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 <hufford1@airmail.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 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: > > >In a message dated 12/16/04 4:06:28 AM Pacific Standard Time, > >pianoman@accessus.net writes: > > > > > >> > >>I think part of the problem is that we are calling these half > >>steps. The > >>distance between E and F is no larger than between F and F#. It > is > >>still > >>100 cents. Why do we insist on calling those things whole steps > >>anyway.? > > > > > > > >James, > > > >These are half-steps(not whole steps), aka half-tones, semi-tones or > >minor seconds, and there are 100 equal divisions between them. Each > >one of these miniscule portions is called a cent. > > > >Dave Stahl > > > _______________________________________________ > pianotech list info: https://www.moypiano.com/resources/#archives
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