Moon Metonic Cycle (Cosmic Octave)
229.22 Hz
Nearest note: A♯3, 29 cents below standard tuning
A tone calculated from a measured cycle, by doubling its frequency 37 times. It is calculated, not recorded.
How well is this supported?
Calculated from a measured value by a stated method. You can check the arithmetic. What the result means is a matter of interpretation.
The cycle is measured. The tone is calculated from it by doubling, so that it can be heard. Nothing in space makes this sound.
The button plays a plain tone. Start with the volume low. Phone and laptop speakers play low notes quietly; headphones or a speaker help.
Where this number comes from
After 235 lunar months, about 19 years, the phases of the Moon fall on the same calendar dates again. This is the Metonic cycle. 1 ÷ 599,589,059 seconds, doubled 37 times, is 229.22 Hz. That is a B♭, about 29 cents below standard tuning.
- Step 1. Start with the length of the cycle
235 synodic months, or about 19 years: 235 synodic months.
- Step 2. Turn it into a frequency
One divided by that many seconds is 1.67 × 10⁻⁹ Hz. That is far too slow to hear.
- Step 3. Double it 37 times
Doubling a frequency raises it by one octave: the same note, higher. After 37 doublings it is 229.22 Hz.
- Step 4. Name the note
229.22 Hz is a B♭, 29 cents below standard tuning. A cent is one hundredth of the step between two neighboring piano keys. To play in tune with this tone, an instrument sets its A to 432.71 Hz instead of 440.
- Step 5. Keep doubling and the number lands in the range of light
41 more doublings give the frequency of light with a wavelength of 595 nm, which is yellow. This is arithmetic. It pairs a tone with a color; it does not show that the two are connected.
The method is Hans Cousto’s. Planet gongs explained walks through it and says what it does and does not show.
Facts
- Frequency
- 229.22 Hz
- One cycle takes
- 19 years
- Wavelength in air (20 °C)
- 1.50 m
- Nearest note
- A♯3, 29 cents below standard tuning
- Kind of statement
- Octave of an astronomical cycle
- Filed under
- Earth, Moon & Sun
Tuning Data
The row for this tone in Hans Cousto’s tables, with the tempo and pendulum length that follow from it.
- Cycle
- 235 synodic months, or about 19 years
- Length of the cycle
- 235 synodic months
- Octaves up
- 37
- Concert pitch (A)
- 432.71 Hz
- Difference from A = 440 Hz
- -28.91 cents
- Tempo
- 107.45 beats per minute
- Pendulum length
- 7.7 cm / 3.05 in
- Color by octave
- Yellow (595 nm)
Tempo and pendulum length, octave by octave
| Octave | Frequency | One cycle | Tempo | Pendulum |
|---|---|---|---|---|
| 30tempo | 1.79 Hz | 558.42 ms | 107.45 BPM | 7.7 cm |
| 31 | 3.58 Hz | 279.21 ms | 214.89 BPM | 1.9 cm |
| 32 | 7.16 Hz | 139.60 ms | Too fast to count | Too short to build |
| 33 | 14.33 Hz | 69.80 ms | Too fast to count | Too short to build |
| 34 | 28.65 Hz | 34.90 ms | Too fast to count | Too short to build |
| 35 | 57.31 Hz | 17.45 ms | Too fast to count | Too short to build |
| 36 | 114.61 Hz | 8.73 ms | Too fast to count | Too short to build |
| 37tone | 229.22 Hz | 4.36 ms | Too fast to count | Too short to build |
Intervals built on this tone
| Ratio | Interval | Frequency | Note | Concert A | Cents from 440 |
|---|---|---|---|---|---|
| 1/1 | Perfect unison | 229.22 Hz | A#3 | 432.71 Hz | -28.92 |
| 81/80 | Syntonic comma | 232.09 Hz | A#3 | 438.12 Hz | -7.42 |
| 531441/524288 | Pythagorean comma | 232.35 Hz | A#3 | 438.61 Hz | -5.46 |
| 128/125 | Diesis | 234.72 Hz | A#3 | 443.09 Hz | +12.13 |
| 648/625 | Greater diesis | 237.66 Hz | A#3 | 448.63 Hz | +33.64 |
| 25/24 | Chroma | 238.77 Hz | A#3 | 450.74 Hz | +41.75 |
| 16/15 | Diatonic semitone | 244.50 Hz | B3 | 435.65 Hz | -17.19 |
| 10/9 | Minor whole tone | 254.69 Hz | C4 | 428.33 Hz | -46.52 |
| 9/8 | Major whole tone | 257.87 Hz | C4 | 433.69 Hz | -25.01 |
| 8/7 | Septimal whole tone | 261.97 Hz | C4 | 440.57 Hz | +2.25 |
| 6/5 | Minor third | 275.06 Hz | C#4 | 436.64 Hz | -13.28 |
| 5/4 | Major third | 286.53 Hz | D4 | 429.30 Hz | -42.61 |
| 4/3 | Perfect fourth | 305.63 Hz | D#4 | 432.22 Hz | -30.88 |
| 3/2 | Perfect fifth | 343.83 Hz | F4 | 433.20 Hz | -26.97 |
| 8/5 | Minor sixth | 366.75 Hz | F#4 | 436.14 Hz | -15.24 |
| 5/3 | Major sixth | 382.03 Hz | G4 | 428.82 Hz | -44.57 |
| 7/4 | Natural seventh | 401.14 Hz | G4 | 450.26 Hz | +39.90 |
| 16/9 | Pythagorean minor seventh | 407.50 Hz | G#4 | 431.73 Hz | -32.83 |
| 9/5 | Just minor seventh | 412.60 Hz | G#4 | 437.13 Hz | -11.33 |
| 15/8 | Major seventh | 429.79 Hz | A4 | 429.79 Hz | -40.66 |
| 2/1 | Octave | 458.44 Hz | A#4 | 432.71 Hz | -28.92 |
Source notes
The Metonic cycle realigns solar and lunar phases after 235 synodic months, roughly every 19 years.
Source: Hans Cousto — Tuning Data / Sun Earth Moon Planets. View the source PDF.
License: CC BY-NC-ND 4.0, as stated in Stimmdaten.pdf (German edition), page 2.
Values are reproduced from Cousto’s tables. Tempo, pendulum length and interval tables are calculated by this site from those values.
See every tone in the tables: Open the tuning data reference.
Sources
- Hans Cousto — Tuning Data: Earth, Moon, Planets, Sun
The tables that the tuning pages on this site reproduce.
Hans Cousto, Tuning Data — Earth Moon Planets Sun. Planetware.
View source: Hans Cousto — Tuning Data: Earth, Moon, Planets, Sun - Hans Cousto — Tuning Data / Sun Earth Moon Planets — Moon — Metonic Cycle
The Metonic cycle realigns solar and lunar phases after 235 synodic months, roughly every 19 years.
View source: Hans Cousto — Tuning Data / Sun Earth Moon Planets — Moon — Metonic Cycle
More about the pitch
The same note in every octave
Each step doubles or halves the frequency. Tap one to hear it.
Entries close in pitch
Within 35 cents of this tone, in any octave. A cent is one hundredth of the step between two neighboring piano keys. Being close in pitch does not mean two things are connected.