Amsterdam is a melodious city

In Dutch, the city of Amsterdam is often called Mokum. It was given this name by Ashkenazi Jews from Eastern Europe who sought refuge there, starting in the 17th century. Amsterdam was called Big Mokum, as opposed to Litte Mokum, which referred to Rotterdam. They also sometimes used the Hebrew first letter of the name: this page about Yiddish mentions Mokum Alef = Amsterdam, Mokum Resh = Rotterdam, Mokum Beth = Berlin.

This name Mokum stems, via Yiddish, from the Hebrew word maqom, in Hebrew script written as מָקוֹם. Its meaning is "place, location". The word's root consists of consonants qof-vav-mem, קום.

Hebrew and Arabic are strongly related languages, and as was to be expected, Arabic also has a root q-w-m, قوم, with the same type of meanings. The Arabic word maqm, written in Arabic script as مَقَامٌ, also means "place, location".

But it has an additional meaning: that of key, tonality, mode. It usually occurs in the plural, maqmt, مقامات. They are series of notes, that make the basis of numerous Arabic musical pieces. These scales contain notes that are in between those normally used in Western music, which is one of the things that gives this music its special sound.

So in a way, looking at random historic links, we could state that Amsterdam is somehow connected to melodies.

The following links give more information about Arabic scales:
Al Amir
Al Baab
Libanon - modes
Libanon - maqmt
Maqam world

The special tone distances, or intervals, are indicated here as, for example, 3/4, which means three-quarters of a whole tone in Western music, or 1.5 semitones. A Western whole tone is the distance between c and d, in other words, a major second. Expressed in cents three-quarters of a whole tone is 150 cents, because 100 cents is a semitone, 200 is a whole tone, and 1200 an octave.

However, all of these are only approximations, based on the equal temperament (better: even temperament) of western music. But Arabic music usually does not use even temperament, except the more modern kinds, in which keyboards and electric guitars play along.
Older Western music too, and strings quartets, string orchestras and a cappella choirs even today, prefer pure (just) intervals, which have frequencies that can be expressed as ratios of two small integers, in other words, as simple fractions.

Pythagoras (in Greek: Πυθαγόρας) accepted only factors 2 (octave) and 3 (fifth) for these ratios. That does produce elegant ratios, except in somewhat more complete scales, when rather large integers appear in the frequency ratios. For example, a major third, built from two major seconds of 9:8, gets the ratio 81:64 (or 407.82 cents). A must nicer ratio is 5:4, also a major third, at 386.31 cents. But this requires the factor 5, which Πυθαγόρας did not want. Aristoxenos (Αριστόξενος in Greek) did.

Arabic music takes this a step further: it also uses the factor 11. (And 7, or so they say, but I have never heard that myself. I have found the factor 17; see below). Three tones with frequency ratios 10:11:12 produce intervals of 165.00 and 150.64 cents, which is approximately 150, or one and a half semitones. Together that clearly makes 315.64, which corresponds to the minor third ratio of 6:5. By combining these intervals with the more "common" ones in several ways, we get the maqmt in this aforementioned link.

The tables below have these entries:

Only the ascending scales are considered here, not the descending varieties.


Sullam maqmt al-bayt ( سلّم مقامات البياتى )

Sound sample

110 60 1:1 - 0.00
211 66 11:1011:10 165.00
312 72 6:5 12:11 315.64
413 ⅓ 80 4:3 10:9 498.04
515 90 3:2 9:8 701.96
616 ½ 99 33:2011:10 866.96
718 108 9:5 12:11 1017.60
820 120 2:1 10:9 1200.00

Sullam maqmt ar-rst ( سلّم مقامات الراست )

Sound sample

1 9 54 1:1 - 0.00
210 60 10:9 10:9 182.40
311 66 11:9 11:10 341.41
412 72 4:3 12:11 498.04
513 ⅓ 80 40:2710:9 680.45
615 90 5:3 9:8 884.36
716 ½ 99 11:6 11:10 1049.36
818 108 2:1 12:11 1200.00

It is striking that ar-rst does not have a just fifth!


Sullam maqmt as-skh ( سلّم مقامات السيكاه )

Sound sample

111 66 1:1 - 0.00
212 72 12:1112:11 150.64
313 ⅓ 80 40:3310:9 333.04
415 90 15:119:8 536.95
516 ½ 99 3:2 11:10 701.96
618 108 18:1112:11 852.59
720 120 20:1110:9 1035.00
822 132 2:1 11:10 1200.00

And as-skh does not have a just fourth!


Al-bayt, ar-rst and as-skh are in fact the same scales, except that the starting point, the keynote or tonic in Western music terminology, is different each time.


Sullam maqmt al-hizm ( سلّم مقامات الهزام )

Sound sample

111 66 1:1 - 0.00
212 72 12:11 12:11 150.64
313 ⅓ 80 40:33 10:9 333.04
414 ⅙ 85 85:60 17:16 438.00
517 102 17:11 6:5 753.64
618 108 18:11 18:17 852.59
720 120 20:11 10:9 1035.00
822 132 2:1 11:10 1200.00

Sullam maqmt as-sznak ( سلّم مقامات السوزْنَك )

Sound sample

1 9 54 1:1 - 0.00
210 60 10:9 10:9 182.40
311 66 11:9 11:10347.41
412 72 4:3 12:11498.04
513 ⅓ 80 40:2710:9 680.45
614 ⅙ 85 85:5417:16785.40
717 102 17:9 6:5 1101.05
818 108 2:1 18:171200.00

Al-hizm and as-sznak are in fact the same scale, but bit a different keynote (tonic).

I am not certain whether the frequency ratios are really as I describe them, but I hardly see any other possibility, considering I need to come close to the pitches indicated, and use relatively small ratio integers.

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