source file: mills2.txt Date: Fri, 3 Jan 1997 05:42:57 -0800 Subject: RE: integral overtones From: "Ashcraft AC (Clif)" ------ extPart_000_01BBF951.1D507560 Content-Type: text/plain; charsets-ascii" Content-Transfer-Encoding: quoted-printable 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 ---------- 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. ------ extPart_000_01BBF951.1D507560 Content-Type: application/ms-tnef Content-Transfer-Encoding: base64 eJ8+Ii4OAQaQCAAEAAAAAAABAAEAAQeQBgAIAAAA5AQAAAAAAADoAAENgAQAAgAAAAIAAgABBJAG ADABAAABAAAADAAAAAMAADADAAAACwAPDgAAAAACAf8PAQAAAE0AAAAAAAAAgSsfpL6jEBmdbgDd AQ9UAgAAAAB0dW5pbmdAZWFydGhhLm1pbGxzLmVkdQBTTVRQAHR1bmluZ0BlYXJ0aGEubWlsbHMu ZWR1AAAAAB4AAjABAAAABQAAAFNNVFAAAAAAHgADMAEAAAAYAAAAdHVuaW5nQGVhcnRoYS5taWxs cy5lZHUAAwAVDAEAAAADAP4PBgAAAB4AATABAAAAGgAAACd0dW5pbmdAZWFydGhhLm1pbGxzLmVk dScAAAACAQswAQAAAB0AAABTTVRQOlRVTklOR0BFQVJUSEEuTUlMTFMuRURVAAAAAAMAADkAAAAA CwBAOgEAAAACAfYPAQAAAAQAAAAAAAADkToBCIAHABgAAABJUE0uTWljcm9zb2Z0IE1haWwuTm90 ZQAxCAEEgAEAFwAAAFJFOiBpbnRlZ3JhbCBvdmVydG9uZXMATAgBBYADAA4AAADNBwEAAwAIACMA KAAFADABASCAAwAOAAAAzQcBAAMACAAcABcABQAYAQEJgAEAIQAAAEFDREZEMTAyNDI2NUQwMTFC RDVBMDA4MDVGMzZBNTU1ABQHAQOQBgC8CQAAEgAAAAsAIwAAAAAAAwAmAAAAAAALACkAAAAAAAMA NgAAAAAAQAA5AOCtaWSD+bsBHgBwAAEAAAAXAAAAUkU6IGludGVncmFsIG92ZXJ0b25lcwAAAgFx AAEAAAAWAAAAAbv5g2RpAtHfrWVCEdC9WgCAXzalVQAAHgAeDAEAAAADAAAATVMAAB4AHwwBAAAA FQAAAFVDQy9CQktOSjAxL0FTSENSQUFDAAAAAAMABhA5AjC4AwAHEI4IAAAeAAgQAQAAAGUAAABU SEVTVElGRk5FU1NPRlJFQUxXSVJFU0NMQU1QRURUT0FTVVBQT1JUQVRUSEVJUkVORFNNQUtFU1RI RU1FRkZFQ1RJVkVMWVNIT1JURVJGT1JISUdIRVJWSUJSQVRJT05BTE1PAAAAAAIBCRABAAAAQQgA AD0IAAAhDgAATFpGdV9kRSn/AAoBDwIVAqgF6wKDAFAC8gkCAGNoCsBzZXQyNwYABsMCgzIDxQIA cHJCcRHic3RlbQKDMzcC5AcTAoM0EswP32Y1exLMFMg2A0UTNBFfAoB9FwqACM8J2Tsb7zI1NQ8C gAqBDbELYG5nMTBeMxRQCwoUUQvyYwBAIPBUaGUgE8AGkALwB5CxBCBvZiAb8AdAIAPwSxvwBCBj C2BtcAmAIBB0byBhIQB1cHC3G5EjMAVAdCDgIkAgCfC2ZAQgAMBrB5EkEW0kYIcN0AWQISB2ZWx5 IQA2aBuRBJAgAhAFwGhphmcg4AXAdmliciPgjmkCICIBBGJzLiAgwf0EACAowSJRI5AAgQJgIPDV JrJwBzBuIyFuEYEEYLEDAGNpdCYRC4BjIPD/JBEm5gqxISAHQAQgCsAg8f0RgXAigANwCrEi4QPw JBB9IwByClAm4Cq1IZMrwmZedSSAIrAJ8AGQbChxIKhJIGQCICcFQGsqUHcH4AaQKnF5AiAusgQg Zfcl4AXAI2BjK5AJgCLhC4D7I1YLgGcjMSHnIQAjICQQvyPjKMQqUCPzIoAyUGUoc/8g8CqMKMEp sAQRJrIbgDQh/zWRA6AiNDVBA6ArICjiJrLTJjM1gmNrIiQsJuAJ8P8rli1hAJAaAAWwM1E4NSqI dznUK8IqIy4KhgGRP+RD2mwxoUEmMAUAYQGACoUjCotAoDE4MALRaS14MTQ0DfAM0ENDC1kxzxkA E1A2ICWhIC1FZwqH10QbDDBE5kYDYTpGbkTmXT/zRABwCJADIFcG8GZAW1NNVFA6HxA2EDIzMi5L cDY2QFUtonURsHIl4C4toV1/Rg9HHQZgAjBIT0lbSABp1TAQeTvgSgBwdQrAJhADHyA74DE5OTcg NWg6MzYUsE1M70cdVBZvTy9JW2FXAWJiMU5AItABoARweS4E8HR2LjLgCsBiTJJTD03+dfxiaiWh VS9JWwuAE9AJwP0iAW8ykSMQIWFBb0JzUrDHQ+cgJUTmKDEpUXEHgnBLdWt1C2AiIETyOvleTCcn B7ArACDwL/AGkH8FsCVQE8AFEB7wBCAD8Gz9AyBnCfAEkCPgIPBdIyaB7V23LmORXkxQBJARgDzQ 7yMyZKMqEAtgeWZCPsI4IusEAAVAdwhgbCLwQKAk4P8jAi2hMDJbQDJCMdUyggqF/zwRCGBdMS3y I0BjkCrxY/69Y5A/Zz0HwC5BJoFkJ5D+dwOgB4AwYTS0KlAFwDHgtzjhMjNE4WQy4CukawuAvyLw IbFkFSshCoUjYGdlYPcTwSLwJyFlO+AAcCLxIOH7G/AhYHdt0nPhCcAxcGjznxvwJZB20SuRJrJn dQVA/2SVdOw5wyPyI+FzzyYQMkK9NhJiCeEjMShBIkFkCoW/GgIA0CZxajErAChwKDDQ/yKwIoBd 0QtxNTZtsSjiI0D+aHVgIPBXsiGiQKAmcSPg/whwIPACIAqFNZMjYFrzJqDbA2Ers0Mj4HkCQW1h fvL5IgFTbysQEcAmEHZSJfD9EbB3dfJbQCLQaEUKhWojn4ORBPJ9AAXALjNleIcx/yEgEbAzYjWT LQEjQDaQA6C+ZyXRZACDcQNwPwFvXSLtEaApKHFeTElyoYDiZTHfJ+CCYSIBLthoxXFRsRPQ8nQ7 4ENoA2AqUGHBftJPjhEjQGFAUlAwLAqFTb9lsQciaBAiUYxwO+BMI0D2TQIhIPBZbXE0MAIQL/H/ OiIhYCuQBBBRwiMRgmAyEd88ZS8EgtcT4BGwbCXgO9H/NhYv6SjRA6A9ISaBIxFlYP82NCmwJeEh ogWgAIAn0SuCfyDgCoUb8I/gIkIocI2hZu9+kTvghsE+xG8i0DOBZKX/IbEoso/lLPMkEQOgaTN9 1v8uMzICKkFwwjvgfQAnoTQh/YDiYi/yAjCOASQQCGAnENsrs4wjdizCfQB0dxCdxP8iQAqFjl8s 8yFxMEEHMSYB96JyOFJ/MUFlMS9zKMSVQPtRICjgZ3IhNBGW6CHQBvDfgpEhwAbgB+BFEWgDAI/g xmWMgF5MQWRkKyAnxF8tokCgNpAnsiGTX3fBZPZfM2FkkXUwMiEAItAlsO8nkDU0MNAhYGcpsH6h IvJ7nAcAwHI7cCNwaaEh8HJ/QKAmgStxCkANsGEzM3Ft70wwhXObMRPQeHqBhsAj5P+wGV42aTJ+ Qh7wB5F2UijzfSyCY2IRdbI1ESeQKiBk/yYBgDyCAaixmYE2AX3oK4P/IyB1kQGgaiEuYL1zIPET s18icS2zviMjEWHkJzJheJ8isavEhdAh8ILGd2GXwT8monSgNCEFAHpidjQoMv9hYCvCvXIDECsi L3ULcCoB/5MCgnKEFrd5BJDAMQpAZNL/OmIKwYQThzElkq0Nw3Iw0P8mQCLQJLCBsYigpLKvJC0C /zYSdKAjYCSAjFEjEARwIzD7BCCuEHPMASthORJl1wqF7122IQAGcShSRsf2KyBbQH8g08+DsuOw ISuzfQBqQWL/MlA+YQRiAyAmsar5sNYhsf8EYGpBtsl2NCjBK8Knx9LV/igG4C5RI5AAkCXCCoV2 Ut+xwSehJeBhYCaydowQK5HdKbBhrhA0InPichoAdZH7J5QocEJ5EX1SCcIhognB/5Jyt3Yb8CsQ AJBpoS4zG/D/2VA9MZWSNmKusomAriEHkb8htrUmtr86s2qSIOBsLYD/IxEb8CXgIgHWY7XwsJJ2 Uv9AoHShL1fS5DJRdxBlMTJR/3VVpfYH0axkhYLYASmBxDL/0TImsrUjJLI0EYyfXr9fzxdE9QqF GxEA7wAAAAADABAQAAAAAAMAERABAAAAQAAHMCBgT2CC+bsBQAAIMCBgT2CC+bsBHgA9AAEAAAAF AAAAUkU6IAAAAACfXw ------ extPart_000_01BBF951.1D507560-- Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 3 Jan 1997 14:56 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01444; Fri, 3 Jan 1997 14:59:24 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA01442 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id FAA21394; Fri, 3 Jan 1997 05:59:18 -0800 Date: Fri, 3 Jan 1997 05:59:18 -0800 Message-Id: <01BBF953.9982AB60@ashcraac.sct.ucarb.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu