Kite's ups and downs notation: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 1,226: / Line 1,226: @@
 The initial consonant remains as before: D, R, M, F, S, L and T
-All consonants other than D and F have an alternate form that is flattened: R becomes Fr (mnemonic: f for flat), M -> N, S -> Sh, L -> Fl and T -> Th (unvoiced as in think).
+All consonants other than D and F have an alternate form that is flattened: R becomes Fr (mnemonic: F for flat), M -> N, S -> Sh, L -> Fl and T -> Th (unvoiced as in <u>th</u>ink).
 The vowels are pronounced as in Spanish or Italian. The vowel indicates up/down/plain. The vowel sequence can vary for different EDOs.
 ==== 41-EDO example ====
-Vowel sequence: u = ^, a = plain, o = v, i = vv. Mnemonic: u = '''<u>u</u>'''p, a = pl'''<u>a</u>'''in, o = d'''<u>o</u>'''wn, i = m'''<u>i</u>'''d.
+Vowel sequence: u = '''<u>u</u>'''p, a = pl'''<u>a</u>'''in, o = d'''<u>o</u>'''wn, i = m'''<u>i</u>'''d.
-* Fro = '''f'''lat-'''r'''e-d'''o'''wn = vm2
+* Fro = '''<u>f</u>'''lat-'''<u>r</u>'''e-d'''<u>o</u>'''wn = vm2
-* Fra = '''f'''lat-'''r'''e-pl'''a'''in = m2
+* Fra = '''<u>f</u>'''lat-'''<u>r</u>'''e-pl'''<u>a</u>'''in = m2
-* Fu = '''f'''lat-'''r'''e-'''u'''p = ^m2
+* Fru = '''<u>f</u>'''lat-'''<u>r</u>'''e-'''<u>u</u>'''p = ^m2
-* Ri = '''r'''e-m'''i'''d = ~2
+* Ri = '''<u>r</u>'''e-m'''<u>i</u>'''d = ~2
-* Ro = '''r'''e-d'''o'''wn = vM2
+* Ro = '''<u>r</u>'''e-d'''<u>o</u>'''wn = vM2
-* Ra = '''r'''e-pl'''a'''in = M2
+* Ra = '''<u>r</u>'''e-pl'''<u>a</u>'''in = M2
-* Ru = '''r'''e-'''u'''p = ^M2
+* Ru = '''<u>r</u>'''e-'''<u>u</u>'''p = ^M2
-A new consonant P indicates a sharpened 4th. (Mnemonic: Sha and Tha sharpen to Sa and Ta, so if Fa were spelled Pha, it would sharpen to Pa.) This lets us name 11/8, 45/32 and 10/7 as 4ths (Fi, Po and Pa).
+A new consonant P indicates a sharpened 4th. (Mnemonic: Sha and Tha sharpen to Sa and Ta, so if Fa were spelled Pha, it would sharpen to Pa.) This lets us name 45/32 and 10/7 as 4ths (Po and Pa).
 * unisons: Da Du
@@ Line 1,253: / Line 1,253: @@
 * 8ves: Do Da (Du)
-To find the octave inverse of any interval:
+Color notation tie-ins: -a = wa, -o = yo or zo, -u = gu or ru, and -i = ila. The zogu 5th is Sha because the -o and -u in zogu cancel to make -a.
-* change the '''degree''' as usual: 2nd <--> 7th, 3rd <--> 6th, and 4th <--> 5th
-* change the '''quality''' as usual: major <--> minor, aug <--> dim, but perfect and mid are unchanged
-* change the '''vowel''' as expected: -o <--> -u,  but -a and -i are unchanged
-For example, Fro = minor-Re-down becomes major-Ti-up = Tu. The rule for changing the quality means the ~4 and the ~5 must be either Fi & Si, or else Pi & Shi. The former is chosen because then the 6 mid intervals Ri Mi Fi Si Li Ti all use the default consonants.
+Example scales:
 * Plain major: Da Ra Ma Fa Sa La Ta Da
-* Plain phrygian: Da Fra Na Fa Sa Fla Tha Da
+* Plain minor: Da Ra Na Fa Sa Fla Tha Da
 * Upmajor: Da Ra Mu Fa Sa Lu Tu Da
 * Upminor: Da Ra Nu Fa Sa Flu Thu Da
@@ Line 1,270: / Line 1,265: @@
 * 2nd mode: Da Ra Mi Fi Sa Li Ti Da
 * Harmonics 8-16: Da Ra Mo Fi Sa Li Tho To Da
+To find the octave inverse of any interval:
+* change the '''degree''' as usual: 2nd <--> 7th, 3rd <--> 6th, and 4th <--> 5th
+* change the '''quality''' as usual: major <--> minor, aug <--> dim, but perfect and mid are unchanged
+* change the '''vowel''' as expected: -o <--> -u,  but -a and -i are unchanged
+For example, Fro = minor-Re-down becomes major-Ti-up = Tu. The rule for changing the quality means the ~4 and the ~5 must be either Fi & Si, or else Pi & Shi. The former is chosen because then the 6 mid intervals Ri Mi Fi Si Li Ti all use the default consonants.
+The 13 -a notes form a chain of 5ths running from the dim 5th to the aug 4th:
+Sha - Fra - Fla - Na - Tha - Fa - Da - Sa - Ra - La - Ma - Ta - Pa
+The aug 4th Pa is also the updim 5th Shu, which is the starting point for another 13-note chain of 5ths, all -u notes. Since Pu = Si, this leads to a 6-note chain of -i notes. This in turn leads to a 13-note -o chain, which leads back to the -a chain. 13 -a notes + 13 -u notes + 13 -o notes + 6 -i notes = 45 names = 41 notes with duplicate names for the 4 tritones. To summarize, the 4 vowels create 4 separate chains of 5ths, and the 4 tritones with duplicate names connect those 4 chains into one 41-note circle.
+{| class="wikitable"
+|+The 45 note names in circle-of-5ths order
+(read left-to-right, top-row-to-bottom-row)
+!d5
+!m2
+!m6
+!m3
+!m7
+!P4
+!P1
+!P5
+!M2
+!M6
+!M3
+!M7
+!A4 (d5)
+|-
+| colspan="6" |
+|Da
+|Sa
+|Ra
+|La
+|Ma
+|Ta
+|Pa (Shu)
+|-
+|Shu
+|Fru
+|Flu
+|Nu
+|Thu
+|Fu
+|Du
+|Su
+|Ru
+|Lu
+|Mu
+|Tu
+|Pu (Si)
+|-
+| colspan="7" |
+|Si
+|Ri
+|Li
+|Mi
+|Ti
+|Fi (Sho)
+|-
+|Sho
+|Fro
+|Flo
+|No
+|Tho
+|Fo
+|Do
+|So
+|Ro
+|Lo
+|Mo
+|To
+|Po (Sha)
+|-
+|Sha
+|Fra
+|Fla
+|Na
+|Tha
+|Fa
+|Da
+| colspan="6" |
+|}
+As a result, it's very easy to find the note a 4th or 5th above any note. It always has the same vowel, and the consonant is as would be expected from conventional interval arithmetic. Thus Ra plus a 4th is Sa, Fro plus a 5th is Flo, etc. However the note a 5th above an aug or mid 4th would be an aug or mid 8ve, which don't exist in this solfege. Therefore one must rename the aug/mid 4th to a dim/mid 5th. Thus Po + 5th = Sha + 5th = Fra. Dim/mid 5ths may also need renaming: Sha + 4th = Po + 4th = To.
+A few minor exceptions arise with the -i notes. Conventionally, M7 + 5th = A4, and indeed Ta + 5th = Pa. But Ti + 5th = Fi not Pi. Likewise Fa + 4th = Tha, a minor 7th as expected, but Fi + 4th = Ti not Thi. These exceptions are not an issue as long as you remember that there is no Pi or Thi in the solfege
+The same rule for 4ths and 5ths also holds for plain major 2nds. Keep the vowel, and change the consonant as expected. Ra + M2 = Ma. Again, aug/dim intervals must be renamed: Po + M2 = Sha + M2 = Fla. But beware, this rule breaks down for major and mid 7ths:
+* Tu + M2 = Ri
+* Ta + M2 = Fru
+* To + M2 = Fra
+* Ti + M2 = Fro
 === Double-vowel solfege ===