Text: Mutations http://www.organstops.org/_apps/Mutations.html The word mutation refers to any single-rank stop that sounds at a pitch other than unison or octaves. The following table shows the relationship between harmonics and mutations. Stop pitches are shown for four different harmonic series. Note that unison and octave sounding pitches are not considered mutations. Independent stops are rarely seen higher than 1' pitch, and pipes are usually not made much smaller than 1/24' (1/2"), the top of a 61-note 1 1/3' rank. For completeness, stop-pitches are shown for all of the first 32 harmonics, even though some of them have never been used. Harmonic# Step/ Name Nearest Note Pitch Lengths Selected Names 1 unison C 64' 32' 16' 8' 4' 2 octave C 32' 16' 8' 4' 2' 3 12th G 21 1/3' 10 2/3' 5 1/3' 2 2/3' 1 1/3' Nasard, Nasat 4 15th C 16' 8' 4' 2' 1' 5 17th E 12 4/5' 6 2/5' 3 1/5' 1 3/5' 4/5' Tierce, Terz 6 19th G 10 2/3' 5 1/3' 2 2/3' 1 1/3' 2/3' Larigot 7 21st b Bb 9 1/7' 4 4/7' 2 2/7' 1 1/7' 4/7' Septiéme 8 22nd C 8' 4' 2' 1' 1/2' 9 23rd D 7 1/9' 3 5/9' 1 7/9' 8/9' 4/9' None 10 24th E 6 2/5' 3 1/5' 1 3/5' 4/5' 2/5' 11 25th F 5 9/11' 2 10/11' 1 5/11' 8/11' 4/11' rare 12 26th G 5 1/3' 2 2/3' 1 1/3' 2/3' 1/3' 13 27th A 4 12/13' 2 6/13' 1 3/13' 8/13' 4/13' Tredezime 14 28th, b Bb 4 4/7' 2 2/7' 1 1/7' 4/7' 2/7' uncommon 15 28th B 4 4/15' 2 2/15' 1 1/15' 8/15' 4/15' 16 29th C 4' 2' 1' 1/2' 1/4' 17 Db 3 13/17' 1 15/17' 16/17' 8/17' 4/17' (see Mollterz) 18 30th D 3 5/9' 1 7/9' 8/9' 4/9' 2/9' 19 Eb 3 7/19' 1 13/19' 16/19' 8/19' 4/19' Mollterz (rare) 20 31st E 3 1/5' 1 3/5' 4/5' 2/5' 1/5' 21 3 1/21' 1 11/21' 16/21' 8/21' 4/21' (see Mollterz) 22 32nd F 2 10/11' 1 5/11' 8/11' 4/11' 2/11' 23 F# 2 18/23' 1 9/23' 16/23' 8/23' 4/23' 24 33rd G 2 2/3' 1 1/3' 2/3' 1/3' 1/6' 25 G# 2 14/25' 1 7/25' 16/25' 8/25' 4/25' 26 34th A 2 6/13' 1 3/13' 8/13' 4/13' 2/13' 27 2 10/27' 1 5/27' 16/27' 8/27' 4/27' 28 35th b Bb 2 2/7' 1 1/7' 4/7' 2/7' 1/7' 29 2 6/29' 1 3/29' 16/29' 8/29' 4/29' 30 35th B 2 2/15' 1 1/15' 8/15' 4/15' 2/15' 31 2 2/31' 1 1/31' 16/31' 8/31' 4/31' 32 36th C 2' 1' 1/2' 1/4' 1/8' 48 40th G 1 1/3' 2/3' 1/3' 1/6' 1/12' Quadragesima 64 43rd C 1' 1/2' 1/4' 1/8' 1/16' You can determine frequencies from a base frequency by using the harmonic number as a multiplier. For example, starting with 256hz for middle C, the C above that will be 2 x 256 = 512hz, the G above that will be 3 x 256 = 768hz, etc. Note that these calculations will, except for octaves, produce different results than using the 12th root of 2 as a multiplier, which is used for determining frequencies in the equally-tempered scale. The graph below compares the frequencies of harmonics 16 through 32 with the frequencies of the nearest notes in the equally tempered scale, based on C = 16hz. Mutation Stops All mutation stops contained in this Encyclopedia are listed below. Assat Corneta Cornetto Decima Nona Decima Settima Eighteenth Eleventh Fifth Flute Quint Fourteenth, Flatted Fullquinte Gedeckt Tierce Gedeckt Twelfth Gedecktquinte Geigen Twelfth Gemshorn Twelfth Grand Quint Gross Nasard Gross Quinte Gross Tierce Grosse Tierce Grossnasat Grossquintenbass Grossterz Harmonic Stopped Twelfth Harmonic Twelfth Hohlquinte Julaquinte Kleinterz Larigot Lieblichnasat Lieblichquinte Major Quinte Mollterz Nasard Nasard Harmonique Nasardo Nassart Nazard Ninth None Octave Quinte Open Twelfth Petite Nazard Quint Quint Bass Quint Diapason Quint Flute Quint Trumpet Quinta Quinte Quinte Bombarde Quintbass Quinte Ouverte Quintenbass Quintflöte Quintspitz Rohrflotenquinte Rohrquinte Rohrnasat Septadecima Septieme Seventeenth Sharp Twentieth Sifflote Sixteenth Spitzquinte Stopped Twelfth String Twelfth Sub Quint Sufflet Tenth Thirty-Fifth, Flatted Thirty-First Thirty-Sixth Thirty-Third Tierce Terz Tertie Tredezime Tromba Quint Trompette Quinte Tuba Quint Twelfth Twenty-Eighth, Flatted Twenty-Fifth Twenty-First, Flatted Twenty-Fourth Twenty-Ninth Twenty-Second Twenty-Sixth Twenty-Third Undezime Viol Quint Viol Tierce Viol Twelfth Waldquinte See also Mixture

See Also: OVERTONE

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