No musical tuning system can be proven superior to another
Evidence
Just intonation is based purely on triads, where the frequencies of the triads C-E-G, G-B-D, and F-A-C have the ratio 4:5:6 and octaves are always tuned to 2:1. Unfortunately, with this method, many intervals are not in tune. For example, the interval D-A should have the ratio 1.5, but in this tuning it is 1.48, which is audibly mistuned. The Pythagorean tuning system has the greatest number of pure fifths and octaves. Unfortunately, the thirds are then mistuned. … We can thus conclude that no single method exists that tunes the seven notes of the diatonic scale so that all the intervals between the notes have intervals with simple integer ratios. Some methods have been developed to overcome this problem. For instance, the mean-tone temperament alters the Pythagorean tuning so that the fifths are tuned a bit narrower, which overcomes some problems of the system. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1306 (
#expands, via linked claim)
Categorization
- XREF: connects to: No evidence supports preferring 432 Hz piano tuning over 440 Hz — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 2054; No tuning system can make all diatonic scale intervals perfectly consonant — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1306; Whether combination tones are musical depends on the tuning system (+7 more)
Broader Connections
- No tuning system can make all diatonic scale intervals perfectly consonant
#expands(0.85) — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 1306 - No keyboard tuning can make every key sound justly intonated
#expands(0.85) - Only the octave stays perfectly in-tune in equal temperament
#exemplifies(0.85) - Whether combination tones are musical depends on the tuning system
#expands(0.80) - Timbre, unlike pitch and loudness, has no objective scale
#expands(0.80) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1481 - Uneven intervals make Just intonation scales impossible to transpose freely.
#exemplifies(0.80) - Timbre lacks a one-dimensional subjective scale unlike pitch and loudness
#expands(0.75) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1425 - Science cannot measure the aesthetic qualities that make music revered
#expands(0.72) — , Toole, Floyd E - Sound reproduction-…, 41 - The mel scale conflicts with musical logarithmic scales but remains useful in technical applications
#complicates(0.72)