Convention Community

Where Are Those Beats?

Ward Guthrie, RPT

1. Recommended resources
   1. “On Pitch" by Rick Baldassin from PTG booth
   2. “PTG Tuning Exam Source Book” from PTG booth
   3. Coleman "Beat Locator" cards
   4. What are beats?
      1. 2 tones nearly same frequency
      2. Volume changes
      3. Where do beats come from?
         1. String produces fundamental and higher partials
            1. String vibrates multiple segments at same time
            2. Oct, 5^th,  4^th,  M3^rd,  m3^rd,  M2^nd,  M2^nd,  m2^nd,  m2^nd, 
         2. what is an interval?

1. 2 notes played at same time
   • Each has its own partial series
2. The 2 notes have coincident partials
   • This is the beat we hear

4. What intervals used in temperament?
   1. 5^th – listen at 3:2
   2. 4^th – listen at 4:3
   3. M3^rd – listen at 5:4
   4. m3^rd – listen at 6:5
   5. M6^th – listen at 5:3
   6. M10^th
   7. octave – many coincident partials
      1. Which coincident partial is used in midrange?
         • 4:2
         • test – M3^rd/M10^th

• is octave stretched or not?

5. How use beats in temperament?
   1. Tests and checks to compare beat rates
   2. which are wide and narrow intervals?
      1. wide: 4^th, M3^rd, M10^th, M6^th
         • how speed up?
      2. narrow: 5^th, m3^rd
         • how speed up?

• What’s happening if want to speed up but instead slows down?
  • Wrong side of pure

1. Would it be nice to find a proof that could tell you if wide or narrow?
   • 4th proof
     • 3rd/6th -- which faster?
   • 5th proof
     • 6th/10th -- which faster?

1. temperament octave proofs?
   • M3^rd/M10^th (checks 4:2)
     • same speed? – 10^th faster
   • 4^th/5^th (also checks 4:2)
     • same speed? – 4^th faster
   • m3^rd/M6^th (checks 6:3)
     • same speed? – 6^th faster
     • more stretch in the octave than the 4:2

6. Set temperament
   1. how large temperament?
   2. 3rd/6th sequence or 4th/5th better?
      1. Emphasize the other for your tests
      2. How apply to improve temperament?
         1. Check & improve
         2. use parallel and contiguous intervals
            1. parallel means?
            2. contiguous means?
         3. start checking contiguous 4th’s
            1. All have same beat rate (almost)
            2. find worst one

• Find three tests to prove if it’s sharp, flat, good
  • If all indicate the same, move it
  • What if some say sharp, some flat?

1. 4^th’s all BETTER, then contiguous 3rds
   1. same process
2. All other intervals
   1. same process
   2. When do you quit?

• MIDRANGE TUNING CHECKS

1. A-440
   1. M17 test (F2 to fork)
      • both beat rates should be the same
   2. common mistakes
      • M10 test (F3 to fork) produces flat A-440
      • use fork to tune A37 produces sharp A-440

2. Octaves
   1. M3-M10: equal beating means pure 4:2 octave
   2. a slight further expansion is good (M10 slightly faster than M3)
   3. Fifths
      1. M6-M10: M6 faster than M10 indicates contracted P5
      2. should sound almost as pure as octaves
      3. Fourths
         1. M3-M6: M6 faster than M3 indicates expanded P4
         2. should sound almost as pure as fifths, but a little faster
         3. Thirds
            1. parallel thirds beat rate should increase smoothly
            2. contiguous thirds in ratio of 4:5
            3. Tests to use
               1. if tune P4 & P5, emphasize M3 & M6 tests
               2. if tune M3 & M6, emphasize P4 & P5 tests
               3. parallel M3 speeds increase, P4 a very slight increase, P5 a very slight increase
               4. parallel & contiguous intervals
               5. bracketing

• PIANO TECHNOLOGY TOPICS
• Albert E. Sanderson
• Registered Piano Technician, Piano Technicians Guild
• President, Inventronics Inc., 171 Lincoln Street, Lowell, MA 01852
• Topic # 7
• CONTIGUOUS-INTERVAL AURAL TUNING TESTS
• Two contiguous musical intervals are intervals that touch each other, in other words, intervals that share one note in the middle. Tests that use contiguous intervals are easy to learn and use, and tell the tuner not just that there are mistakes in the temperament, but tell him explicitly which notes are at fault and what to do to correct them.
• Contiguous major thirds, for example, should beat in the ratio of four to five, because the major third itself consists of two notes whose frequencies are in the ratio of four to five. Displacing any interval up the keyboard will theoretically speed it up in the ratio of the frequencies of the two root notes involved. Therefore two contiguous major thirds should beat in the ratio of four to five, two contiguous minor thirds in the ratio of five to six. Similarly, two contiguous fourths should beat in the ratio of three to four, and two contiguous fifths in the ratio of two to three. However, on the piano this theoretical relationship holds well only for the major and minor thirds. The fourths and fifths are so strongly affected by inharmonicity that these contiguous intervals beat at almost the same speeds.
• Using the above facts, we can develop a test for one note of the piano at a time. Take C4 for example. Play down a third and up a third, G#3-C4 and C4-E4, keeping time at the rate of four beats of the lower one, and then at the rate of five beats of the upper one. Think of it as four beats to the measure, followed by five beats to the measure. The tempo of the two kinds of measure should agree. If the upper beat rate is too fast, it indicates that C4 may be flat and vice versa.
• Before moving C4, we need more evidence. Play down a fourth and up a fourth, G3-C4 and C4-F4, and listen for either equal beat rates, or an upper beat rate just slightly faster than the lower. If C4 is flat, the upper beat will be too fast and the lower too slow, and vice versa. If both the fourth test and the third test indicate that C4 is flat, for example, then this is very strong evidence that C4 should be moved. But to nail down your decision! you can add a contiguous-fifth test as well.
• To check contiguous fifths, play down a fifth and up a fifth, F3-C4 and C4-G4. If C4 is flat, the lower fifth will beat faster than the upper, and vice versa.
• In our example, we have now used three tests involving six other notes to check up on one note. If all the tests indicate that C4 is flat, then it is a good idea to move C4 after all, the odds are six to one that C4 is in fact flat! If some tests say flat and some say sharp, then leave C4 where it is and go on to test other notes. Eventually you will find the main culprit or culprits, the notes for which all tests say the same thing. Move these notes without hesitation. Your temperament will improve steadily as you find and correct each note that fails all three of these tests .
• The range of this contiguous-interval test is at least from C3 to C5, a two-octave span. After tuning the whole piano, unisons and all, start applying this test at C3. Move up one semitone at a time, and correct any note that fails all three tests before moving on. Go all the way up to C5 this way. If you like, you may make a second pass from C3 to C5 and polish your tuning even more. Eventually you will reach the point where no notes can be improved upon, and at that point you will have an extremely fine tuning. A supertuning if you will!