User:Dummy index/About harmonics

Odd-harmonic sounds

If you play 4:5:6:7 tetrad with several EDOs and some synths, you'll hear a clear beat. Play 4:5, 4:6, 4:7, ... and you'll found that the beat is mainly caused by 5:7 interval. Synth's preset sound is often square wave or triangular wave, both odd-harmonics. They don't have 4th harmonics, so 4:7 dyad actually no wah, no beat. 5:7 is the only pair available to beating. Therefore I care about 7/5 interval in User:Dummy index/Random lists of temperaments by generator size.

Odd-harmonic sounds also suppress the beat of 1:2. It's insensitive to octave stretching/shrinking.

Is it reducing the dissonance, or reducing the consonance?

Piano sounds

Striking point of the string.

λ/7 (traditional?):

• suppress all x:7.

λ/8 (recent grand piano?):

• suppress 4:8, 8:16, get clearer octave, almost free from inharmonicity.
• suppress 8:9, clearer 200¢.
• suppress 19:24, clearer 400¢.
• suppress 5:8, clearer 800¢.

λ/6 (upright piano?):

• suppress 4:6, 6:9, 8:12, get clear perfect-fifth, easy to hear the beat of 2:3, suitable for beat-based tuning techniques.
• suppress 5:6, clearer 300¢.
• suppress 19:24, clearer 400¢.
• suppress 12:19, clearer 800¢.