Fundamental tuning question

[Beemer]

Assuming Equal Temperament. But in any temperament the octaves should be in tune, except for any stretching. Other than Equal Temperament, the reference note is generally "C" rather than "A".

I tune pianos and my understanding is that stretch only applies to wire and copper wound wire strings not reeds. Are you using the term stretch in the context of musette tuning, e.g. French or Scottish?

 

[debra]

I tune pianos and my understanding is that stretch only applies to wire and copper wound wire strings not reeds. Are you using the term stretch in the context of musette tuning, e.g. French or Scottish?

Stretch means that as you go up the octaves the frequency slightly more than doubles with each octave. (And without stretch it doubles exactly.)
Stretch can be applied or not in string and reed instruments because they allow tuning of individual notes. (In string instruments it's a matter of finger placement.) In most woodwind and brass instruments stretch is an property of the instrument and cannot be changed (except by redesigning them with different hole positions).
Stretch is desired by the human hearing system (ears + brain). When you play the lowest A (in the M register) followed by the highest A that highest A to our ears sounds like it is tuned too low. Our hearing essentially favors stretch tuning. However, on an instrument where octaves are commonly used, and more than one at the same time,... stretch tuning simply sounds "out of tune". When you play the LH register you would hear a slight tremolo if the H reed (which is 2 octaves up) is tuned at just over 4 times the frequency of the L reed. You can also easily play 2 octaves on a button accordion and that too should play without any tremolo caused by stretch tuning.
In orchestral music stretch tuning is generally unwanted, and to achieve this melodies move between instruments. From each instrument only a "center" part of its note range is used, and when the melody moves out of that part the melody continues on a different instrument. It can thus move from a bassoon up to a clarinet and then further up to an oboe... and then it blends well with other instruments that are tuned without any stretch (like an accordion).

 

[Beemer]

Stretch as it applies to pianos is inharmonicity caused by thicker wires not following the discovery by Pythagoras of frequency ratios as applied to a wire. Equal temperament piano tuning theoretically has each successive note differing by the twelfth root of 2. In order to correct inharmonicity the piano tuning process follows a 'Railsback Curve' and lowers the frequency of lower notes and increases the frequency of higher notes. Stretch in a piano differs depending on the size of the piano e.g. less stretch in a concert grand (because of the higher ratio of string speaking length to the wire diameter compared to a small piano. The tuning process follows a 'Railsback Curve' which accommodates the required stretch, but we do not deliberately 'add stretch'.
I have yet to read that a single vibrating reed exhibits inharmonicity in relation to other single reeds in the same bank and would be interested in any citation.

 

[Ikesaccordions]

My opinion is that some very slight stretching on the trebe side of an accordion may be pleasing to most players.
Otherwise an octave will not sound like 2 reeds. However, some people may find the absence of ant stretching, pleasig to the ear.
I have noticed a fair amount of stretching on all accordions, but I would not necessarily assume all of that was done at the factory. Some undoubtedly, I have on good authority.
However, the higher reeds can "go sharp" from old wax, loose leathers, etc.