10edo: Difference between revisions
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*adding the ratios of 3, 5 and 9 introduces greater [[error|error]] while giving several more harmonic identities to the 10-EDO intervals. | *adding the ratios of 3, 5 and 9 introduces greater [[error|error]] while giving several more harmonic identities to the 10-EDO intervals. | ||
This is a heptatonic notation generated by 5ths (5th meaning 3/2). Alternative notations include pentatonic fifth-generated and heptatonic 3rd-generated. | |||
'''<u>Pentatonic 5th-generated</u>: D * E * G * A * C * D''' (generator = 3/2 = 6\10 = perfect 5thoid) | |||
D - D^/Ev - E - E^/Gv - G - G^/Av - A - A^/Cv - C - C^/Dv - D | |||
1 - ^1/vs3 - s3 - ^s3/v4d - 4d - ^4d/v5d - 5d - ^5d/vs7 - s7 - ^s7/v8d - 8d (s = sub-, d = -oid) | |||
pentatonic gencircles of fifths: ...D - A - E - C - G - D... and ...^D - ^A - ^E - ^C - ^G - ^D... (or equivalently ...vD - vA - vE - vC - vG - vD...) | |||
pentatonic gencircles of fifths: ...1 - 5d - s3 - s7 - 4d - 1... and ...^1 - ^5d - ^s3 - ^s7 - ^4d - ^1... (or equivalently ...v1 - v5d - vs3 - vs7 - v4d - v1...) (s = sub-, d = -oid) | |||
'''<u>Heptatonic 3rd-generated</u>: D E * F G * A B * C D''' (generator = 3\10 = perfect 3rd) | |||
D - E - E#/Fb - F - G - G#/Ab - A - B - B#/Cb - C - D | |||
P1 - m2 - M2 - P3 - m4 - M4/m5 - M5 - P6 - m7 - M7 - P8 | |||
genchain of 3rds: ...Db - Fb - Ab - Cb - E - G - B - D - F - A - C - E# - G# - B# - D#... ("Every good boy deserves fudge and candy") | |||
genchain of 3rds: ...d8 - d3 - m5 - m7 - m2 - m4 - P6 - P1 - P3 - M5 - M7 - M2 - M4 - A6 - A1... | |||
[[File:10ed2-001.svg|alt=alt : Your browser has no SVG support.]] | [[File:10ed2-001.svg|alt=alt : Your browser has no SVG support.]] | ||