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Nexus between brass and strings in just intonation

 

Temporary conclusion: the best nexus pitch is a C.

 

I’ve been composing a just intonation piece for 6 horns and decided to re-write some of it for a mixed ensemble of flute, 2 horns, violin, cello, double bass and soprano. In this blog I’ll show some of the tuning detail and the issues of working with strings and brass. Most of the tuning issues will be the same when composing in equal divisions.

 

• 2 main tuning issues

 

1.Brass players and wind players determine how to achieve a pitch ratio by calculating the distance below a pitch played without using valves or keys. String players determine how to achieve a pitch ratio by calculating the distance above pitch played on an open string. Brass players and other wind instruments players do something additional to using the open tube resulting in the pitch lowering, ie. put down a finger onto a valve or key and the pitch goes down. String players do something additional to using the open string resulting in the pitch raising, ie.put down a finger onto a string and the pitch goes up.

 

2.Tuning issues arose in this particular composition due to conceiving the original work for horns.

 

1. Brass: establish a relationship between the main tube length and a pitch in the composition. Tune the valve slides to other pitches in the composition.

Strings: establishing a starting pitch with at least one open string matching a particular pitch in the composition.

Find a nexus between the two.

 

Example: tune strings to brass: 

Starting pitch B^♭ (central reference pitch or perhaps the tonic) for trumpets, trombones, B^♭ side of the standard double (french) horn, some tubas, euphoniums, baritones. 

Call this pitch the ratio 1:1 and tune it in ‘normal’ relation to A=440Hz. 

Match the D string of orchestral strings (violins, violas, cellos, double basses) to the 5:4 ratio. This would mean the D string would be tuned lower than usual. The other strings if tuned normally would also need to be lower than usual.

Example: tune brass to strings: 

Starting pitch D (central reference pitch or perhaps the tonic) for orchestral strings. 

Call this pitch the ratio 1:1 and tune it in ‘normal’ relation to A=440Hz. 

Match brass B^♭to the 8:5 ratio. This would mean the B^♭ would be tuned higher than usual.

 

A more straightforward nexus comes with tuning brass to the C string of the cello and viola.