::: I should point out that it is precisely because of the differing relationships that 7/4 engages in in the intervals 14/11 (in which it acts as a type of major third) and 7/6 (in which it also acts as a subminor third) that lead me to question the status of 7/4. Given that 11/8 can be solidly considered a fourth relative to the Tonic, and given that a third up from a fourth makes a sixth, that would make 7/4 a type of sixth. At the same time, since 3/2 is a solid fifth relative to the Tonic, and a third up from a fifth makes a seventh, that would make 7/4 a type of seventh. So, which one is it? Or is it somehow both at the same time?

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 ::::::::::::::::::::: S1 sm2 m2 Qm2 qM2 M2 SM2 sm3 m3 Qm3 qM3 M3 SM3 s4 P4 Q4 qA4 A4 or d5 Qd5 q5 P5 S5 sm6 m6 Qm6 qM6 M6 SM6 sm7 m7 Qm7 qM7 M7 SM7 s8 P8. where Qm and qM are septimal neutral intervals. This was much easier than 2.5 haha. I wonder why you chose a 9-note scale for your Alpharabian harmonic scale, and not either of the more even 11-note or 13-note MOS scales. The 11 and 13-note scales generated by 11/8 were used first by Wyschnegradsky, in 24edo, who called 11/8 the 'Major Fourth', as you have, and I did once (probably after reading on Wyschnegradsky). Maybe given the reminder of this historical context I may yet come back around... We could write Major and minor, where (Para)Major and (para)minor is implied for M and m fourths and fifths, since we can't agree on anything else, at least yet... Tbh could even just say for fourths and fifths, major and minor means x, and then there aren't any problems... maybe should see what others think of that. Actually then P is between M and m, and N/n is/are between M and m, and the scale of Perfects and Neutrals is 2.3.11 - Mohajira[7]: n2/N2 n3/N3 P4 P5 n6/N6 n7/N7 P8. Mohajira[10]: n2/N2 M2 n3/N3 P4 M4 P5 n6/N6 m7 n7/N7 P8. I kinda want U1/u8 to be M1/m8 as well, so we can have Mohajira[17]: M1 n2/N2 M2 m3 n3/N3 M3 P4 M4 m5 P5 m6 n6/N6 M6 m7 n7/N7 m8 P8, and Mohajira[24]: M1 m2 n2/N2 M2 UM2 m3 n3/N3 M3 m4 P4 M4 A4 or d5 m5 P5 M5 m6 n6/N6 M6 um7 m7 n7/N7 M7 m8 P8. --[[User:Lhearne|Lhearne]] ([[User talk:Lhearne|talk]]) 19:13, 11 February 2021 (UTC)
-:::::::::::::::::::::: The reason I consider the 11-prime to be more structural has most everything to do with how it only takes two types of undecimal quartertones (33/32 and 4096/3993) to add up to a 9/8 whole tone, and that the 2.3.11 subgroup does this with simpler interval ratios than do either 7, 13, 17 or even 19- yes, I've checked this mathematically.  Simultaneously, quartertones are the smallest intervals which seem to somewhat widely have a sense of their own unique identity.  See [[User:Aura/Aura's Ideas on Tonality#Navigational Primes and the Parachromatic-Paradiatonic Contrast|the relevant section on this rather messy page]] in which I detail the specifics of my findings in this realm.
+:::::::::::::::::::::: The reason I consider the 11-prime to be more structural has most everything to do with how it only takes two types of undecimal quartertones (33/32 and 4096/3993) to add up to a 9/8 whole tone, and that the 2.3.11 subgroup does this with simpler interval ratios than do either 2.3.7, 2.3.13, 2.3.17 or even 2.3.19- yes, I've checked this mathematically.  Simultaneously, quartertones are the smallest intervals which seem to somewhat widely have a sense of their own unique identity.  See [[User:Aura/Aura's Ideas on Tonality#Navigational Primes and the Parachromatic-Paradiatonic Contrast|the relevant section on this rather messy page]] in which I detail the specifics of my findings in this realm.
 :::::::::::::::::::::: I should point out that it is precisely because of the differing relationships that 7/4 engages in in the intervals 14/11 (in which it acts as a type of major third) and 7/6 (in which it also acts as a subminor third) that lead me to question the status of 7/4.  Given that 11/8 can be solidly considered a fourth relative to the Tonic, and given that a third up from a fourth makes a sixth, that would make 7/4 a type of sixth.  At the same time, since 3/2 is a solid fifth relative to the Tonic, and a third up from a fifth makes a seventh, that would make 7/4 a type of seventh.  So, which one is it?  Or is it somehow both at the same time?