<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <meta http-equiv="Content-Type" content="text/html;charset=ISO-8859-1"> <title></title> </head> <body text="#000000" bgcolor="#ffffff"> 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 o<tt>thers 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 </tt><a class="moz-txt-link-abbreviated" href="mailto:iannaman@aol.com">iannaman@aol.com</a> wrote: <blockquote type="cite" cite="mid194.34434b5c.2ef2e47a@aol.com">In a message dated 12/16/04 4:06:28 AM Pacific Standard Time, <a class="moz-txt-link-abbreviated" href="mailto:pianoman@accessus.net">pianoman@accessus.net</a> writes: <blockquote type="CITE" style="border-left: 2px solid rgb(0, 0, 255); margin-left: 5px; margin-right: 0px; padding-left: 5px;"> 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.? </blockquote> 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</blockquote> </body> </html>