[Function]

(harmonics low high {keyword value}*)

Returns the harmonic series between harmonic numbers low and high (inclusive) as a list of ratios, hertz values or floating point keynums according to keyword arguments.

harmonics supports the following keyword arguments:

:hertz number

The frequency base of the returned series. The default value of 1 Hz returns rational frequency ratios.

:keynum {keynum | note}

A keynum specification of the base frequency returns floating point key numbers.

:undertones boolean

If true then undertones are generated, i.e. the reciprocals of the harmonics between low and high in decreasing order. The default value is false.

:invert boolean

If true the harmonic series between low and high is inverted, or flipped. The default value is false.

:rescale number

If provided the entire series is rescaled to lie between the values :hertz and :rescale (inclusive). If :keynum is specified then the value of :rescale must be a key number as well.

:scale-order {false | :reverse | :up | :down | :random}

Optionally reorders the series. If false then overtones are returned in ascending order and undertones in decending order. The value :reverse reverses this. The value :up reverses undertones without affecting overtones and :down does the opposite. The value :random returns a random permutation of the list. The default value is false.

:harmonic integer

If specified then integer must be a harmonic number between low and high (inclusive) and only that harmonic value is returned.

Examples:

(harmonics 1 8)
⇒ (1 2 3 4 5 6 7 8)

(harmonics 8 16)
⇒ (1 9/8 5/4 11/8 3/2 13/8 7/4 15/8 2)

(harmonics 1 8 :undertones #t)
⇒ (1 1/2 1/3 1/4 1/5 1/6 1/7 1/8)

(harmonics 8 16 :undertones #t)
⇒ (1 8/9 4/5 8/11 2/3 8/13 4/7 8/15 1/2)

(harmonics 1 8 :invert #t)
⇒ (1 8/7 4/3 8/5 2 8/3 4 8)

(harmonics 1 8 :undertones #t :invert #t)
⇒ (1 7/8 3/4 5/8 1/2 3/8 1/4 1/8)

(define septimal-scale
  (new tuning :ratios (harmonics 7 14)))

(harmonics 1 8 :hertz 100)
⇒ (100 200 300 400 500 600 700 800)

(harmonics 6 12 :hertz 100.0)
⇒ (100.0 116.666664 133.33334 150.0 166.66666 183.33334 200.0)

(harmonics 1 8 :keynum 'c2)
⇒ (35.999992 47.999992 55.019547 60.0 63.863136 67.01955 69.68826 72.0)

(harmonics 8 12 :keynum 'a4 :scale-order ':random)
⇒ (74.51318 76.019554 71.03909 79.88269 69.0 72.86314 78.68826 77.40527 81.0)

(harmonics 1 4 :keynum 60 :harmonic 3)
⇒ 79.01955

See also:

• fm-spectrum [Function]
• rm-spectrum [Function]