Moon Synodic Month (Cosmic Octave)
210.42 Hz
Nearest note: G♯3, 23 cents above standard tuning
A tone calculated from a measured cycle, by doubling its frequency 29 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
The Moon takes 29.530588 days to go from one new moon to the next. 1 ÷ 2,551,443 seconds, doubled 29 times, is 210.42 Hz. That is a G♯, about 23 cents above standard tuning.
- Step 1. Start with the length of the cycle
Moon orbit from new moon to new moon: 29.530588 days.
- Step 2. Turn it into a frequency
One divided by that many seconds is 3.92 × 10⁻⁷ Hz. That is far too slow to hear.
- Step 3. Double it 29 times
Doubling a frequency raises it by one octave: the same note, higher. After 29 doublings it is 210.42 Hz.
- Step 4. Name the note
210.42 Hz is a G♯, 23 cents above 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 445.86 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 648 nm, which is orange. 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.
What is said about it
What is said, not what was measured
In planetary gong practice this tone is associated with emotion, fluids and cycles.
Facts
- Frequency
- 210.42 Hz
- One cycle takes
- 29.53 days
- Wavelength in air (20 °C)
- 1.63 m
- Nearest note
- G♯3, 23 cents above 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
- Moon orbit from new moon to new moon
- Length of the cycle
- 29.530588 days
- Octaves up
- 29
- Concert pitch (A)
- 445.86 Hz
- Difference from A = 440 Hz
- +22.91 cents
- Tempo
- 98.63 beats per minute
- Pendulum length
- 9.2 cm / 3.62 in
- Color by octave
- Orange (648 nm)
Tempo and pendulum length, octave by octave
| Octave | Frequency | One cycle | Tempo | Pendulum |
|---|---|---|---|---|
| 22tempo | 1.64 Hz | 608.31 ms | 98.63 BPM | 9.2 cm |
| 23 | 3.29 Hz | 304.15 ms | 197.27 BPM | 2.3 cm |
| 24 | 6.58 Hz | 152.08 ms | Too fast to count | Too short to build |
| 25 | 13.15 Hz | 76.04 ms | Too fast to count | Too short to build |
| 26 | 26.30 Hz | 38.02 ms | Too fast to count | Too short to build |
| 27 | 52.61 Hz | 19.01 ms | Too fast to count | Too short to build |
| 28 | 105.21 Hz | 9.50 ms | Too fast to count | Too short to build |
| 29tone | 210.42 Hz | 4.75 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 | 210.42 Hz | G#3 | 445.86 Hz | +22.92 |
| 81/80 | Syntonic comma | 213.05 Hz | G#3 | 451.44 Hz | +44.43 |
| 531441/524288 | Pythagorean comma | 213.29 Hz | G#3 | 451.95 Hz | +46.38 |
| 128/125 | Diesis | 215.47 Hz | A3 | 430.94 Hz | -36.02 |
| 648/625 | Greater diesis | 218.16 Hz | A3 | 436.33 Hz | -14.51 |
| 25/24 | Chroma | 219.19 Hz | A3 | 438.38 Hz | -6.41 |
| 16/15 | Diatonic semitone | 224.45 Hz | A3 | 448.90 Hz | +34.65 |
| 10/9 | Minor whole tone | 233.80 Hz | A#3 | 441.36 Hz | +5.33 |
| 9/8 | Major whole tone | 236.72 Hz | A#3 | 446.87 Hz | +26.83 |
| 8/7 | Septimal whole tone | 240.48 Hz | B3 | 428.49 Hz | -45.90 |
| 6/5 | Minor third | 252.50 Hz | B3 | 449.91 Hz | +38.56 |
| 5/4 | Major third | 263.03 Hz | C4 | 442.35 Hz | +9.24 |
| 4/3 | Perfect fourth | 280.56 Hz | C#4 | 445.36 Hz | +20.97 |
| 3/2 | Perfect fifth | 315.63 Hz | D#4 | 446.37 Hz | +24.88 |
| 8/5 | Minor sixth | 336.67 Hz | E4 | 449.40 Hz | +36.61 |
| 5/3 | Major sixth | 350.70 Hz | F4 | 441.85 Hz | +7.28 |
| 7/4 | Natural seventh | 368.23 Hz | F#4 | 437.91 Hz | -8.25 |
| 16/9 | Pythagorean minor seventh | 374.08 Hz | F#4 | 444.86 Hz | +19.01 |
| 9/5 | Just minor seventh | 378.76 Hz | F#4 | 450.42 Hz | +40.52 |
| 15/8 | Major seventh | 394.54 Hz | G4 | 442.85 Hz | +11.19 |
| 2/1 | Octave | 420.84 Hz | G#4 | 445.86 Hz | +22.92 |
Source notes
The synodic month measures the lunar cycle by the changing relationship between Moon and Sun.
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 — Synodic Month
The synodic month measures the lunar cycle by the changing relationship between Moon and Sun.
View source: Hans Cousto — Tuning Data / Sun Earth Moon Planets — Moon — Synodic Month
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.