<html><body bgcolor="#FFFFFF"><div>Tom,</div><div> </div><div>I think you are conflating two terms, and along with them, the concepts to which they refer. </div><div> </div><div>Inharmonicity is the non-harmonic frequency of a partial (which would otherwise be called a harmonic) due to, in the case of the piano, the stiffness of the wire. </div><div> </div><div>When the same note is spelled differently depending on the harmonic context, the change is called enharmonic. </div><div> </div><div>It is arguable whether a singer or instrumentalist would have to change their intonation when the spelling changes - if the harmonic context were provided by a fixed-pitch instrument that was tuned in equal temperament, no change would be required at all. </div><div> </div><div>But a chord does not contain inharmonicity, unless the instrument(s) playing the chord have inharmonic partials, as the piano does. </div><div> </div><div>An ensemble of non-fixed-pitch instruments such as a string quartet may well adjust their tuning toward greater consonance when not constrained by fixed pitch instruments like keyboards and lutes. But that goes more to the question of temperaments than to the spelling of enharmonic equivalents such as G#-Ab. Hope this helps. </div><div><div> <div> </div></div></div><div> On Sep 27, 2011, at 1:00 PM, "Tom Rhea, Jr." <<a href="mailto:rheapiano@cox.net">rheapiano@cox.net</a>> wrote: </div><div></div><blockquote type="cite"><div><o:smarttagtype namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="PersonName">  <style>  </style> <div class="Section1"> Hi Paul,<o:p></o:p> <o:p> </o:p> An instrumentalist generally only plays one note at a time but all of the notes of the score must be harmonically related.  That’s true even with a vocalist.  If you look at a score (piano, orchestral, choral, etc) and analyze each chord, you’ll find that they can be broken down into a very logical, though sometimes extremely complex, structure.  What confuses me at times, is a note (G# for instance) that crosses a bar line and becomes an A flat.  Musically, they’re the same note but harmonically they’re not because the other notes in the chord have changed, making the entire structure into something different, even though the two notes (G# and A flat) sound the same to the ear.  Instrumentalists, but especially vocalists, have to be aware that the A flat must be tuned slightly when going from a G# because of the inharmonicity within the chord structure.  As piano technicians, we have to be aware of the same inharmonicity when tuning since some of the intervals need to be stretched or compressed slightly to match the temperament.  The same occurs in instrumental or vocal music, too, especially with string instrumentalists and vocalists.<o:p></o:p> <o:p> </o:p> I hope this hasn’t been too long-winded and makes some sort of sense.<o:p></o:p> <o:p> </o:p> Regards,<o:p></o:p> Tom<o:p></o:p> <o:p> </o:p> <o:p> </o:p> <div> <div class="MsoNormal" align="center" style="text-align:center"> <hr size="2" width="100%" align="center" tabindex="-1"> </div> From: <a href="mailto:pianotech-bounces@ptg.org">pianotech-bounces@ptg.org</a> [mailto:pianotech-bounces@ptg.org] On Behalf Of Paul T Williams Sent: Tuesday, September 27, 2011 3:30 PM To: <st1:personname w:st="on"><a href="mailto:pianotech@ptg.org">pianotech@ptg.org</a></st1:personname> Subject: Re: [pianotech] theory question<o:p></o:p> </div> <o:p> </o:p> Ahhh!   Makes sense to me. Thanks for clarifying this.  I always wondered that, too.  But;  why do this, when the notes are just written in the score?  Would a bassist wonder why he/she is playing an E or G when it's a C chord?  I've always just played what's written. Am I missing something? Best, Paul <o:p></o:p> <table class="MsoNormalTable" border="0" cellpadding="0" width="100%" style="width:100.0%"> <tbody><tr> <td valign="top" style="padding:.75pt .75pt .75pt .75pt"> From: <o:p></o:p> </td> <td valign="top" style="padding:.75pt .75pt .75pt .75pt"> "Tom Rhea, Jr." <<a href="mailto:rheapiano@cox.net">rheapiano@cox.net</a>> <o:p></o:p> </td> </tr> <tr> <td valign="top" style="padding:.75pt .75pt .75pt .75pt"> To: <o:p></o:p> </td> <td valign="top" style="padding:.75pt .75pt .75pt .75pt"> <<st1:personname w:st="on"><a href="mailto:joegarrett@earthlink.net">joegarrett@earthlink.net</a></st1:personname>>, <<st1:personname w:st="on"><a href="mailto:pianotech@ptg.org">pianotech@ptg.org</a></st1:personname>> <o:p></o:p> </td> </tr> <tr> <td valign="top" style="padding:.75pt .75pt .75pt .75pt"> Date: <o:p></o:p> </td> <td valign="top" style="padding:.75pt .75pt .75pt .75pt"> 09/27/2011 02:04 PM <o:p></o:p> </td> </tr> <tr> <td valign="top" style="padding:.75pt .75pt .75pt .75pt"> Subject: <o:p></o:p> </td> <td valign="top" style="padding:.75pt .75pt .75pt .75pt"> Re: [pianotech] theory question<o:p></o:p> </td> </tr> </tbody></table> <o:p> </o:p> <div class="MsoNormal" align="center" style="text-align:center"> <hr size="2" width="100%" noshade="" color="#aca899" align="center"> </div> <tt>Hi Joe, et al,</tt> <tt>The actual theory behind this convention is this:</tt> <tt>Consider the CEG major chord and the note positions when being played.  All</tt> <tt>the notes are said to be in their root positions.</tt> <tt>When a first inversion of the CEG chord is being played, the E and G are in</tt> <tt>their root positions but the C has been moved up an octave and is now a 4th</tt> <tt>interval above the highest adjacent root note, the G.  This position, EGC,</tt> <tt>is said to be a C Major 4 or first inversion of the C Major chord.</tt> <tt>In the second inversion of the CEG chord, the only note still in its root</tt> <tt>position is the G.  The C and E are moved an octave above their root</tt> <tt>positions, such that the E is a 6th interval above the G (in its root</tt> <tt>position) and the C is a 4th interval from the G (in its root position),</tt> <tt>hence a C Major 6/4.</tt> <tt>All of the chords are spelled from the bottom.  However, the intervals which</tt> <tt>comprise the inversions are labeled from the highest note still in its root</tt> <tt>position to the one or two notes that have been moved up an octave from</tt> <tt>their root positions, either a 4th interval for a first inversion or a 6th</tt> <tt>and a 4th interval for a second inversion.  The labeling of the inversion</tt> <tt>intervals is always from the highest interval first.</tt> <tt>I hope this helps with understanding the theory question.</tt> <tt>Regards,</tt> <tt>Tom</tt> <tt>-----Original Message-----</tt> <tt>From: <a href="mailto:pianotech-bounces@ptg.org">pianotech-bounces@ptg.org</a> [</tt><a href="mailto:pianotech-bounces@ptg.org"><tt>mailto:pianotech-bounces@ptg.org</tt></a><tt>] On Behalf</tt> <tt>Of Joseph Garrett</tt> <tt>Sent: Tuesday, September 27, 2011 2:26 PM</tt> <tt>To: pianotech</tt> <tt>Subject: Re: [pianotech] theory question</tt> <tt>Ken said: "I concur with Tom. You count from the bottom up. A "6" is the</tt> <tt>interval between the E and the C when in first inversion. In second</tt> <tt>inversion, G, C, E, there is a 4th between the G-C and an "6" between the</tt> <tt>G-E."</tt> <tt>Ken Gerler (I was a theory major in college)</tt> <tt>Hmmm? if that were the case, then the later would be a 4/6 rather than a</tt> <tt>6/4. Right?<G> Personally, I prefer the Jazz Musicians way of saying</tt> <tt>something like "the C chord with a G in the bass.<G></tt> <tt>That's my take on that.</tt> <tt>Joe</tt> <tt>Joe Garrett, R.P.T.</tt> <tt>Captain of the Tool Police</tt> <tt>Squares R I</tt> <o:p></o:p> </div> </o:smarttagtype></div></blockquote></body></html>