RE: integral overtones

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The stiffness of real wires clamped to a support at their ends makes them effectively shorter for higher vibrational modes. This is responsible for piano anharmonicity since the higher partials are sharp compared with true harmonics of the fundamental. I don't know if anyone has ever succeeded in supporting a real wire so that this is not the case. The anharmonicity is less for long thin wires than it is for short thick wires, hence the harpsichord is less anharmonic than the piano.
Clif Ashcraft

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From: Daniel Wolf[SMTP:106232.3266@compuserve.com]
Sent: Friday, January 03, 1997 5:36 AM
To: aaaabb1@peabody.sct.ucarb.com
Subject: integral overtones

(1) James Kukula wrote:

'' Nice uniform strings will generate integer overtones.''

Perhaps a string player on this list would like to comment: has anyone ever
encountered a ''nice uniform string''?

Neither drawn metal wire nor nylon has produce the kind of uniformity
suggested here, and the renewed and growing preference for gut strings
suggests that that kind of uniformity has not been a desired
characteristic. (I am certain that there is a huge body of literature on
this subject from the Catgut Acoustical Society and elsewhere: perhaps a
list subscriber with expertise in this area can give us some pointers). In his all natural harmonics string quartet, Chronos Kristalla (1990,
Material Press), La Monte Young found it necessary to tune the harmonics
themselves, not the fundamentals in order to get the level of consonance he
requires. In fact, when the open strings of his quartet are then played
with one another, beating is abundant although the intervals between their
natural harmonics are essentially beatless. (All of this is said ignoring
the role of bow technique).

Additional complications of _wind_ instrument spectra that I neglected to
remark upon earlier include (1) in musical contexts what the instruments
play changes and is rearticulated so rapidly that there is little or no
chance to establish stable systems comparable to Kukula's example of ocean
waves forming crests, and (2) the stability of the air pressure from the
player's lungs is far from perfect.

(2) I hope my observations are not misunderstood as dismissing the integer
overtone series. Far from it: The series remains the best basic model for
the spectra of most instruments, and is the essential model (both positive
and negative) for voice leading and orchestration. But a degree of greater
precision with regard to the complexities of real musical instruments
should help to reveal the extent and limits of the model as well as suggest
new technical possibilities for music making.



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