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<div data-externalstyle="false" dir="ltr" style="font-family: 'Calibri', 'Segoe UI', 'Meiryo', 'Microsoft YaHei UI', 'Microsoft JhengHei UI', 'Malgun Gothic', 'sans-serif';font-size:12pt;"><div>I’m afraid that, as a trombonist as well as a theorist, I must chime in with a slight correction. Trombones, at least, are not in fact built to play in equal temperament. Every trombonist learns to make the slide adjustments necessary to play in tune with equally-tempered instruments; as would be expected by comparing just intonation to equal temperament, our 3rd/6th/etc. partials are naturally a bit high, our 5th and 10th partials are naturally low, and our 7th partial is so flat that first position is unusable in this partial. I am not trained enough on other brass instruments to speak regarding their natural tuning inclinations 100% from personal experience, but I do know that my trumpeter friends often make lip adjustments or adjust a small tubing extension with their little finger to play in tune. Whether brass instrument tuning justifies the derivation of western pitch collections, intervals, and particularly triads from the overtone series is, as evidenced by this particular thread of discussion, a separate matter entirely.</div><div><br></div><div>Nathan Baker</div><div>Music Theory Coordinator</div><div>Chair, Faculty Senate</div><div>Casper College, Wyoming</div><div><a href="mailto:nbaker@caspercollege.edu">nbaker@caspercollege.edu</a><br></div><div data-signatureblock="true"><br></div><div style="padding-top: 5px; border-top-color: rgb(229, 229, 229); border-top-width: 1px; border-top-style: solid;"><div>----------------------------------------------------------------------<br>Message: 1<br>Date: Wed, 23 Jul 2014 10:51:48 +0200<br>From: Nicolas Mee?s <nicolas.meeus@scarlet.be><br>To: CARSON FARLEY <ccfarley@embarqmail.com>,<br> smt-talk@lists.societymusictheory.org<br>Subject: Re: [Smt-talk] Harmonics<br>Message-ID: <53CF77A4.3060404@scarlet.be><br>Content-Type: text/plain; charset="utf-8"; Format="flowed"<br><br>It is disappointing to see that the same misunderstandings come back and <br>again. In such conditions, the whole discussion is pointless. Let me try <br>for the last time:<br><br>1. The question of enharmonic notes produced on a string or overblowing <br>a wind instrument and that of harmonic overtones are only remotely <br>related. Consider the following facts:<br>? Brass winds usually are built today to play in ET. This is obtained by <br>complex adjustments of the bore, with the result that the different <br>notes obtained by overblowing correspond to those in ET and not to just <br>intonation. Yet, these instruments still can produce harmonic overtones <br>for each of their notes, the harmonicity of overtones in this case being <br>more dependent on the conditions of blowing than on conditions of the bore.<br><br></div></div></div>
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