Notes on Concertina Pitch

Roger Digby and I have mailed each other over his pitch and temperament notes, but for those of you a little lost over what its all about, here is some background information, hopefully at an easy to understand level.

Pitch

The pitch of a note is determined by how many vibrations it makes in a second. The more vibrations the note makes, the higher the pitch.

Today the standard pitch for concertinas and all other instruments is A=440, so the note A vibrates exactly 440 times a second. This standard was agreed in 1939. It gives us a pitch for C of 523.25 vibrations per second.

Earlier however, there were lots of different standards for pitch. From the 1850s, pitches got higher and higher as orchestras tried to get more volume out of their wind instruments. Different standards became adopted in different countries and it became very difficult for musicians to play with one another without prior arrangement of what pitch they were to play in.

A mid 1920s price list from Lachenal indicates something of the confusion that was going on. Customers were required to state the pitch they wanted for their instrument when ordering, and Lachenal offered 4 pitches as standard.

Normal : C=517.20
New Philharmonic : C=522
Society of Arts : C=530
Old Philharmonic : C=540

By the mid 1930s, a Wheatstone price list offered three of these pitches; Society of Arts pitch was not offered and their normal pitch was C=517.30, insignificantly different to the Lachenal pitch of the 1920s.

This table lists the vibrations per second of notes in the various pitches. You can see for instance that C in Old Philharmonic pitch is almost the same as C# in normal pitch. Have you ever tried to play along with someone a semitone sharp? It sounds ***** awful!

Tuners use cents to measure the difference in pitch. One cent is a hundredth of a semitone. So we can express the difference of these older pitches from modern pitch in cents approximately as follows:

Normal : 20 cents lower
New Philharmonic : 4 cents lower
Society of Arts : 22 cents higher
Old Philharmonic : 54 cents higher

Temperament

Modern instruments use equal temperament. This means that a semitone step is equal between each sucessive note. This however is an approximation which allows the instrument to play in any key without sounding too out of tune. Musically, however, every scale is out of tune!

To get a musically correct scale, the note pitches must be in whole number ratios. The easiest to understand is the octave, where the pitch of a note an octave higher is exactly twice. So modern pitch A notes are 110, 220 440, 880, 1760, etc.

Other notes in the same scale are also pitch related by whole numbers. For instance, if we wanted a modern pitch scale in A=440, the pitch of the note E above would be 660, a ratio of 2 to 3. You can see from the table that the pitch actually used is 659.26, slightly flat for a true musical scale. These whole number ratios also lead eventually to the musically correct statement that Db is not the same as C#!

Because the anglo is a two key based instrument, it is possible to tune it to be more correct musically for the scales in those two keys, at the expense of making scales (and chords) in other keys more out of tune. This is the unequal temperament that Roger is referring to.