Ternary scale theorems: Difference between revisions
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==== Statement (4) ==== | ==== Statement (4) ==== | ||
The {{nowrap|''n'' − 1}} stacked AGS terms are identified when the equinumerous step sizes are equated. Thus we have a binary scale with a generator (occurring at {{nowrap|''n'' − 1}} positions), hence being a primitive MOS. | |||
==== Statement (5) ==== | ==== Statement (5) ==== | ||
By part (2), we have that ''s'' has step signature {{nowrap|''a'''''X''' ''b'''''Y''' ''b'''''Z'''}}, ''a'' odd. By part (4), we have that {{nowrap|''T''('''X''', '''W''') {{=}} ''s''('''X''', '''W''', '''W''')}} is a MOS scale ''a'''''X'''2''b'''''W'''. If {{nowrap|''b'' {{=}} 1}}, there's nothing to prove, so assume {{nowrap|''b'' > 1}}. | By part (2), we have that ''s'' has step signature {{nowrap|''a'''''X''' ''b'''''Y''' ''b'''''Z'''}}, ''a'' odd. By part (4), we have that {{nowrap|''T''('''X''', '''W''') {{=}} ''s''('''X''', '''W''', '''W''')}} is a MOS scale ''a'''''X'''2''b'''''W'''. If {{nowrap|''b'' {{=}} 1}}, there's nothing to prove, so assume {{nowrap|''b'' > 1}}. | ||