Cello Extremes
Connor has collaborated with cellist Carolina Rodriguez de Armas to explore some less conventional sounds on the cello. This collaboration and its findings has been documented in the video demonstration found below. Some of these explorations were to seek impractical, stratospherically-high sounds for other projects. Other explorations were made with the intent of possibly including some sounds or techniques in future compositions.
[1] Natural Harmonics
[2] Sub Ponticello (Below the Bridge)
[3] Extreme High Range
[4] Subharmonics
[5] Plucking Inside the Pegbox
Last Updated: December 21, 2024
[1] Natural Harmonics
[2] Sub Ponticello (Below the Bridge)
[3] Extreme High Range
[4] Subharmonics
[5] Plucking Inside the Pegbox
Last Updated: December 21, 2024
[1] Natural Harmonics
In contemporary playing, one may not expect to play higher than the 8th harmonic, sounding 3 octaves higher. The resource Cello Map has researched harmonics — and multiphonics — at length, and includes information for playing up to the 13th harmonic. For most performing and composition contexts, the 3rd and 4th harmonics are the most typical to use. (These would be the Touch 5th — 1 octave and a fifth — and Touch 4th harmonics — 2 octaves — respectively, which are especially useful with artificial harmonics in accessing very-high pitch content.)
Instead of a super high partial in the harmonic series, it is more reasonable for a composer to ask:
[1] For a specific pitch in a specific octave;
[2] For that pitch to be achieved by an artificial harmonic, if the harmonic timbre is necessary
[3] For that pitch to not be restricted to a specific string, allowing for it to be on a higher string at a lower position
[4] For tuning adjustment to be approximate or rounded to a quarter tone, VS "+41 cents" (for example), if necessary
[2] For that pitch to be achieved by an artificial harmonic, if the harmonic timbre is necessary
[3] For that pitch to not be restricted to a specific string, allowing for it to be on a higher string at a lower position
[4] For tuning adjustment to be approximate or rounded to a quarter tone, VS "+41 cents" (for example), if necessary
Carolina played as many natural harmonics as possible and Connor isolated as many as possible afterward. On the A string, partials 1–20 were all sequentially produced, and then partials 22, 24, and 29. For reference:
C String (IV)
Partial 1 (Open String): C2 Partial 8 (3 Octaves): C5 Partial 13: Ab5 +41¢ Partial 20: E6 -14¢ Partial 22: F#6 -49¢ Partial 24: G6 Partial 29: Bb6 +30¢ G String (III) Partial 1 (Open String): G2 Partial 8 (3 Octaves): G5 Partial 13: Eb6 +41¢ Partial 20: B6 -14¢ Partial 22: C#7 -49¢ Partial 24: D7 Partial 29: F7 +30¢ |
D String (II)
Partial 1 (Open String): D3 Partial 8 (3 Octaves): D6 Partial 13: Bb6 +41¢ Partial 20: F#7 -14¢ Partial 22: G#7 -49¢ Partial 24: A7 Partial 29: C8 +30¢ A String (I) Partial 1 (Open String): A3 Partial 8 (3 Octaves): A6 Partial 13: F7 +41¢ Partial 20: C#8 -14¢ Partial 22: D#8 -49¢ Partial 24: E8 Partial 29: G8 +30¢ |
[Fun Side Note] It is already extremely impractical to produce the 29th partial, even in complete isolation outside of performance, so it would be impossible to produce partials at the limit of human hearing. If it were possible, though, that would correspond to the following partials: 305 (IV) — 204 (III) — 136 (II) — 90 (I), each of these ranging between 19800–19992 Hz.
• • • • •
In a separate experiment, Connor stopped the strings on Carolina's cello so that she could still play natural harmonics, one hand lightly touching the string and the other hand holding the bow. Connor stopped the string as to make the string smaller, raising the fundamental pitch of the string. This would make the producible harmonics sound much higher, but the number of producible harmonics dramatically decreases.
Fundamental: ~A4
Highest Partial: 10 Approximate Pitch: ~C#8 Theoretically Highest Partial *: 45 Fundamental: ~C#5 Highest Partial: 10 ** Approximate Pitch: ~F8 Theoretically Highest Partial *: 36 Fundamental: ~Bb5 Highest Partial: 5 Approximate Pitch: ~D8 Theoretically Highest Partial *: 21 |
Fundamental: ~C6
Highest Partial: 5 Approximate Pitch: ~E8 Theoretically Highest Partial *: 19 Fundamental: ~C#6 Highest Partial: 3 Approximate Pitch: ~G#7 Theoretically Highest Partial *: 18 |
[*] The inclusion of these values is for fun, but they are helpful to illustrate the scale of the harmonic series.
[**] It was extremely quiet and impossible to "sustain," but the 12th partial [of ~C#5] ~A8 did pop out!
[**] It was extremely quiet and impossible to "sustain," but the 12th partial [of ~C#5] ~A8 did pop out!
[2] Sub Ponticello
Bowing the string below (sub) the bridge (ponticello) on the string's afterlength can result in some squealing pitches. The pitch can be changed by stopping the string, but this can also result in "natural harmonics." With experimentation [on individual instruments], it could be possible to learn where to bow below the bridge to quickly produce a note that is in a very high position, especially on the A string. The findings from the experiments captured in the above video are summarized below:
C String (IV)
Open String (ord.) *: C2 Open String (sub pont.): G#4 Highest Pitch **: G#6 Timbre: "Standard" G String (III) Open String (ord.) *: G2 Open String (sub pont.): D5 +50¢ Highest Pitch **: E7; C8 Timbre: "Standard"; "Harmonic" |
D String (II)
Open String (ord.) *: D3 Open String (sub pont.): A5 Highest Pitch **: F#6; Bb7 Timbre: "Standard"; "Harmonic" A String (I) Open String (ord.) *: A3 Open String (sub pont.): D#6 Highest Pitch **: F8 +50¢ Timbre: Hard to Define *** |
[*] The cello used for this experiment produced an open string pitch approximately 2 ½ octaves higher when bowed sub ponticello. The findings suggest a producible range of approximately 2 octaves.
[**] These findings recorded are what were observed, not factual definitions. e.g. It may be possible to play higher than F#6 sub ponticello on the D string, but that wasn't captured at time-of-recording. One might expect this with the C string being able to produce G#6 sub ponticello.
[***] At such a register, it's hard to judge whether the pitch is a "fundamental" or a "harmonic." (Not unlike playing far, far off the fingerboard but on the normal side of the bridge.) One could definitively say, "An eighth-octave F was produced" without any further qualifiers and be fully correct.
[**] These findings recorded are what were observed, not factual definitions. e.g. It may be possible to play higher than F#6 sub ponticello on the D string, but that wasn't captured at time-of-recording. One might expect this with the C string being able to produce G#6 sub ponticello.
[***] At such a register, it's hard to judge whether the pitch is a "fundamental" or a "harmonic." (Not unlike playing far, far off the fingerboard but on the normal side of the bridge.) One could definitively say, "An eighth-octave F was produced" without any further qualifiers and be fully correct.
[3] Extreme High Range
Prior to 2024, Connor had learned through experimenting with other cellists that the highest producible (speaking) pitch on the A string was approximately E8. Experimenting with Carolina showed that up to A8 was attainable, with some pitches hovering around B8 — a little sharp or flat — appearing to be the absolute highest sounds possible. Being able to "nail" a pitch up here will be extremely impractical, and if a player has larger fingers it may not be possible to inch as close to the bridge as Carolina was able to. (Hence past experiments offered a lower pitch.) It might be easier to produce sounds this high with artificial harmonics.
[4] Subharmonics / Undertones / ALFs
At the time-of-recording, Carolina had minimal experience producing subharmonics. Cello Map has a webpage discussing details of plucking, striking, and bowing the strings. This page refers to subharmonics as undertones. Valerie Welbanks' dissertation Foundations of Modern Cello Technique touches on different kinds of "undertones," those that follow an inverse harmonic series, better known as an undertone series, and those which do not correspond mathematically but are below the fundamental of the open string, better referred to as ALFs, or Anomalous Low Frequencies (pp 97-100).
In the experimentation video above, Carolina is able to produce three "undertones." There are certainly more possible, and this video has zero intention on serving as a technical resource for producing these sounds.
C String (IV)
Open String: C2 Stopped Pitch: ~C3 Undertone Produced: D2 Interval: ~Minor 7th Below Stopped Pitch; Major 2nd Above Open String G String (III) Open String: G2 Stopped Pitch: D3 Undertone Produced: Eb2 Interval: Major 7th Below Stopped Pitch; Major 3rd Below Open String |
D String (II)
Open String: D3 Stopped Pitch: A3 Undertone Produced: Bb2 Interval: Minor 7th Below Stopped Pitch; Major 3rd Below Open String (and many more are possible...) |
[5] Plucking Inside the Pegbox
It is possible to pluck the strings inside of the pegbox, although the pitch content is limited and not all strings are always accessible. In the demonstration video, Carolina is able to pluck the strings for 3 unique pitches: F5 + ~50¢, Bb6, and F7.