Tuning the Temperament using a Sequence.
(For aural tuners only)
So, we all have our sequence of notes to tune the temperament and we all feel that any particular sequence that we are using at any one time is the best one for this piano and for us.
But let’s say we are trying to tune an accurate equal temperament. How can we be sure that the sequence is the most accurate?
What would happen if we were to tune an ideal piano, one with no inharmonicty, and we were able to set each interval in our sequence to a very high accuracy?
If our sequence is accurate, shouldn’t the resulting frequencies agree with the equal-tempered frequencies?
That’s exactly what I have done. I used a spreadsheet to calculate the beat speeds of any interval, and then I tuned each note in a sequence so that its interval agreed with the sequence’s criteria for that note.
I then set a standard that after each note is tuned, it must be within 0.3 cents of the equal-tempered frequency, or the tuning would begin to lose marks. – 1% for every 0.1 cents.
Here are the sequences and the results. Note: These results do not take into account our inability to set certain intervals within a certain tolerance. For example, M3’s are easier to set to a certain speed than P4/P5 are, but the P4/P5 sequence was not penalized for that in this scoring.
P4/P4 – Criteria: Tune all P4 at 1 bps and all P5 at 3 beats in 5 seconds.
Mark: 38% !!!
Go APE Aural Piano Tuning System – Criteria: Set intervals exactly between two other already tuned intervals (called the Window)
Mark: 75%
Go APE Modified Equal Beating – Criteria: Set intervals halfway but lean towards one side for two specific windows.
Mark: 100% !!!
You can see the spreadsheet HERE
You can play with this spreadsheet by copying it to your own Google Drive. It will then be all yours and you can change any values you like.
Click THIS LINK to get a copy of your own spreadsheet:
Do you have a sequence that you are using and feel is very accurate? Or maybe you have a sequence you have been told is accurate, but you just aren’t sure? SEND ME THE STEPS and I can plug it into the spreadsheet and see how well it does.
