This page is under construction so bear with me.
Here we go into a dangerous topic. It is about hearing the pitch, It is about playing in tune with other musicians, It is about how one sounds but it is mostly about blending with other voices.
The following playback recordings are 12 tone rows (base upon an equal tempered chromatic scale) of parallel intervals that are NOT equal temperament. The higher note of the two tones is derived from a rational number interval. It would be the interval that would occur in the overtone (or undertone) series and is closest to the corresponding tone from from the equal tempered scale.
Some of you will be here because we’ve had a discussion about intonation and the difference between Equal Temperament and Just Intonation / Overtone Series. To cut to the chase, the following is the difference between the two systems. A negative number represents the amount flatter the equal tempered interval be adjusted to become a perfectly in tune interval. A positive number for the amount sharper the note is adjusted to be a perfect interval:
- perfect 5th 3/2 -> +2 cents to become 3/2 ratio
- perfect 4th -> -2 cents to become 4/3 ratio
- major 3rd -> -14 cents to become 5/4 ratio
- minor 3rd -> +16 cents to become 6/5 ratio
- major 6th -> -16 cents to become 5/3 ratio
- minor 6th -> +14 cents to become 8/5 ratio
- major 2nd -> +4 cents to become 9/8 ratio
- flat 7th -> -4cents to become 16/9 ratio
- major 7th -> -12 cents to become 15/8 ratio
- flat 2nd -> +12 cents to become 16/15 ratio
- tritone, diminished 5th -> – 17.5 cents to become 10/7 ratio
The following two tracks exemplify the difference between equal and just tuning. The first version is all equal temperament and the second version is a where a just interval is sounded and a saxophone blending with what is heard i.e. adjusting the various tones to fit best.
Equal V.S. Just: (example to come)
In order for you to fully appreciate the difference between Equal and Just you will need to LISTEN to the tracks and then SING along and then PLAY along.
The actual tones being played can be found in the following PDF Perfecting Intonation but I highly recommend just jumping right in by singing or playing any note that occurs to you. From that note adjust up or down to discover the notes being sounded and then build your ideas about intervals and scale tones from them. Just sing or play and let the resultant group of notes inform you. Build a picture or conception from what you hear. Play and sing along with the tracks to learn about intervals and intonation. Explore the sounds with your voice. “Play by Ear” so that you can learn by ear. Develop a conception of intervals by directly connecting to them with your voice.
Flat (Minor) 7th:
Root + 3rd & 7th
Dominant 7 Sus 4
Quartal triads (voiced from bottom up)
Perfect 4 + Perfect 4
Perfect 4th + Augmented 4th:
Augmented 4th + Perfect 4th:
Augmented 4th + Diminished 4th:
Diminished 4th + Augmented 4th:
Diminished 4th + Augmented 4th (Low 7th 7/4 ratio that is more consonant than standard ratio or equal tempered versions):