User talk:Lhearne: Difference between revisions

Line 113:

::::::::::::::::: I can see you are working towards an interval naming scheme taking some ideas from mine, but based on an Alpharabian rather than Pythagorean system. I don't yet know the Alpharabian interval arithmetic, or which scale you might be basing it on, but your ideas all sound logical. I like the idea of ">" and "<" in general, and, for this Alpharabia interval name system, N and n.

::::::::::::::::: For my/the Pythagorean-based I think I would like to add a prefix for the diaschisma. It seems more necessary to me so far than the septimal kleisma. The problem I'm having however is that 'd' is already used for 'diminished' :/ --[[User:Lhearne|Lhearne]] ([[User talk:Lhearne|talk]]) 14:12, 8 February 2021 (UTC)

:::::::::::::::::: For the record, the Alpharabian system as a whole contains the Pythagorean system within it, and thus the system requires both Alpharabian and Pythagorean axes. In effect, I'm basing this on these two scales:

:::::::::::::::::: The Pythagorean Chromatic Scale:

:::::::::::::::::: 1/1 (P1), 256/243 (m2), 9/8 (M2), 32/27 (m3), 81/64 (M3), 4/3 (P4), 729/512 (A4), 1024/729 (d5), 3/2 (P5), 128/81 (m6), 27/16 (M6), 16/9 (m7), 243/128 (M7), 2/1 (P8)

:::::::::::::::::: The Alpharabian Harmonic Scale:

:::::::::::::::::: 1/1 (P1), 128/121 (Rm2), 16384/14641 (RRd3), 1331/1024 (rUM3), 11/8 (M4), 16/11 (m5), 2048/1331 (Rum6), 14641/8192 (rrA6), 121/64 (rM7), 2/1 (P8)

:::::::::::::::::: (Since the Alpharabian Harmonic scales is made from nothing but the 2.11 subgroup, I trust you can deduce the interval arithmetic of the Alpharabian Axis from this)

:::::::::::::::::: To make a Parachromatic scale resembling a more just version of the note selection of 24edo, we need the following intervals relative to the Tonic:

:::::::::::::::::: 1/1 (P1), 33/32 (U1), 8192/8019 (um2), 256/243 (m2), 88/81 (n2), 12/11 (N2), 9/8 (M2), 297/256 (UM2), 1024/891 (um3), 32/27 (m3), 11/9 (n3), 27/22 (N3), 81/64 (M3), 2673/2048 (UM3), 128/99 (m4), 4/3 (P4), 11/8 (M4), 729/512 (A4), 1024/729 (d5), 16/11 (m5), 3/2 (P5), 99/64 (M5), 4096/2673 (um6), 128/81 (m6), 44/27 (n6), 18/11 (N6), 27/16 (M6), 891/512 (UM6), 512/297 (um7), 16/9 (m7), 11/6 (n7), 81/44 (N7), 243/128 (M7), 8019/4096 (UM7), 64/33 (u8), 2/1 (P8)

:::::::::::::::::: I hope all this gives you a better picture as to what I'm doing here. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:39, 8 February 2021 (UTC)

@@ Line 113: / Line 113: @@
 ::::::::::::::::: I can see you are working towards an interval naming scheme taking some ideas from mine, but based on an Alpharabian rather than Pythagorean system. I don't yet know the Alpharabian interval arithmetic, or which scale you might be basing it on, but your ideas all sound logical. I like the idea of ">" and "<" in general, and, for this Alpharabia interval name system, N and n.
 ::::::::::::::::: For my/the Pythagorean-based I think I would like to add a prefix for the diaschisma. It seems more necessary to me so far than the septimal kleisma. The problem I'm having however is that 'd' is already used for 'diminished' :/ --[[User:Lhearne|Lhearne]] ([[User talk:Lhearne|talk]]) 14:12, 8 February 2021 (UTC)
+:::::::::::::::::: For the record, the Alpharabian system as a whole contains the Pythagorean system within it, and thus the system requires both Alpharabian and Pythagorean axes.  In effect, I'm basing this on these two scales:
+:::::::::::::::::: The Pythagorean Chromatic Scale:
+:::::::::::::::::: 1/1 (P1), 256/243 (m2), 9/8 (M2), 32/27 (m3), 81/64 (M3), 4/3 (P4), 729/512 (A4), 1024/729 (d5), 3/2 (P5), 128/81 (m6), 27/16 (M6), 16/9 (m7), 243/128 (M7), 2/1 (P8)
+:::::::::::::::::: The Alpharabian Harmonic Scale:
+:::::::::::::::::: 1/1 (P1), 128/121 (Rm2), 16384/14641 (RRd3), 1331/1024 (rUM3), 11/8 (M4), 16/11 (m5), 2048/1331 (Rum6), 14641/8192 (rrA6), 121/64 (rM7), 2/1 (P8)
+:::::::::::::::::: (Since the Alpharabian Harmonic scales is made from nothing but the 2.11 subgroup, I trust you can deduce the interval arithmetic of the Alpharabian Axis from this)
+:::::::::::::::::: To make a Parachromatic scale resembling a more just version of the note selection of 24edo, we need the following intervals relative to the Tonic:
+:::::::::::::::::: 1/1 (P1), 33/32 (U1), 8192/8019 (um2), 256/243 (m2), 88/81 (n2), 12/11 (N2), 9/8 (M2), 297/256 (UM2), 1024/891 (um3), 32/27 (m3), 11/9 (n3), 27/22 (N3), 81/64 (M3), 2673/2048 (UM3), 128/99 (m4), 4/3 (P4), 11/8 (M4), 729/512 (A4), 1024/729 (d5), 16/11 (m5), 3/2 (P5), 99/64 (M5), 4096/2673 (um6), 128/81 (m6), 44/27 (n6), 18/11 (N6), 27/16 (M6), 891/512 (UM6), 512/297 (um7), 16/9 (m7), 11/6 (n7), 81/44 (N7), 243/128 (M7), 8019/4096 (UM7), 64/33 (u8), 2/1 (P8)
+:::::::::::::::::: I hope all this gives you a better picture as to what I'm doing here. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:39, 8 February 2021 (UTC)