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| === Single-vowel solfege === | | === Single-vowel solfege === |
| The initial consonant remains as before: D, R, M, F, S, L and T | | The initial consonant remains as before: D, R, M, F, S, L and T. The vowel indicates up/down/plain etc. The vowel sequence varies for different EDOs. See [[22edo Solfege|22edo solfege]], [[31edo solfege]] and [[41edo solfege]]. |
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| 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).
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| The vowels are pronounced as in Spanish or Italian. The vowel indicates up/down/plain. The vowel sequence can vary for different EDOs.
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| ==== 41-EDO example ====
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| 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.
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| * Fro = '''<u>f</u>'''lat-'''<u>r</u>'''e-d'''<u>o</u>'''wn = vm2
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| * Fra = '''<u>f</u>'''lat-'''<u>r</u>'''e-pl'''<u>a</u>'''in = m2
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| * Fru = '''<u>f</u>'''lat-'''<u>r</u>'''e-'''<u>u</u>'''p = ^m2
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| * Ri = '''<u>r</u>'''e-m'''<u>i</u>'''d = ~2
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| * Ro = '''<u>r</u>'''e-d'''<u>o</u>'''wn = vM2
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| * Ra = '''<u>r</u>'''e-pl'''<u>a</u>'''in = M2
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| * Ru = '''<u>r</u>'''e-'''<u>u</u>'''p = ^M2
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| 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).
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| * unisons: Da Du
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| * 2nds: Fro Fra Fru Ri Ro Ra Ru
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| * 3rds: No Na Nu Mi Mo Ma Mu
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| * 4ths: Fo Fa Fu
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| * tritones: Fi/Sho Po/Sha Pa/Shu Pu/Si
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| * 5ths: So Sa Su
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| * 6ths: Flo Fla Flu Li Lo La Lu
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| * 7ths: Tho Tha Thu Ti To Ta Tu
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| * 8ves: Do Da (Du)
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| 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.
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| Example scales:
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| * Plain major: Da Ra Ma Fa Sa La Ta Da
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| * Plain minor: Da Ra Na Fa Sa Fla Tha Da
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| * Upmajor: Da Ra Mu Fa Sa Lu Tu Da
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| * Upminor: Da Ra Nu Fa Sa Flu Thu Da
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| * Downmajor: Da Ra Mo Fa Sa Lo To Da
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| * Downminor: Da Ra No Fa Sa Flo Tho Da
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| * 3rd mode of [[243/242#Neutral|Lulu/Rastmic[7]]]: Da Ra Mi Fa Sa Li Ti Da
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| * 2nd mode: Da Ra Mi Fi Sa Li Ti Da
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| * Harmonics 8-16: Da Ra Mo Fi Sa Li Tho To Da
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| To find the octave inverse of any interval:
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| * change the '''degree''' as usual: 2nd <--> 7th, 3rd <--> 6th, and 4th <--> 5th
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| * change the '''quality''' as usual: major <--> minor, aug <--> dim, but perfect and mid are unchanged
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| * change the '''vowel''' as expected: -o <--> -u, but -a and -i are unchanged
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| 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.
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| The 13 -a notes form a chain of 5ths running from the dim 5th to the aug 4th:
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| Sha - Fra - Fla - Na - Tha - Fa - Da - Sa - Ra - La - Ma - Ta - Pa
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| 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.
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| {| class="wikitable"
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| |+The 45 note names in circle-of-5ths order
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| (read left-to-right, top-row-to-bottom-row)
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| !d5
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| !m2
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| !m6
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| !m3
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| !m7
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| !P4
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| !P1
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| !P5
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| !M2
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| !M6
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| !M3
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| !M7
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| !A4 (d5)
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| |-
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| | colspan="6" |
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| |Da
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| |Sa
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| |Ra
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| |La
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| |Ma
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| |Ta
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| |Pa (Shu)
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| |-
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| |Shu
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| |Fru
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| |Flu
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| |Nu
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| |Thu
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| |Fu
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| |Du
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| |Su
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| |Ru
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| |Lu
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| |Mu
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| |Tu
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| |Pu (Si)
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| |-
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| | colspan="7" |
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| |Si
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| |Ri
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| |Li
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| |Mi
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| |Ti
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| |Fi (Sho)
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| |-
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| |Sho
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| |Fro
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| |Flo
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| |No
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| |Tho
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| |Fo
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| |Do
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| |So
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| |Ro
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| |Lo
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| |Mo
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| |To
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| |Po (Sha)
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| |-
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| |Sha
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| |Fra
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| |Fla
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| |Na
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| |Tha
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| |Fa
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| |Da
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| | colspan="6" |
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| |}
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| 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.
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| 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
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| 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, Fi to Si is a minor 2nd, and Fi + M2 = Flo. Furthermore, this rule breaks down for major and mid 7ths, due to the lack of aug and mid 8ves.
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| * Tu + M2 = Ri
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| * Ta + M2 = Fru
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| * To + M2 = Fra
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| * Ti + M2 = Fro
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| === Double-vowel solfege === | | === Double-vowel solfege === |