Tuning the Skeleton F3A3C#4F4A4
When tuning contiguous major thirds – that is, major thirds that share a note,
easily imagined as an augmented chord such as F3A3C#4 for example –
the beat speeds of these thirds in equal temperament change about 26% from one interval to the next
(when no inharmonicity is considered.).
The Skeleton (See HERE) is a method I teach that requires the tuner to tune one beat speed exactly between two other beat speeds.
Exactly between means so that the beat speed ratios are the same. For example, 10, 11, and 12 are not even because 10 to 11 is 10%, but 11 to 12 is 9.1%. The correct beat speed progression would be 10, 10.95(9.5%), and 12(9.5%).
The steps for tuning accurate skeleton notes – F3, A3, C#4, F4, and A4 –
are:
1) Tune A4
2) Tune A3A4 beatless
3) Tune F3A3 about 7bps
4) Tune F3F4 beatless
5) Tune C#4 so that F3A3, A3C#4, and C#4F4 all change speed by the same amount.
That means the speeds work out to:
F3A3 – A3C#4 – C#4F4
SLOW – MEDIUM – FAST, or
MEDIUM – MEDIUM – MEDIUM, or
FAST – MEDIUM – SLOW, or
VERY SLOW – MEDIUM – VERY FAST, or
VERY FAST – MEDIUM – VERY SLOW, etc.
In each case above, the change in beat speed from F3A3 to A3C#4 equals the change
in beat speed from A3C#4 to C#4F4.
I.e. SLOW – MEDIUM is the same increase as MEDIUM to FAST.
VERY FAST to MEDIUM is the same decrease as MEDIUM to VERY SLOW.
Notice that A3C#4 is always MEDIUM.
Since A3 is never touched, then C#4 is always at the same pitch if we
preserve that the changes in beat speeds are constant.
Also, understand that the pitch of F3 determines which situation we end up with (FAST – MEDIUM – SLOW, or whatever).
We cannot force a beat speed progression onto the lower skeleton.
The hard part is tuning the C#4 so that each pair of M3’s changes by the same amount, exactly.
Many technicians deride this method but that is because they are not being picky enough when tuning that first C#4.
The test below has F and A octaves tuned so that they will produce a SLOW F3A3, MEDIUM A3C#4, and FAST
C#4F4, when C#4 is tuned correctly.
Each M3 pair must increase in speed by about 22%, in this case.
Tune the C#4 so that each M3 pair increases by the same ratio, 22%.
(22% is not audible. You just have to compare each M3 pair and judge that they change by the same amount.)
Click the SCORE button when you are done and see how close you got.
Have Fun!
TEST YOUR BEAT SPEED DIFFERENCE SENSITIVITY
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You may have to play them a second time
so that both notes sound at the same time.
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//WAVEFORMS
var f3 = "https://howtotunepianos.com/wp-content/uploads/2015/08/KF3.mp3"; var a3 = "https://howtotunepianos.com/wp-content/uploads/2015/08/KA3.mp3";
var cSharp4 = [ "https://howtotunepianos.com/wp-content/uploads/2015/08/KCs4a00.mp3", "https://howtotunepianos.com/wp-content/uploads/2015/08/KCs4a01.mp3", "https://howtotunepianos.com/wp-content/uploads/2015/08/KCs4a02.mp3", "https://howtotunepianos.com/wp-content/uploads/2015/08/KCs4a03.mp3", "https://howtotunepianos.com/wp-content/uploads/2015/08/KCs4a04.mp3", "https://howtotunepianos.com/wp-content/uploads/2015/08/KCs4a05.mp3", "https://howtotunepianos.com/wp-content/uploads/2015/08/KCs4a06.mp3", "https://howtotunepianos.com/wp-content/uploads/2015/08/KCs4a071.mp3", "https://howtotunepianos.com/wp-content/uploads/2015/08/KCs4a072.mp3", "https://howtotunepianos.com/wp-content/uploads/2015/08/KCs4a089.mp3", "https://howtotunepianos.com/wp-content/uploads/2015/08/KCs4a08.mp3", "https://howtotunepianos.com/wp-content/uploads/2015/08/KCs4a09.mp3", "https://howtotunepianos.com/wp-content/uploads/2015/08/KCs4a10.mp3"
];
var results = [ "C#4 is way too low.\n A3C#4 is actually slower than F3A3.\nA3C#4 needs to be faster than F3A3.", "C#4 is way too low. \nA3C#4 is actually slower than F3A3.\nA3C#4 needs to be faster than F3A3.", "C#4 is too low. A3C#4 is actually the same speed as F3A3.\nA3C#4 needs to be faster than F3A3.", "C#4 is too low. A3C#4 is actually the same speed as F3A3.\nA3C#4 needs to be faster than F3A3.", "A3C#4 is faster than F3A3, but not enough. C#4 is too low. \nA3C#4 is too close to F3A3. Make it faster.", "A3C#4 is faster than F3A3, but not enough. C#4 is too low. \nA3C#4 is too close to F3A3. Make it a bit faster.", "A3C#4 is faster than F3A3, but not enough. \nA3C#4 is too close to F3A3. Make it a bit faster.", "Really close, but C#4 is still low. \nA3C#4 is too close to F3A3. Make it a tiny bit faster.", "Yay! You did it! \nRatios are 24% and 22%. \nYou've tuned C#4 within 0.5 cents.", "Really close, but C#4 is still high. \nA3C#4 is too close to C#4F4. Make it a tiny bit slower.", "A3C#4 is faster than F3A3, but too fast. C#4 is too high. \nA3C#4 is too close to C#4F4. Make it a bit slower.", "A3C#4 is faster than F3A3, but too fast. C#4 is too high. \nA3C#4 is too close to C#4F4. Make it slower.", "C#4 is too high. \nA3C#4 is actually the same speed as C#4F4.\nA3C#4 needs to be slower than C#4F4." ];
var mark = [ "0%", "10%", "20%", "30%", "40%", "50%", "60%", "80%", "100%", "80%", "60%", "40%", "20%" ];
var f4 = "https://howtotunepianos.com/wp-content/uploads/2015/08/KF4.mp3";
var iii = Math.floor(Math.random()*13); //FUNCTIONS
function playF3A3(){
//Define the two octave wave files to be played track1 = new Audio(f3); track2 = new Audio(a3);
//Play the two wave files simultaneously track1.play(); track2.play(); }
function playA3CSharp4(){
//Define the two octave wave files to be played track1 = new Audio(a3); track2 = new Audio(cSharp4[iii]);
//Play the two wave files simultaneously track1.play(); track2.play(); }
function playCSharp4F4(){
//Define the two octave wave files to be played track1 = new Audio(cSharp4[iii]); track2 = new Audio(f4);
//Play the two wave files simultaneously track1.play(); track2.play(); }
function raiseCSharp4(){ iii = iii + 1; if (iii>12) {iii = 12;}
track1 = new Audio(a3); track2 = new Audio(cSharp4[iii]); track1.play(); track2.play(); }
function lowerCSharp4(){ iii = iii - 1; if (iii<0) {iii = 0;} track1 = new Audio(a3); track2 = new Audio(cSharp4[iii]); track1.play(); track2.play(); } function score(){ window.alert("Your score is " + mark[iii] + "\n\nComments: \n" + results[iii] + "\n\nPress OK/Close to go back and listen again. Try to confirm what your results were.") } function again(){ location.reload(); }