A piano that's, say 100 cents flat at A4; that string is vibrating 25 cps slower than it should at A440, and is thus A415, or a-flat, or G#, depending on how you look at it. Enharmonics Terry Peterson ----Original Message Follows---- From: "James Grebe" <pianoman@accessus.net> Reply-To: Pianotech <pianotech@ptg.org> To: "Pianotech" <pianotech@ptg.org> Subject: Re: Help with "bad" tuning...need help Date: Fri, 17 Dec 2004 15:12:04 -0600 Hi Terry, At A-4, 1 CPS = 3.8 cents James Grebe Piano-Forte Tuning & Repair Creator of Handsome Hardwood Caster Cups (314) 608-4137 WWW.JamesGrebe.com 1526 Raspberry Lane Arnold, MO 63010 BECOME WHAT YOU BELIEVE! pianoman@accessus.net ----- Original Message ----- From: "pianolover 88" <pianolover88@hotmail.com> To: <pianotech@ptg.org> Sent: Friday, December 17, 2004 12:09 PM Subject: Re: Help with "bad" tuning...need help >another way to look at it is "cycles". Each cycle is comprised of 4 >cents. So, 100 cents flat, or 1/2 step flat is 25 cycles flat, or A >415. > >Terry Peterson > > > >----Original Message Follows---- >From: Robin Hufford &lt;hufford1@airmail.net&gt; >Reply-To: Pianotech &lt;pianotech@ptg.org&gt; >To: Pianotech &lt;pianotech@ptg.org&gt; >Subject: Re: Help with &quot;bad&quot; tuning...need help >Date: Fri, 17 Dec 2004 14:58:39 -0600 > >List, > A half step is an adjacent key in the context of a piano >keyboard. It may be white to white as in the case of e-f, or b-c. >It may be a white key to an adjacent black key, or a black key to a >white one. There are two adjacent pairs of white keys on the piano, >those mentioned above. There are no black to black half steps as a >white key will always be in between any two black keys chosen so as >to be as close together as is possible. Two half steps means an >interval of a whole step, usually referred to as a whole tone. This >may be white to white, black to black, white to black or black to >white. > The foregoing emanates from the layout of the keys on the >keyboard itself without reference to notation. A second >consideration obtains when notation is taken into account. Half >steps must have adjacent letters names, that is they must be >proximate to one another in the sequence of the musical alphabet >which is (a, b , c, d, e, f, g, a, g, ......). The same >requirement occurs for whole tones, that is the interval must be >named with proximate letters. (A to b) is one such proximate pair, >as is ( b to c), along with the others. Well, which is it? Half >or whole? This is determined by reference to the natural layout of >the keyboard and the use or absence of a sharp or flat sign to >indicate the half steps found on the keyboard referred to in the >first paragraph above. > Intervals are named for the number of letter names they >contain: For example, counting upwards, (a-a) is a unison, (a-b) >is a second as it contains two letter names. Similarly (a-c) is a >third;(a-d), a fourth. etc. You can count up and name any interval >you wish, although some are more standard than others. The >number of half steps contained in the interval determines, in the >case of the second, whether it is a major or a minor second, that is >a half tone or whole tone, or, alternatively, a half step or a whole >step. ALL WHOLE TONES MUST CONTAIN ONLY TWO HALF STEPS. B to c is >intrinsincally a half step on the keyboard, as mentioned above. B- >c(sharp) is now a hole tone as it contains two half steps. So is >b(flat) to c. There are other somewhat arcane complexities, for >example what is b(flat) to c(sharp)? This is an augmented, major >second. For technicians who are not musicians, it is best to ignore >such things. This method of naming may be applied similarly to any >note on the keyboard subject to certain limitations which are in the >nature of definitions. The reference to whole tones contained above >is just such one definition. There are others some of which are ALL >MAJOR THIRDS MUST CONTAIN FOUR HALF STEPS, MINORS THIRDS MUST BE >ONLY THREE HALF STEPS. etc. > There is no major third, as technicians are sometimes wont to >do, which can correctly be referred to as a to D(flat). This would, >as it contains four letter names, be a contracted, or diminished >fourth, even though acoustically, it would be, in fact, the sound of >the major third, which should correctly be referred to as a to >c(sharp). This seems paradoxical but there is an underlying logic >and utility in these rules of naming as they correspond, in an >amazingly logical way considering that they have developed from >musicians, to the harmonic motion inherent in the actual music which >the notation attempts to express. In the cents notation, which >expresses the logarithmic aspect of equal temperament, one octave >itself comprises 1200 cents, which encompasses an actual doubling of >frequency. Obviously each half step contains 100 cents, which means > a whole tone or step comprises 200, a whole tone and a half step, >300, etc. These are equal ratios and not counts of frequencies per >second. One can not impose upon the frequency difference of any two >adjacent notes, by definition a half step or a hundred cents, an >equal division of the frequency difference and arrive at a value for >a cent, as 100 cents are, in actuality, not an equal division by a >hundred, but, rather, a hundred equal ratios, as Bob Scott pointed >out only a few weeks ago. This means, for example, if you could >find a half step comprised of a hundred hertz, or arbitrarily >defined it such, that a cent does not equal one hertz. Rather, a >cent is the number, which, when multiplied by the frequency of the >lower note and, done, 99 more times, will produce the frequency of >the upper note. These are equal ratios, not equal divisions. >Regards, Robin Hufford in iannaman@aol.com wrote: > >&gt;In a message dated 12/16/04 4:06:28 AM Pacific Standard Time, >&gt;pianoman@accessus.net writes: >&gt; >&gt; >&gt;&gt; >&gt;&gt;I think part of the problem is that we are calling these >half >&gt;&gt;steps. The >&gt;&gt;distance between E and F is no larger than between F and F#. > It is >&gt;&gt;still >&gt;&gt;100 cents. Why do we insist on calling those things whole >steps >&gt;&gt;anyway.? >&gt; >&gt; >&gt; >&gt;James, >&gt; >&gt;These are half-steps(not whole steps), aka half-tones, >semi-tones or >&gt;minor seconds, and there are 100 equal divisions between them. >Each >&gt;one of these miniscule portions is called a cent. >&gt; >&gt;Dave Stahl > > >_______________________________________________ >pianotech list info: https://www.moypiano.com/resources/#archives _______________________________________________ pianotech list info: https://www.moypiano.com/resources/#archives
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