The Landmark Peaks “Tony & Dominic”
All the non-experimental music you will ever deal with uses the same two landmarks: tonic and dominant, a.k.a. “Tony and Dominic”. Once you have the domino-tonic relation clear in the ear and named, you find yourself making better sense in both your improv on breaks, reading, chord recognition in unwritten ensemble work, and composition. You can get Tony and Dominic set firm and working for you.
It’s just a matter of familiarity. 1) You abstract them as a specimen pair apart; 2) you use clear, simple tunes for context in which to recognize when they occur; and 3) you take the Dom-Tony relation as your basic example of practical intervals and name them. Material at earfirst.net is there to objectify the work.
The mathematically simplest musical interval is the octave [12 frets], heard when two notes with frequency ratio 2:1 sound together or as successive notes. Two notes in octave relation are given the same pattern-function name: C, G, Bb, F# for examples in the keyboard alphabet, or 1, 5, Z, X in my version of Nashville studio chording, Noshville. These two notes sound “somehow the same” even though one is higher and the other lower. A beginner in ear work is not well-advised to begin with the octave. The vocal effort is rather athletic: “Chest-nuts roasting on an open fire”. If you have a stringed instrument, experiment with the mid-string harmonic, your fingerboard finger just lightly touching.
Of course, two notes of the same frequency (sounded on guitar and fiddle together, for instance) are at the 1:1 frequency relation, “simpler” yet.
“Tony and Dominic” are the place to start and devote early earwork to. The frequency intervals between them are 3\2 [7 frets] and 4\3 [5 frets] [higher\lower]. Dom\Tony is among the 3\2 intervals (P5; plain fifth) in a scale. Tony\Dom is among the 4\3 intervals (P4; plain fourth) in a scale.
The two domino-tonic intervals split the octave nearly into equal halves. The interval that divides the octave exactly in half is the tritone (TT [6 frets]; augmented fourth; diminished fifth). The tritone frequency relation is sqrt(2):1. Hear it in Leonard Bernstein’s “Ma/ri-a! I/just met a girl named Maria!” from West Side Story.
Guitar tuning uses the plain fourth, 4:3 [5 frets], between all string neighbors except B\G [4 frets].
Violin, viola, ‘cello strings are tuned in plain fifths. Lately string bassists have been tuning in fifths as well, an octave below each ‘cello string. For centuries, bass tuning was in fourths, depriving the orchestra bass section of the ability to double the ‘cellos in the lowest notes.
The domino-tonic relation gives you two stable landmarks for navigating all practical music.