7th World Congress on Mummy Studies University of San Diego San ...
7th World Congress on Mummy Studies University of San Diego San ...
7th World Congress on Mummy Studies University of San Diego San ...
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and. these. may. be. described. as. points. <strong>on</strong>. the. D. (dominant). x. M.<br />
(Mediant).rectangular.or.triangular.lattice,.the.latter.having.a.third.<br />
axis.for.the.C<strong>on</strong>jugate.(D-M).interval..Examples.<strong>of</strong>.harm<strong>on</strong>ic.scales.<br />
include. the. Principal. Trichordals. <strong>of</strong>. Ellis,. the. 5-limit. Incipient.<br />
T<strong>on</strong>ality.Diam<strong>on</strong>d.<strong>of</strong>.Partch,.the.Gipsy.Minor.scale.and,.<strong>of</strong>.course,.<br />
the.major.mode.and.the.harm<strong>on</strong>ic.and.melodic.minor.scales..This.<br />
set.<strong>of</strong>.52.species.may.be.further.reduced.to.six.equivalence.classes.<br />
related.by.linear.transformati<strong>on</strong>s.when.the.notes.<strong>of</strong>.the.scales.are.<br />
expressed.as.vectors.in.the.D.x.M.plane..<br />
S<strong>of</strong>tware.has.been.written.in.TrueBasic.to.analyse.the.properties.<strong>of</strong>.these.scales.as.D.and.M.each.vary.over.the.range.from.<br />
0. to. 1200. cents.. Functi<strong>on</strong>s. computed. include. harm<strong>on</strong>ic. functi<strong>on</strong>.<br />
sequence,. Rothenberg-propriety,. interval. sequence,. interval. c<strong>on</strong>tent,.number.<strong>of</strong>.in-tune.triads,.heteromorphic.pr<strong>of</strong>ile,.and.the.number.<strong>of</strong>.interval.differences..For.example,.the.major.mode,.expressed.<br />
as.functi<strong>on</strong>s.<strong>of</strong>.D.and.M.by.0.2*D.M.1200-D.D.M-D.D+M.1200.in.<br />
cents,.has.32.harm<strong>on</strong>ic.functi<strong>on</strong>.sequences.and.6.regi<strong>on</strong>s.<strong>of</strong>.Strictly.<br />
Proper.or.coherent.tunings.and.16.<strong>of</strong>.R-Proper..The.output.<strong>of</strong>.these.<br />
programs.is.graphical.and.tabular..Selected.examples.are.available.<br />
in.Scala.format.for.sound.synthesis.<br />
113 Temperament <strong>of</strong> Mind: Hector Berlioz and Evariste Galois,.<br />
JEFF JOHANNES (Mathematics.Department,.South.Hall,.State.<br />
<strong>University</strong>. College. <strong>of</strong>. Arts. and. Sciences,. Geneseo,. NY. 14454-<br />
1401;.johannes@geneseo.edu).<br />
Composer.Hector.Berlioz.and.mathematician.Evariste.Galois.<br />
were.both.revoluti<strong>on</strong>arising.their.disciplines.in.Paris.during.the.restorati<strong>on</strong>..In.this.talk.we.will.examine.several.parallels.in.their.lives.<br />
and. in. their. art.. We. will. also. c<strong>on</strong>sider. to. what. extent. they. were.<br />
merely.a.product.<strong>of</strong>.their.tumultuous.time.<br />
114 An Analytical Oboe Design, RONALD L. FOX 1 * and E.<br />
RANDOLPH HAGER 2 * ( 1,2 Retired,.General.Atomics,.3550.General.Atomics.<br />
Ct.,. La. Jolla,. CA. 92037;. 2 <strong>San</strong>. <strong>Diego</strong>. State. <strong>University</strong>,.Campanile.Dr,.<strong>San</strong>.<strong>Diego</strong>.CA;.<br />
1 current;.2973.Fried.Ave.,.<strong>San</strong>.<br />
<strong>Diego</strong>,.CA.92122,.rlfox55@aol.com; .2 current;.2322.Bahia.Drive,.<br />
La.Jolla,.CA.92037,.randyhager@aol.com).<br />
The.typical.present.day.oboe.is.based.<strong>on</strong>.the.empirical.design.<br />
developments. <strong>of</strong>. several. centuries. <strong>of</strong>. hand. crafting.. Each. instrument.requires.careful.tuning.based.<strong>on</strong>.positi<strong>on</strong>.and.modificati<strong>on</strong>.<strong>of</strong>.<br />
t<strong>on</strong>e.holes.and.their.respective.back-countersinks..Such.fine.tuning.<br />
applies.primarily.to.first.class.orchestral.instruments,.and.even.these.<br />
are,.at.best,.a.compromise.in.uniformity.<strong>of</strong>.t<strong>on</strong>e.quality,.in.relative.<br />
int<strong>on</strong>ati<strong>on</strong>.and.tuning.stability..T<strong>on</strong>e.quality.is.related.to.the.number.<br />
<strong>of</strong>.harm<strong>on</strong>ics.present,.their.relative.amplitudes.and.their.positi<strong>on</strong>s.<br />
with.respect.to.the.fundamental.frequency.or.first.harm<strong>on</strong>ic..Relative.int<strong>on</strong>ati<strong>on</strong>.within.the.fundamental.range.or.first.register.<strong>of</strong>.the.<br />
instrument.is.related.to.t<strong>on</strong>e.hole.positi<strong>on</strong>,.size,.shape,.and.depth.for.<br />
each.hole..Relative.int<strong>on</strong>ati<strong>on</strong>.between.the.fundamental.range.and.<br />
its.sec<strong>on</strong>d.harm<strong>on</strong>ic.or.octave.range.depends.<strong>on</strong>.bore.uniformity,.<br />
which.includes.uniformity.<strong>of</strong>.the.type.<strong>of</strong>.bore.aberrati<strong>on</strong>s.caused.by.<br />
the.existence.<strong>of</strong>.the.closed.t<strong>on</strong>e.holes..Current.oboes.possess.sufficient.empirical.compromise.that.the.harm<strong>on</strong>ics.deviate.from.perfect.<br />
multiples.<strong>of</strong>.the.fundamental.frequencies.beginning.with.some.3 rd ,.<br />
and. particularly. with. 5 th . and. higher. harm<strong>on</strong>ics..This. affects. t<strong>on</strong>e.<br />
quality.and.requires.special.fingerings.in.the.third.octave.range..A.<br />
relatively.small.and.c<strong>on</strong>stant.ratio.<strong>of</strong>.t<strong>on</strong>e.hole.size.to.that.<strong>of</strong>.the.<br />
bore.is.required.to.yield.a.spectrum.<strong>of</strong>.harm<strong>on</strong>ics.<strong>of</strong>.roughly.equal.<br />
amplitude.and.<strong>of</strong>.correct.multiples.<strong>of</strong>.its.fundamental.frequency.for.<br />
each.note.<br />
ABSTRACTS.–.Symposia<br />
The. mathematical. principles. derived. by.Arthur. Benade. and.<br />
others.were.used.to.calculate.t<strong>on</strong>e.hole.positi<strong>on</strong>s.and.dimensi<strong>on</strong>s.<br />
for.a.theoretical.oboe.design..This.included.correcti<strong>on</strong>.factors.for.<br />
the.reed.cavity,.effect.<strong>of</strong>.closed.holes,.and.<strong>of</strong>.the.straight.secti<strong>on</strong>.<br />
without.holes..The.str<strong>on</strong>g.interdependence.between.bore.and.t<strong>on</strong>e.<br />
holes.was.programmed.for.calculati<strong>on</strong>,.iterati<strong>on</strong>,.and.c<strong>on</strong>verging.to.<br />
the.initial.oboe.design.specificati<strong>on</strong>s,.from.which.the.first.oboe.was.<br />
c<strong>on</strong>structed. and. tested.. From. this,. the. effect. <strong>of</strong>. small. open. holes.<br />
was.measured,.and.a.further.uniform.correcti<strong>on</strong>.was.defined.empirically..Small.open.holes.add.a.more.critical.step.to.tuning.than.those.<br />
<strong>of</strong>.the.open.end.cylindrical.flute,.etc.,.whose.t<strong>on</strong>e.hole.diameters.are.<br />
almost.comparable.with.that.<strong>of</strong>.the.bore..Applying.the.final.correcti<strong>on</strong>,.a.sec<strong>on</strong>d.instrument.was.c<strong>on</strong>structed.and.tested..This.showed.<br />
accuracy.<strong>of</strong>.tuning.to.the.equal.tempered.chromatic.scale.base.<strong>on</strong>.<br />
A.=.440.Hz.within.a.few.10ths.<strong>of</strong>.a.cycle.for.each.note..Further,.<br />
the.octave.range.<strong>of</strong>.2 nd .harm<strong>on</strong>ics.were.in.tune,.as.were.the.3 rd .and.<br />
4 th . playable. harm<strong>on</strong>ics..The. instrument. represents. a. current. state.<br />
<strong>of</strong>.achievement.and.pro<strong>of</strong>.<strong>of</strong>.c<strong>on</strong>cept.for.a.model.based.<strong>on</strong>.certain.<br />
principles.<strong>of</strong>.acoustics..The.next.step.could.be.to.add.a.bell.and.set.<br />
<strong>of</strong>.keys.to.make.a.playable.instrument.<br />
115 Using Vocal Spectroscopy to Take the Guesswork Out <strong>of</strong> Powerful<br />
Singing,.RONALD SHAHEEN.(Music.Department,.<strong>University</strong>.<strong>of</strong>.<strong>San</strong>.<strong>Diego</strong>,.5998.Alcala.Park,.<strong>San</strong>.<strong>Diego</strong>,.CA.92110;.rshaheen@sandiego.edu).<br />
As.an.important.part.<strong>of</strong>.their.training,.classical.singers.learn.<br />
to.produce.a.full,.res<strong>on</strong>ant.sound.that.can.be.heard.over.an.orchestra.without.the.use.<strong>of</strong>.microph<strong>on</strong>es..That.process.has.traditi<strong>on</strong>ally.<br />
relied.<strong>on</strong>.the.singers’.percepti<strong>on</strong>.<strong>of</strong>.vibratory.sensati<strong>on</strong>s.inside.their.<br />
own.bodies.and.<strong>on</strong>.the.ears.<strong>of</strong>.their.voice.teachers,.a.method.that.<br />
is.highly.subjective.and.sometimes.unreliable..Nowadays.the.act.<br />
<strong>of</strong>.maximizing.res<strong>on</strong>ance.for.efficient.and.effective.singing.can.be.<br />
objectively.seen.by.using.a.computer.program.called.“Voce.Vista”.<br />
(“The.Visible.Voice”),.which.is.essentially.a.portable.sound.spectrometer..This.presentati<strong>on</strong>.will.review.the.relevant.basics.<strong>of</strong>.acoustics.as.they.pertain.to.singing,.and.then.discuss.the.related.c<strong>on</strong>cepts.<br />
<strong>of</strong>.vowel.formants,.vowel.modificati<strong>on</strong>,.and.res<strong>on</strong>ance.tuning..This.<br />
presentati<strong>on</strong>.will.then.show.how,.by.using.Voce.Vista,.singers.can.<br />
actually.see.(not.just.feel.or.hear).how.to.align.the.str<strong>on</strong>gest.harm<strong>on</strong>ic.<strong>of</strong>.a.pitch.with.the.str<strong>on</strong>gest.frequencies.<strong>of</strong>.the.vowel.formant,.<br />
and. thus,. based. <strong>on</strong>. scientific. data,. maximize. the. power. <strong>of</strong>.<br />
their.voices.<br />
116 Objective and Subjective Analyses <strong>of</strong> the Steel-String Acoustic<br />
Guitar,.DAVID M. MALICKy (Department.<strong>of</strong>.Engineering,.<br />
<strong>University</strong>.<strong>of</strong>.<strong>San</strong>.<strong>Diego</strong>,.5998.Alcala.Park,.<strong>San</strong>.<strong>Diego</strong>,.CA.92110;.<br />
dmalicky@sandiego.edu).<br />
Through.trial-and-error,.keen.sensitivity,.and.some.objective.<br />
methods,.luthiers.and.factories.have.developed.the.design,.materials,.and.manufacturing.processes.<strong>of</strong>.the.steel-string.acoustic.guitar.to.a.relatively.refined.level..The.scientific.relati<strong>on</strong>ship.<strong>of</strong>.the.guitar’s.subjective.sound.qualities.to.material.and.comp<strong>on</strong>ent.properties.(stiffness,.density,.thickness,.damping,.res<strong>on</strong>ance,.etc).is.poorly.<br />
understood..The.aim.<strong>of</strong>.this.pilot.study.is.to.examine.some.initial.<br />
correlati<strong>on</strong>s.am<strong>on</strong>g.comp<strong>on</strong>ent.properties,.acoustic.res<strong>on</strong>ances,.and.<br />
the.subjective.sound.qualities.<strong>of</strong>.the.acoustic.guitar..<br />
Twenty-five. Sitka. spruce. tops. (soundboards). were. prepared.<br />
using. comm<strong>on</strong>. luthier. practices.. Tops. were. assessed. for. density.<br />
and. bidirecti<strong>on</strong>al. bending. stiffnesses,. and. two. comm<strong>on</strong>. subjective.acoustic.measures:.shake-t<strong>on</strong>e.strength.and.tap-t<strong>on</strong>e.strength..<br />
87
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