(I have been a little busier than I anticipated, so this post refers back about a week to my previous two posts on this subject.) This third post looks at the "F number," the tenor break, and tuning the bass. The "F number" is the measured difference between the 4th and 8th partials of F3 (read by tuning F3 to 0.0 cents at F5 and measuring at F6). I haven't yet found a place where this number "shows up" in the FAC tuning, like the "A and C numbers". The functions of the "F number" is clear, however: it extends the tuning downward from F3 to A0. The larger the number, the lower these numbers will be tuned, with the greatest difference being towards the bottom, near A0. The "F number may affect some notes from F#3 to B6, but never (in my experience) more than 0.1 or 0.2 cents either direction. I consider the affect on this area to be insignificant, so I ignore it. On well- and evenly-scaled instruments, like Steinway grands and most Yamaha uprights and grands, the "F number presents few problems. It can generally be counted on to "put you in the ballpark," and in these cases I normally just use the figures the FAC provides. Most (though not all) spinets and consoles, many larger uprights, and some grands (including the Yamaha GH-1) have large jumps in inharmonicity between the wound and plain wire strings. What to do? This question is most poignant when applied to certain models of piano, where the maker retains the same overall scale, but adds a few wrapped string unisons to the treble bridge. When F3 was a plain string, it might have measured an "F number" of around 20.0 The newer model of the same piano, changed only by the altering of two strings from plain to wrapped, could have a wrapped F3 measuring an "F number" of about 7.0 Obviously, the basses of these two pianos should be tuned essentially the same, but the two "F numbers' will generate quite different tuning curves. My empirical solution to this conundrum (arrived at through trial and error) is as follows: 1) If F3 is a wrapped string, measure the "F number," but also measure the "F number" of the lowest plain wire unison. (eg, if the lowest plain wire unison is G3, set the SAT to G5 at 0.0 cents. Tune G3 to stop the lights. 8ve up to G6 and measure). 2) If F3 is a plain wire and the "F number" is 10.0 or greater, measure the "F number of the highest wrapped unison (as above). Compare the two values. Some typical extremes: Wurlitzer spinet, F3 (wrapped) 12.9; G3 (plain) 21.2 Kimball spinet, F3 (plain) 19.3, E3 (wrapped) 8.4 Kawai 502M console, F3 (wrapped) 5.9, G3 (plain) 15.0 Acrosonic 36", F3 (wrapped) 7.9, G3 (plain) 24.8) Baldwin 243 (Hamilton studio), F3 (plain) 18.5, D3 (wrapped) 4.4 Cable console, F3 (wrapped) 3.9, G3 (plain) 12.6 If the difference between the two numbers is 5.0 cents or greater, We will probably want to do something about smoothing the transition over the break. More about that later. Meanwhile, what number to enter? Most of these pianos are small, with short bass strings, and scales which don't allow for much stretch in the bass. My tendency is to take the "F number" of the highest wrapped string, and increase it somewhat. But for most spinets and consoles, I find an "F number" over 10.0 stretches the bass more than I like, so in a case like the Wurlitzer spinet, above, I would enter 10.0. Now what about the break? Jim Coleman's suggestion, distributed with current SAT manuals, calls for using two separate pages of memory, one for wrapped and one for plain strings. This is sometimes a neat solution. However, in most of these pianos, the lowest plain wire is F3 or above. Since the "F number" only affects F3 and below, the page of memory with the higher "F number", to be used in Jim's method for the plain wires, will not be significantly different from the page with the lower "F number" in the area of the lowest plain wire unisons. In other words, one might as well simply use the page 2 tuning throughout. My preference in these cases is to have only one FAC tuning, based on the "F number" of the highest wrapped string as described above, and to alter the top several wrapped unisons and the lowest plain unisons individually. The greater the difference between "F numbers", the greater the alteration, up to a maximum as follows: bottom plain unison -0.4 cents, next higher -0.3 cents, next -0.2, next -0.1. Top wrapped unison +0.4 cents, next lower +0.3 cents, next +0.3, next +0.2, next +0.2, next +0.1. For the sake of brevity, I won't go into the why further than to say that larger alterations cause unacceptably (to me) narrow 5ths and wide 4ths, and problematic octaves. This alteration scheme is enough to my ear to make even the most uneven break acceptable, with M3's progressing as evenly as they can without causing other problems. The foregoing has been a little "denser" and complicated than I'd like. If there are problems following it, or any questions, please let me know and I'll try to clarify. To continue, and discuss the tuning of the bass: I prefer to start by tuning from C3 up by half steps to B5. I then begin at B2, and tune downward to A0. This order allows me to check the bass the FAC calculated against notes already tuned in the midrange. (I think most FAC users would agree that C3-B4 is where the FAC really excels, with a little help on pianos with bad breaks). For most pianos, and especially for well- and evenly-scaled pianos, the FAC produces a bass that has somewhat wide 6:3 8ves all the way down, from B2 to A0. It also produces (usually) somewhat narrow 6:4 5ths in the same range. These are easy to check for. Set the SAT to B2. It is prepared to tune the 6th partial, F#5. Play B3 and observe the lights (you are measuring the 3rd partial of B3). If the lights are rotating slowly sharp, you will be creating a wide 6:3 8ve when you tune B2 to this pitch. Play F#3 and observe the lights (you are reading the 4th partial). If they rotate flat,the 6:4 5th will be narrow. (You can also play F#4 and F#5. Normally the lights will rotate somewhat sharp, indicating a wide 6:2 octave 5th and a wide 6:1 double octave 5th). For the average piano, this is what I want to see. If playing the 8ve above the note I'm about to tune makes the lights drift not too fast sharp, and the fifth above makes the lights drift not too fast flat, the tuning will be acceptable. Some pianos require a narrow 6:3 8ve in the upper bass. This should be judged by ear. If a narrow 6:3 octave is needed, this can be done "visually" as follows: using B2 as an example, set the SAT to B2, play B3, and observe the lights. Change the cents setting by pressing the cents up button until B3 causes the lights to rotate just flat. Tune B2 and check by ear. I'll leave the rest for the reader to work out, as this is getting too long already. I will send one final post with a few additional thoughts on this general topic in a day or two. Hope that those who have waded their way through these have found them useful. Best regards, Fred Sturm Albuquerque
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