Mutations

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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.

Harm-
onic #
Step/
Name
Nearest
Note
PitchesSelected 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.


Original site compiled by Edward L. Stauff. For educational use only.
Introduction.html - Last updated 4 February 2002.
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