State variable inside an expression
============================================================================================================================================


**04-let-function.py**

User can create state variable with the keyword `let`. This is
useful to set an intermediate state to be used in multiple places
in the processing chain. The syntax is:

.. code-block:: scheme

    (let #var (body))

The variable name must begin with a `#`.

The prefix expression `documentation`_ gives common use cases where we
may want to use state variables.

.. _documentation: http://ajaxsoundstudio.com/pyodoc/api/classes/expression.html

The following example implements a phase-aligned formant (PAF) generator, as 
described by Miller Puckette in "The Theory and Technique of Electronic
Music", p158.

.. code-block:: python

    from pyo import *
    
    s = Server().boot()
    
    expression = """// PAF generator (single formant) //
    // User variables
    (let #fund 100) // fundamental frequency
    (let #band 600) // formant bandwidth
    (let #form 600) // formant center frequency
    // Intermediate variables
    (let #bw (/ #band #fund))
    (let #cf (/ #form #fund))
    (let #ph (* (- (~ #fund) 0.5) twopi))
    (let #car ( // Carrier
        (cos (max (min (* #ph #bw) pi) (- 0 pi)))
        )
    )
    (let #mod ( // Modulator
        (let #oct (floor #cf))
        (let #frac (% #cf 1))
        (+ (* (cos (* #ph #oct)) (- 1 #frac))
           (* (cos (* #ph (+ #oct 1))) #frac)
           )
        )
    )
    * (* #car #mod) 0.5
    """
    
    expr = Expr(Sig(0), expression, mul=0.5)
    expr.editor()
    
    sp = Spectrum(expr)
    
    pan = Pan(expr).out()
    
    s.gui(locals())