Posted by: Andrea Day | November 27, 2013

Tuning; the Barbershop way

Recently I was lucky enough to be invited to Holland with my barbershop quartet, The MIX, to co-host an education day for 16 Holland Harmony and DABS quartets.  As part of the weekend, I needed to prepare a session on “How to be a great Tenor” to deliver to all the tenor delegates.

Having only sung tenor for 18 months or so, I wanted to make sure that I read up on all the material from as many awesome and well established tenors that I could find.  There were some great notes from Sandy Marron, Charla Esser, Patty Cobb and Kipp Buckner that I managed to get my mitts on that really helped with the bulk of the session.  But, I wanted to add a bit more “me” into the session too.

I’m pretty techy and love my music technology and physics, so I took the rather big step to help fellow tenors understand some pretty complex ideas around tuning.

So having done all the work and made all the pretty pictures, I thought that I would share it here, incase anyone else found it useful too.  Do let let me know what you think… your feedback will make really interesting reading!


One of the most important things about being a tenor is tuning correctly;  and singing the highest part in Barbershop means that its much easier to make mistakes as you are working with smaller differences between notes and they carry much further too.

Let me explain with a bit of maths, history and even a touch of physics.


Sound is a wave of air at different pressures and is called a “waveform”.  When these waveforms of different notes are played together they interact with each other.




HF and LF wave

Sounds with a high pitch (like a tenor) have a high frequency wave and sounds with a lower pitch (like a bass) have a lower frequency wave.

If two or more pitches are played at the same time and their waveforms physically “fit” into each other then they sound really pleasant.






Here are three different pitches that are being sung at the same time, each one being represented by a waveform of a different colour; the lowest in blue, the highest in purple and one in between in red.  See how they all fit together?

For these wave forms to fit, they need to be simple ratios of eachother.  The red line goes up and

concordant sounddown twice for every time the blue line does, giving it a ratio of 2:1 and meaning it is double the frequency.  When a note is double the frequency it is the octave of the original note.

When the waveforms don’t quite fit with each other you can hear a pulsing sound in the note that is being sung which in scientific circles is called a “beat”.  To demonstrate this beat, it is most easily heard when two notes are being played that are very close to each other in pitch but not quite.  Listen for the beat in this example.

If you are still with me, well done… thats most of the hard concept stuff sorted… but hang fire for the tables and graphs bit, after we do the little bit of history…


Before music was written down and orchestras were around where lots of different types of instruments played together, tuning was done by ear and notes and the differences between them were “pure” using the simple ratios that we saw before. The waveforms always fitted into each other and sounded perfect, exact and “just”.

But then, composers wanted to to get all clever and use orchestras with lots of different instruments in different pitches.  They also wanted to write things down and transpose music into different keys.

This “just” tuning system wouldn’t work as the gaps between each note in a scale weren’t exactly mathematically the same and equal. It meant that when music was transposed into different keys, it didn’t sound right. So, they fudged it; the musicians created “equal temperament” – the posh way of saying that the gap between all the notes in a scale is exactly the same.

Before equal temperament, all the notes “fitted” together in a chord perfectly and sounded marvellous.  Now, when we use equal temperament they don’t quite fit by the tiniest of margins – and when that happens you get the pulsing sound and not quite exactly tuned chords. The margins that we are talking about here are so small that most of the time you can’t hear them – even the sharpest of ears don’t get offended when a chord is played on a well tuned equal temperament piano.  Take a look at the table below……

difference table between just and equal temperament

Screen Shot 2013-11-27 at 19.45.34

This table shows the slight variations between the just tuning system and the equal temperament tuning using the frequency values of the notes. The bar chart shows the same information, but hopefully in a way that you visual peeps (including me!) can understand the differences between the two. See how the two tuning systems are different… but only by a very small amount? Most people cant really hear the difference between the two systems, but in Barbershop, the differences between these two notes is what hooks us and keeps us coming back for more!

On a piano keyboard you see these notes which have been tuned using the equal temperament tuning system – the frequency gap between is each note is the exactly the same:

Screen Shot 2013-11-27 at 19.59.08

But when we sing, we don’t have to stick to the fixed notes that a piano has; our voices are a very flexible instrument and can sing every pitch that there is, even the ones in between the notes on a keyboard.  So think of the notes that your voice can sing as being more like this:

Screen Shot 2013-11-27 at 19.59.21

When we sing unaccompanied we aren’t limited to the 12 equally spaced notes on a piano keyboard which use equal temperament, so we can use just tuning to make the notes in a chord fit together and sound perfect.  In Barbershop, this “fitting” of the pitches in a chord is often referred to as “lock”.

When this lock is achieved in Barbershop singing it creates new notes above and below the ones that you are singing, all through the power of maths and physics.  Its actually pretty cool – well…if you are a geek like me, that is.

These new notes that are created are called overtones and undertones. When they are created they are referred to in Barbershop as “expanded singing” or sometimes as “ringing a chord” or “the 5th voice”.

Most importantly, here is what this science all means to your barbershop singing:

  • the notes written on the sheet music might not be the exact ones that you need to sing to make the chord ring, you might have to sing slightly sharper (higher) or flatter (lower) to tune the note and get that “lock and ring”.
  • if you have two notes on the music one after the other that are written the same on the music, then its likely that you will need to adjust your tuning to sing the right part of the note to get the chord to lock, particularly if the other parts are moving around you.
  • if you learn from computer generated teach tracks, they will almost certainly use equal tempered tuning, so wont have any lock and ring – be aware that when you sing it yourself the notes might sound different! Getting sung teach tracks maybe more expensive, but they are more accurate – which can feel counter intuitive.
  • if you are struggling with a note when you are learning something sat in front of a piano, when you sing it in person with the rest of the chord around you, you are likely to just get the note without any issues as your ear will find it. It’s likely to have been a note that is in between the ones that you can play on the piano.
  • the lead and the bass will most often be on the notes of the chord that need the least tuning – the bari and the tenor are normally on the notes that need the most tuning – often leading to the commonly seen “Bari shoulder”, and the “tenor tiptoe”.


  1. A great article Andrea, well explained and easy to understand. This can all be very complicated, but your graphics and explanations make it easy to understand (and this coming from a piano tuner!). I will share with my chorus if that’s okay?
    Thanks, Barry

    • Of course Barry, you are welcome to share. Thanks for the feedback – and coming from someone in your profession, its a big compliment!

  2. This is a fab piece Andrea. Really educational!!! 🙂

    • Thanks for your feedback! all the lovely comments have just blown me away!

  3. Fabulous thanks Andrea, as one of those visual peeps I do love a diagram and a graph or 5 !

    • Thanks Dulcie…. a picture speaks a thousand words and all that! 🙂

  4. Nice one Andrea. Thanks for making it ‘make sense’ – it’s only taken me 20 years …. But, I’m still hooked on it. Pearl

  5. Nicely explained; thanks!

  6. What is a bari shoulder?

    • Its that funny position that the baris tend to pull when they are tuning a note… just often it is the right shoulder that lifts up with a squiffy face while they tune the note. Its nothing official, but something that is commonly referred to with baris.

  7. It’s lovely to have all the science I know about tuning so clearly explained. Definitely something to share, if that’s ok?

    • Of course! Share away. 🙂

  8. Everything else sounds spot on, but I believe the term ‘undertones’ was used out of context… Would you explain a bit further on this? The best I both recall undertones are produced in a way which could be seen as somewhat ‘artificial ‘, such as striking a tuning fork and holding a piece of paper to the side of one oscillating tine…

    • Yes… you are right in that undertones are created in a different way to overtones. Overtones are part of the harmonic series (I feel another blog post coming on with that mention…) and undertones are created using sum and difference effects on two wave forms. I’m less clear on undertones so thats about as far as I can explain them without doing a bit more research… and there is my third blog post sorted! heh heh
      Thanks for reading and your feedback.

  9. Greetings from Ireland Andrea…this is great and is being circulated around Ireland 🙂 Thanks for taking the time to write this – it explains the vexation of comparing a chord on piano to the one sung – won’t waste too much time on that comparison in future! I have often asked people if electric keyboards can be flat – now I know why!
    Olwyn (IU)

    • Im really pleased that my explanation helped you with your singing – knowing the theory behind something really helps my singing, so pleased to know that I am not the only one out there. Its been great to see the places that everyone has shared this – Im a little overwhelmed that it got all around Europe, USA, Canada, Oz and even New Zealand!

  10. Hi Andrea, great to read your post. Now I’m finally coming to grips with just tuning and equal temperment. Thanks for giving them meaning and I loved your post… techy stuff and all
    Cheers from Amsterdam

  11. […] the blend right then nail the tuning on top, you can make the chords ring and have an expanded […]

  12. I enjoyed the post. I love the beautiful graph. If I trace the lines right, I think what I might be seeing is 3 octaves overlapping (1:2:4)? I wonder if an octave and a fifth overlapping would be visually appealing too? Using round numbers, if A2 is 110, the A3 an octave up is 220. The sum tone is 330, and I think that is the E4 (fifth). I’m not sure if that 1:2:3 relationship will be “pretty” on a graph or not, but I think it is pretty to my ear. If we divide any frequency by 2, we should get an octave. To put that 5th between the 2 notes of the octave, the 330 would be divided by 2 to get 165 (E3 instead of E4). So, I wonder which would be graphically prettier, the 1:2:3 or the 1:1.5:2?

    • Hi Charley,
      Really pleased that you enjoyed the post. You are right in saying that the beautiful graph is three octaves overlapping and your ratios are correct too.

      Your calculations on the sum frequency is correct – and any ratio with a small whole number is pleasing to the ear… its pleasing as it “fits” nicely and therefore has a pretty graph to go along side it.

      Its a pretty special relationship between the root and a fifth – often the notes that are sung by the lead and the bass – this is why the blend between those two parts has to be pretty awesome for the barbershop to work. I think thats another area that I can explore in a blog post in the future!

      Thank again for your comments,

  13. Good article Andrea. Very clear. Its being circulated in my chorus. I hope that’s ok. As an engineer and barbershopper I love this geeky stuff too. If you’ve not already seen it the American Barbershop Harmony Society has a publication (stock no 4084 I think) called “The Physics of Barbershop Sound”. It has a “lockability” rating for chords which sounds like it will appeal to you! Thanks Peter

    • Thanks for your comment Peter! And of course it is ok for you to circulate around your chorus. It’s wonderful that you feel that it will be useful to them.
      I have briefly seen the book you refer to I believe and had a flick through. It was just at the start of my Barbershop journey so was a little overwhelmed by it – but I think it might be on my next Christmas list!

  14. Hello Andrea, I publish a monthly newsletter for Brothers in Harmony. (Hamilton Square, NJ chapter BHS) I came across your article through a friend on Facebook. You’ve written a wonderful article. It is so accessible to the lay reader

    May I have permission to republish it in our newsletter with proper attribution?

    • I’ve sent you a direct email – let me know if you haven’t got it. Thanks for your interest!

  15. […] Tuning; the Barbershop way and […]

  16. I’m a sound engineer and partner of a talented Sweet Adelines tenor, who passed “the Big “O”” to me. Well done. Previously, I cornered some Sweet Ads in our living room and had them sing for the spectrum analyzer, then tune the lines together. I don’t think that many understand tuning, which I’ve come to learn as “natural” and “tempered”, so I’m excited to see a resource I can share.

  17. […] makes you listen and it uses the just tuning system rather than equal temperament (check out a previous blog post about this if you aren’t familiar with the terms).  You can really hear the […]

  18. This was amazing thank you for your explanation. It is very informative I am not tenor but love trying to figure out this barbershop ring.

  19. One way to hear a beat is to blow a note on the pitchpipe and hum it at the same time. As you move the hum slightly up or down, the beat will be heard but if you hum exactly the same pitch as the pipe, there will be no beat.

  20. So where is the fourth voice?

  21. Yo I just found this article and I really enjoyed. I’m a barbershopper in high school and I actually just learned about all this stuff in physics last week. I plan on showing this to my physics teacher if that’s OK!

    • Of course it is! Glad you found it useful.

  22. Thanks for that nice technical explanation
    I recall wondering if there were notes between the cracks so to speak. Singing tenor now with island a capella in PEI Canada.

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