User talk:Lhearne: Difference between revisions

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::::::::::::::::::::: 'Large' and 'little' are great prefixes to use, but I was hoping to use them for alterations of 896/891 these days, where 14/11 is a Large Major 3rd. I'm unsure how 2.11 is necessarily more 'structural' than 2.5 or 2.7. Is it because you get to small intervals (<~50c) sooner? After only 3 5s or 5 7s? As opposed to 12 3s or 13 11s? It takes 10 13s, so maybe 13 is 'structural' as well? 7/4 is a type of minor seventh for me, and for many, and so is defined as sm7, as it was by Helmholtz in 1863 (translated into English by Ellis in 1875). The first comma we need in 2.7 would be 49/48, which I want to call Q. Amazingly, an interval of such size is known as a 'quark', so I can, in fact, use Q. Our obvious tempering to 2.3.7 is via the gamalisma 1029/1024, where Q=S. We can have our 2.7 'lattice' SM2 q4 Q5 sm7 P8. I think a pentatonic lattice is appropriate, though it may be extended to a 36-tone lattice when combined with the Pythagorean lattice, akin to the 24-note alpharabian/pythagorean lattice, for the 2.3.7 Gamelismic sixth-tone lattice

::::::::::::::::::::: 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.

:::::::::::::::::::::: 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?

:::::::::::::::::::::: I chose the Alpharabian Harmonic Scale in part because of the immense difficulty I'm currently having in reconciling the interval math with the Pythagorean system. Truth be told, however, I am willing to go with a more even scale, but I'm just keeping things relatively simple at the moment, and I am familiar with the Harmonic scale from more classical-style music. I hope this sheds more light on why I'm going the way I'm going at the moment. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:48, 11 February 2021 (UTC)

: In other news, I have called [[45/44]] 'O' after Ocean Stegasaurus Tardigrade's cake story associated with the comma, given that 'c' is already taken. Using this, and R, I have given 94edo well-ordered names:

: P1 R1 S1/C1 O1 U1/om2 sm2 rm2 m2 Rm2 Cm2 Om2 n2 N2 oM2 cM2 rM2 M2 RM2 SM2 OM2 om3 sm3 rm3 m3 Rm3 Cm3 Om3 n3 N3 oM3 cM3 rM3 M3 RM3 SM3 m4 o4 s4 r4 P4 R4 C4 O4 M4 uA4/sd5 oA4/rd5 cA4/d5 rA4/Rd5 A4/Cd5 RA4/Od5 SA4/Ud5 m5 o5 c5 r5 P5 R5 S5 O5 M5 sm6 rm6 m6 Rm6 Cm6 Om6 n6 N6 oM6 cM6 rM6 M6 RM6 SM6 OM6 om7 sm7 rm7 m7 Rm7 Cm7 Om7 n7 N7 oM7 cM7 rM7 M7 RM7 SM7 OM7/u8 o8 s8/c8 r8 P8 (I'm writing this out of order, and I just realised that I could have used Q instead of O here. Since we're treating 94edo as 11-limit, I can't see one being any better than the other, though I guess O leads to some simpler intervals).

: most importantly this gives us 11/10 as oM2 and 15/11 as O4. I'd like to call these intervals the oceanic major second and oceanic fourth, because those names work for me, and whenever o prefixes M, A, or P5, and O prefixes m, d, or P4, and elsewhere 'ocean-Wide' and 'ocean-narrow'. Could also be 'Over' and 'off', or 'On' and 'off'. This is exactly akin to my use of R, C, but I haven't got a pair like super/sub for those letters.

: I should redo 72edo now (11-limit): P1 C1 S1 U1 sm2 lm2 m2 Cm2 Qm2 n2/N2 qM2 cM2 M2 LM2 SM2 UM2/um3 sm3 lm3 m3 Cm3 Qm3 n3/N3 qM3 cM3 M3 LM3 SM3 m4 s4 l4 P4 C4 Q4 M4 qA4/sd5 cA4 A4/d5 Cd5 SA4/Qd5 m5 q5 c5 P5 L5 S5 M5 sm6 lm6 m6 Cm6 Qm6 n6/N6 qM6 cM6 M6 LM6 SM6 UM6/um7 sm7 lm7 m7 Cm7 Qm7 N7 qM7 cM7 M7 LM7 SM7 u8 s8 c8 P8. I guess M1 and m8 are unlikely to be accepted... --[[User:Lhearne|Lhearne]] ([[User talk:Lhearne|talk]]) 19:14, 11 February 2021 (UTC)

:: I certainly like the developments for "O" and "Q" on this front. However, I do have very serious doubts about the likelihood of M1 and m8 ever being accepted. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:48, 11 February 2021 (UTC)

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 ::::::::::::::::::::: 'Large' and 'little' are great prefixes to use, but I was hoping to use them for alterations of 896/891 these days, where 14/11 is a Large Major 3rd. I'm unsure how 2.11 is necessarily more 'structural' than 2.5 or 2.7. Is it because you get to small intervals (<~50c) sooner? After only 3 5s or 5 7s? As opposed to 12 3s or 13 11s? It takes 10 13s, so maybe 13 is 'structural' as well? 7/4 is a type of minor seventh for me, and for many, and so is defined as sm7, as it was by Helmholtz in 1863 (translated into English by Ellis in 1875). The first comma we need in 2.7 would be 49/48, which I want to call Q. Amazingly, an interval of such size is known as a 'quark', so I can, in fact, use Q. Our obvious tempering to 2.3.7 is via the gamalisma 1029/1024, where Q=S. We can have our 2.7 'lattice' SM2 q4 Q5 sm7 P8. I think a pentatonic lattice is appropriate, though it may be extended to a 36-tone lattice when combined with the Pythagorean lattice, akin to the 24-note alpharabian/pythagorean lattice, for the 2.3.7 Gamelismic sixth-tone lattice
 ::::::::::::::::::::: 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.
+:::::::::::::::::::::: 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?
+:::::::::::::::::::::: I chose the Alpharabian Harmonic Scale in part because of the immense difficulty I'm currently having in reconciling the interval math with the Pythagorean system.  Truth be told, however, I am willing to go with a more even scale, but I'm just keeping things relatively simple at the moment, and I am familiar with the Harmonic scale from more classical-style music.  I hope this sheds more light on why I'm going the way I'm going at the moment. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:48, 11 February 2021 (UTC)
 : In other news, I have called [[45/44]] 'O' after Ocean Stegasaurus Tardigrade's cake story associated with the comma, given that 'c' is already taken. Using this, and R, I have given 94edo well-ordered names:
 : P1 R1 S1/C1 O1 U1/om2 sm2 rm2 m2 Rm2 Cm2 Om2 n2 N2 oM2 cM2 rM2 M2 RM2 SM2 OM2 om3 sm3 rm3 m3 Rm3 Cm3 Om3 n3 N3 oM3 cM3 rM3 M3 RM3 SM3 m4 o4 s4 r4 P4 R4 C4 O4 M4 uA4/sd5 oA4/rd5 cA4/d5 rA4/Rd5 A4/Cd5 RA4/Od5 SA4/Ud5 m5 o5 c5 r5 P5 R5 S5 O5 M5 sm6 rm6 m6 Rm6 Cm6 Om6 n6 N6 oM6 cM6 rM6 M6 RM6 SM6 OM6 om7 sm7 rm7 m7 Rm7 Cm7 Om7 n7 N7 oM7 cM7 rM7 M7 RM7 SM7 OM7/u8 o8 s8/c8 r8 P8 (I'm writing this out of order, and I just realised that I could have used Q instead of O here. Since we're treating 94edo as 11-limit, I can't see one being any better than the other, though I guess O leads to some simpler intervals).
 : most importantly this gives us 11/10 as oM2 and 15/11 as O4. I'd like to call these intervals the oceanic major second and oceanic fourth, because those names work for me, and whenever o prefixes M, A, or P5, and O prefixes m, d, or P4, and elsewhere 'ocean-Wide' and 'ocean-narrow'. Could also be 'Over' and 'off', or 'On' and 'off'. This is exactly akin to my use of R, C, but I haven't got a pair like super/sub for those letters.
 : I should redo 72edo now (11-limit): P1 C1 S1 U1 sm2 lm2 m2 Cm2 Qm2 n2/N2 qM2 cM2 M2 LM2 SM2 UM2/um3 sm3 lm3 m3 Cm3 Qm3 n3/N3 qM3 cM3 M3 LM3 SM3 m4 s4 l4 P4 C4 Q4 M4 qA4/sd5 cA4 A4/d5 Cd5 SA4/Qd5 m5 q5 c5 P5 L5 S5 M5 sm6 lm6 m6 Cm6 Qm6 n6/N6 qM6 cM6 M6 LM6 SM6 UM6/um7 sm7 lm7 m7 Cm7 Qm7 N7 qM7 cM7 M7 LM7 SM7 u8 s8 c8 P8. I guess M1 and m8 are unlikely to be accepted... --[[User:Lhearne|Lhearne]] ([[User talk:Lhearne|talk]]) 19:14, 11 February 2021 (UTC)
+:: I certainly like the developments for "O" and "Q" on this front.  However, I do have very serious doubts about the likelihood of M1 and m8 ever being accepted. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:48, 11 February 2021 (UTC)