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| undertone_series [2023/01/05 13:44] – [Methods to play an undertone series] mete | undertone_series [2023/01/05 13:56] (current) – [Methods to play an undertone series] mete | ||
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| - | The Undertone series, also commonly called the subharmonic series is a series of pitches with mathematical relationships to one another that are a naturally occurring sequence the can be represented by divisions or additions | + | The Undertone series, also commonly called the subharmonic series is a series of pitches with mathematical relationships to one another that are a naturally occurring sequence the can be represented by divisions or multiplications |
| ====Methods to play an undertone series==== | ====Methods to play an undertone series==== | ||
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| ==on Lamells== | ==on Lamells== | ||
| - | The only example of this phenomena can be seen on is the terpodion, which is bowed lamellaphone that bows tongues with large flat pads at the ends on each tongue. The tongues are bowed against a rosined cylinder by the force of the tongues attempting to return to a resting position which is at tension against the cylinder, and when the cylinder spins the tongues are moved transversely and repeat the process based off the degree of mass at the end of the tongue. Much like the action of forced vibration on corrugated surfaces these tongues may not always return to position at the resonate pitch, and with the correct regulation the tongues can play an undertone or an overtone of the original pitch. | + | The only example of this phenomena can be seen on is the terpodion, which is bowed lamellaphone that bows tongues with large flat pads at the ends on each tongue. The tongues are bowed against a rosined cylinder by the force of the tongues attempting to return to a resting position which is at tension against the cylinder, and when the cylinder spins the tongues are moved transversely and repeat the process based off the degree of mass at the end of the tongue. Much like the action of forced vibration on corrugated surfaces these tongues may not always return to position at the resonate pitch, and with the correct regulation the tongues can play an undertone or an overtone of the original pitch. |
| + | {{https:// | ||
| ===Forced vibration instruments=== | ===Forced vibration instruments=== | ||
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| ===Extension of length=== | ===Extension of length=== | ||
| Just as the overtone series can be generated from equal divisions of a length-- for example dividing a strings length by half, thirds, quarters, fifths and so on... The same sequence can be reversed and the length is increased from an original length by the same degrees, generating an undertone series by doubling, tripling, or quadrupling (and so forth) the original length of a string. The same can be done by dividing the length of a tube (possible by the addition of holes as well) and can be done in the reverse by increasing the length of the tube (buy covering holes as well) all by equal divisions of multiplications of the original length. This method of generating the undertone series should not be viewed as a pure form of the series and does not fully represent the phenomena in the natural manner it occurs in the other examples listed above, this is more of a mathematical modeling that leads of pitches that are in common with the natural phenomena, though from a sound generating position they are both the same. | Just as the overtone series can be generated from equal divisions of a length-- for example dividing a strings length by half, thirds, quarters, fifths and so on... The same sequence can be reversed and the length is increased from an original length by the same degrees, generating an undertone series by doubling, tripling, or quadrupling (and so forth) the original length of a string. The same can be done by dividing the length of a tube (possible by the addition of holes as well) and can be done in the reverse by increasing the length of the tube (buy covering holes as well) all by equal divisions of multiplications of the original length. This method of generating the undertone series should not be viewed as a pure form of the series and does not fully represent the phenomena in the natural manner it occurs in the other examples listed above, this is more of a mathematical modeling that leads of pitches that are in common with the natural phenomena, though from a sound generating position they are both the same. | ||
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| + | ===Notes=== | ||
| + | All of these techniques are only producible on large instruments. The highest starting pitch that is capable of generating this series is on the Terpodion, which is under high resistance with fast spinning, representing a degree of force difficult to make on most instruments that are directly played by a player. The undertone sequence has great potential to allow for instruments to play far lower pitches than are commonly available for a given length of instrument. I wonder if there is a relationship to stopped pipes and the undertone series (a cylinder like a clarinet is 1 octave lower than a conical instrument of the same length) and this may represent the first harmonic of the series. It is also ambiguous how the octave above a fundamental relates to the octave below it and now those relate to both the undertone and overtone series (when moving from the undertone series to the harmonic series is is there a total of 4 octaves or 3 octaves in a row when shifting from one series to another... or perhaps its 2, with the fundamental of each series being the first harmonic of the other). \\ | ||
| + | \\ | ||
| + | [[Harry Partch]] described it as 4 octaves in total in his theory of Otonality and Utonality \\ | ||
| + | {{https:// | ||
